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- - + + \ No newline at end of file diff --git a/CNAME b/CNAME index 4c91a2c..5b0fb91 100644 --- a/CNAME +++ b/CNAME @@ -1 +1 @@ -blog.mfocko.xyz \ No newline at end of file +blog.mfocko.xyz diff --git a/assets/js/2523321d.4bb20fbb.js b/assets/js/2523321d.a50d1761.js similarity index 99% rename from assets/js/2523321d.4bb20fbb.js rename to assets/js/2523321d.a50d1761.js index dc3af99..038e069 100644 --- a/assets/js/2523321d.4bb20fbb.js +++ b/assets/js/2523321d.a50d1761.js @@ -1 +1 @@ -"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[9193],{3905:(e,t,n)=>{n.d(t,{Zo:()=>p,kt:()=>k});var i=n(7294);function a(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function r(e,t){var n=Object.keys(e);if(Object.getOwnPropertySymbols){var i=Object.getOwnPropertySymbols(e);t&&(i=i.filter((function(t){return Object.getOwnPropertyDescriptor(e,t).enumerable}))),n.push.apply(n,i)}return n}function o(e){for(var t=1;t=0||(a[n]=e[n]);return a}(e,t);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(e);for(i=0;i=0||Object.prototype.propertyIsEnumerable.call(e,n)&&(a[n]=e[n])}return a}var s=i.createContext({}),u=function(e){var t=i.useContext(s),n=t;return e&&(n="function"==typeof e?e(t):o(o({},t),e)),n},p=function(e){var t=u(e.components);return i.createElement(s.Provider,{value:t},e.children)},c="mdxType",m={inlineCode:"code",wrapper:function(e){var t=e.children;return i.createElement(i.Fragment,{},t)}},d=i.forwardRef((function(e,t){var n=e.components,a=e.mdxType,r=e.originalType,s=e.parentName,p=l(e,["components","mdxType","originalType","parentName"]),c=u(n),d=a,k=c["".concat(s,".").concat(d)]||c[d]||m[d]||r;return n?i.createElement(k,o(o({ref:t},p),{},{components:n})):i.createElement(k,o({ref:t},p))}));function k(e,t){var n=arguments,a=t&&t.mdxType;if("string"==typeof e||a){var r=n.length,o=new Array(r);o[0]=d;var l={};for(var s in t)hasOwnProperty.call(t,s)&&(l[s]=t[s]);l.originalType=e,l[c]="string"==typeof e?e:a,o[1]=l;for(var u=2;u{n.r(t),n.d(t,{assets:()=>s,contentTitle:()=>o,default:()=>m,frontMatter:()=>r,metadata:()=>l,toc:()=>u});var i=n(7462),a=(n(7294),n(3905));const r={id:"seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n"},o="8th seminar bonus assignment",l={unversionedId:"bonuses/seminar-08",id:"bonuses/seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n",source:"@site/pb071/bonuses/08.md",sourceDirName:"bonuses",slug:"/bonuses/seminar-08",permalink:"/pb071/bonuses/seminar-08",draft:!1,editUrl:"https://github.com/mfocko/blog/tree/main/pb071/bonuses/08.md",tags:[],version:"current",lastUpdatedAt:1694959505,formattedLastUpdatedAt:"Sep 17, 2023",frontMatter:{id:"seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n"},sidebar:"autogeneratedBar",previous:{title:"5th and 6th seminar",permalink:"/pb071/bonuses/seminar-05-06"},next:{title:"10th seminar",permalink:"/pb071/bonuses/seminar-10"}},s={},u=[{value:"Introduction",id:"introduction",level:2},{value:"Warning",id:"warning",level:2},{value:"Testing",id:"testing",level:2},{value:"Task no. 1: Counting (0.75 K\u20a1)",id:"task-no-1-counting-075-k",level:2},{value:"Requirements",id:"requirements",level:3},{value:"Bonus part (0.75 K\u20a1)",id:"bonus-part-075-k",level:3},{value:"Task no. 2: Weird trees (1 K\u20a1)",id:"task-no-2-weird-trees-1-k",level:2},{value:"Submitting",id:"submitting",level:2}],p={toc:u},c="wrapper";function m(e){let{components:t,...r}=e;return(0,a.kt)(c,(0,i.Z)({},p,r,{components:t,mdxType:"MDXLayout"}),(0,a.kt)("h1",{id:"8th-seminar-bonus-assignment"},"8th seminar bonus assignment"),(0,a.kt)("p",null,(0,a.kt)("a",{parentName:"p",href:"pathname:///files/pb071/bonuses/08.tar.gz"},"Source")),(0,a.kt)("h2",{id:"introduction"},"Introduction"),(0,a.kt)("p",null,"In this bonus you can implement two tasks, one of them has a bonus part with generic\nsolution."),(0,a.kt)("p",null,"One is focused on counting ananas or in case of generic version any substring in\nthe file, but with a restriction on the function you use."),(0,a.kt)("p",null,"Other one has a more algorithmic spirit."),(0,a.kt)("p",null,"For this bonus you can get at maximum 2.5 K\u20a1."),(0,a.kt)("h2",{id:"warning"},"Warning"),(0,a.kt)("p",null,(0,a.kt)("strong",{parentName:"p"},"DO NOT COMMIT test data")," to your own git repository, since the tests include\nfiles that exceed 10MB by themselves. 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Functions like ",(0,a.kt)("inlineCode",{parentName:"p"},"fprintf")," (except for ",(0,a.kt)("inlineCode",{parentName:"p"},"stderr")," or logging) and\n",(0,a.kt)("inlineCode",{parentName:"p"},"fscanf")," are ",(0,a.kt)("strong",{parentName:"p"},"forbidden"),"."),(0,a.kt)("p",null,"In case you struggle and want to use one of those functions, the solution will be\npenalized by 50% of points."),(0,a.kt)("h3",{id:"bonus-part-075-k"},"Bonus part (0.75 K\u20a1)"),(0,a.kt)("p",null,"Bonus part of this assignment is to implement ",(0,a.kt)("inlineCode",{parentName:"p"},"count_anything")," rather than ",(0,a.kt)("inlineCode",{parentName:"p"},"count_ananas"),"."),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"Smaller hint: This task does not need dynamic allocation :) You just need one\ngood helper function and the right idea ;)")),(0,a.kt)("h2",{id:"task-no-2-weird-trees-1-k"},"Task no. 2: Weird trees (1 K\u20a1)"),(0,a.kt)("p",null,"In this task we are crossing our paths with ",(0,a.kt)("em",{parentName:"p"},"algorithms and data structures"),".\nYour task is to write a program that constructs tree from the file that is given\nas an argument and pretty-prints it."),(0,a.kt)("p",null,"Input file consists of lines, that include ",(0,a.kt)("inlineCode",{parentName:"p"},"key")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"rank")," in form ",(0,a.kt)("inlineCode",{parentName:"p"},"key;rank"),"\nor ",(0,a.kt)("inlineCode",{parentName:"p"},"nil"),". Why would we have ",(0,a.kt)("inlineCode",{parentName:"p"},"nil")," in a file? The file represents pre-order iteration\nthrough the tree. Leaves never have rank different than 0, so you can safely assume\n2 non-existing ",(0,a.kt)("inlineCode",{parentName:"p"},"nil"),"s in the input after you read such node ;)"),(0,a.kt)("table",null,(0,a.kt)("tr",null,(0,a.kt)("th",null,"Example input file"),(0,a.kt)("th",null,"Tree it represents")),(0,a.kt)("tr",null,(0,a.kt)("td",null,(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"8;4\n5;3\n3;2\n2;1\n1;0\nnil\n4;0\n7;1\n6;0\nnil\n11;2\n10;1\n9;0\nnil\n12;0\n"))),(0,a.kt)("td",null,(0,a.kt)("p",null,(0,a.kt)("img",{alt:"tree",src:n(4860).Z,width:"633",height:"684"}))))),(0,a.kt)("p",null,"In this task you are only provided with different trees in the ",(0,a.kt)("inlineCode",{parentName:"p"},"test-trees")," directory.\nImplementation and format of the pretty-print is totally up to you. :)"),(0,a.kt)("p",null,"Example of mine for the tree above:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"8 (rank = 4)\n+-- 5 (rank = 3)\n| +-- 3 (rank = 2)\n| | +-- 2 (rank = 1)\n| | | +-- 1 (rank = 0)\n| | +-- 4 (rank = 0)\n| +-- 7 (rank = 1)\n| +-- 6 (rank = 0)\n+-- 11 (rank = 2)\n +-- 10 (rank = 1)\n | +-- 9 (rank = 0)\n +-- 12 (rank = 0)\n")),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"Can you find out what are those trees? :)")),(0,a.kt)("h2",{id:"submitting"},"Submitting"),(0,a.kt)("p",null,"In case you have any questions, feel free to reach out to me."),(0,a.kt)("hr",null))}m.isMDXComponent=!0},4860:(e,t,n)=>{n.d(t,{Z:()=>i});const i=n.p+"assets/images/tree-c9e37f87f9095c00fad33ea034485ce6.png"}}]); \ No newline at end of file +"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[9193],{3905:(e,t,n)=>{n.d(t,{Zo:()=>p,kt:()=>k});var i=n(7294);function a(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function r(e,t){var n=Object.keys(e);if(Object.getOwnPropertySymbols){var i=Object.getOwnPropertySymbols(e);t&&(i=i.filter((function(t){return Object.getOwnPropertyDescriptor(e,t).enumerable}))),n.push.apply(n,i)}return n}function o(e){for(var t=1;t=0||(a[n]=e[n]);return a}(e,t);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(e);for(i=0;i=0||Object.prototype.propertyIsEnumerable.call(e,n)&&(a[n]=e[n])}return a}var s=i.createContext({}),u=function(e){var t=i.useContext(s),n=t;return e&&(n="function"==typeof e?e(t):o(o({},t),e)),n},p=function(e){var t=u(e.components);return i.createElement(s.Provider,{value:t},e.children)},c="mdxType",m={inlineCode:"code",wrapper:function(e){var t=e.children;return i.createElement(i.Fragment,{},t)}},d=i.forwardRef((function(e,t){var n=e.components,a=e.mdxType,r=e.originalType,s=e.parentName,p=l(e,["components","mdxType","originalType","parentName"]),c=u(n),d=a,k=c["".concat(s,".").concat(d)]||c[d]||m[d]||r;return n?i.createElement(k,o(o({ref:t},p),{},{components:n})):i.createElement(k,o({ref:t},p))}));function k(e,t){var n=arguments,a=t&&t.mdxType;if("string"==typeof e||a){var r=n.length,o=new Array(r);o[0]=d;var l={};for(var s in t)hasOwnProperty.call(t,s)&&(l[s]=t[s]);l.originalType=e,l[c]="string"==typeof e?e:a,o[1]=l;for(var u=2;u{n.r(t),n.d(t,{assets:()=>s,contentTitle:()=>o,default:()=>m,frontMatter:()=>r,metadata:()=>l,toc:()=>u});var i=n(7462),a=(n(7294),n(3905));const r={id:"seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n"},o="8th seminar bonus assignment",l={unversionedId:"bonuses/seminar-08",id:"bonuses/seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n",source:"@site/pb071/bonuses/08.md",sourceDirName:"bonuses",slug:"/bonuses/seminar-08",permalink:"/pb071/bonuses/seminar-08",draft:!1,editUrl:"https://github.com/mfocko/blog/tree/main/pb071/bonuses/08.md",tags:[],version:"current",lastUpdatedAt:1694960869,formattedLastUpdatedAt:"Sep 17, 2023",frontMatter:{id:"seminar-08",title:"8th seminar",description:"Manipulating with files only char-by-char and a magic tree.\n"},sidebar:"autogeneratedBar",previous:{title:"5th and 6th seminar",permalink:"/pb071/bonuses/seminar-05-06"},next:{title:"10th seminar",permalink:"/pb071/bonuses/seminar-10"}},s={},u=[{value:"Introduction",id:"introduction",level:2},{value:"Warning",id:"warning",level:2},{value:"Testing",id:"testing",level:2},{value:"Task no. 1: Counting (0.75 K\u20a1)",id:"task-no-1-counting-075-k",level:2},{value:"Requirements",id:"requirements",level:3},{value:"Bonus part (0.75 K\u20a1)",id:"bonus-part-075-k",level:3},{value:"Task no. 2: Weird trees (1 K\u20a1)",id:"task-no-2-weird-trees-1-k",level:2},{value:"Submitting",id:"submitting",level:2}],p={toc:u},c="wrapper";function m(e){let{components:t,...r}=e;return(0,a.kt)(c,(0,i.Z)({},p,r,{components:t,mdxType:"MDXLayout"}),(0,a.kt)("h1",{id:"8th-seminar-bonus-assignment"},"8th seminar bonus assignment"),(0,a.kt)("p",null,(0,a.kt)("a",{parentName:"p",href:"pathname:///files/pb071/bonuses/08.tar.gz"},"Source")),(0,a.kt)("h2",{id:"introduction"},"Introduction"),(0,a.kt)("p",null,"In this bonus you can implement two tasks, one of them has a bonus part with generic\nsolution."),(0,a.kt)("p",null,"One is focused on counting ananas or in case of generic version any substring in\nthe file, but with a restriction on the function you use."),(0,a.kt)("p",null,"Other one has a more algorithmic spirit."),(0,a.kt)("p",null,"For this bonus you can get at maximum 2.5 K\u20a1."),(0,a.kt)("h2",{id:"warning"},"Warning"),(0,a.kt)("p",null,(0,a.kt)("strong",{parentName:"p"},"DO NOT COMMIT test data")," to your own git repository, since the tests include\nfiles that exceed 10MB by themselves. 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Functions like ",(0,a.kt)("inlineCode",{parentName:"p"},"fprintf")," (except for ",(0,a.kt)("inlineCode",{parentName:"p"},"stderr")," or logging) and\n",(0,a.kt)("inlineCode",{parentName:"p"},"fscanf")," are ",(0,a.kt)("strong",{parentName:"p"},"forbidden"),"."),(0,a.kt)("p",null,"In case you struggle and want to use one of those functions, the solution will be\npenalized by 50% of points."),(0,a.kt)("h3",{id:"bonus-part-075-k"},"Bonus part (0.75 K\u20a1)"),(0,a.kt)("p",null,"Bonus part of this assignment is to implement ",(0,a.kt)("inlineCode",{parentName:"p"},"count_anything")," rather than ",(0,a.kt)("inlineCode",{parentName:"p"},"count_ananas"),"."),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"Smaller hint: This task does not need dynamic allocation :) You just need one\ngood helper function and the right idea ;)")),(0,a.kt)("h2",{id:"task-no-2-weird-trees-1-k"},"Task no. 2: Weird trees (1 K\u20a1)"),(0,a.kt)("p",null,"In this task we are crossing our paths with ",(0,a.kt)("em",{parentName:"p"},"algorithms and data structures"),".\nYour task is to write a program that constructs tree from the file that is given\nas an argument and pretty-prints it."),(0,a.kt)("p",null,"Input file consists of lines, that include ",(0,a.kt)("inlineCode",{parentName:"p"},"key")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"rank")," in form ",(0,a.kt)("inlineCode",{parentName:"p"},"key;rank"),"\nor ",(0,a.kt)("inlineCode",{parentName:"p"},"nil"),". Why would we have ",(0,a.kt)("inlineCode",{parentName:"p"},"nil")," in a file? The file represents pre-order iteration\nthrough the tree. 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Your\ntask is to try the game, in case you find any bugs point them out and cover as\nmuch of the game as possible with tests."),(0,r.kt)("p",null,"For this bonus you can get at maximum 2 K\u20a1."),(0,r.kt)("table",null,(0,r.kt)("thead",{parentName:"table"},(0,r.kt)("tr",{parentName:"thead"},(0,r.kt)("th",{parentName:"tr",align:null},"Item"),(0,r.kt)("th",{parentName:"tr",align:null},"Bonus"))),(0,r.kt)("tbody",{parentName:"table"},(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Fixing bugs from failing tests"),(0,r.kt)("td",{parentName:"tr",align:null},"0.25")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("inlineCode",{parentName:"td"},"word_guessed")),(0,r.kt)("td",{parentName:"tr",align:null},"0.50")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Hidden bug"),(0,r.kt)("td",{parentName:"tr",align:null},"0.50")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Extending tests, undetectable bugs or evil bug"),(0,r.kt)("td",{parentName:"tr",align:null},"0.37")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Refactor"),(0,r.kt)("td",{parentName:"tr",align:null},"0.38")))),(0,r.kt)("h2",{id:"project"},"Project"),(0,r.kt)("p",null,"Project consists of 2 source files - ",(0,r.kt)("inlineCode",{parentName:"p"},"hangman.c")," and ",(0,r.kt)("inlineCode",{parentName:"p"},"main.c"),"."),(0,r.kt)("p",null,(0,r.kt)("inlineCode",{parentName:"p"},"main.c")," is quite short and concise, there is nothing for you to do."),(0,r.kt)("p",null,(0,r.kt)("inlineCode",{parentName:"p"},"hangman.c")," contains implementation of the game. 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Therefore try to follow this succession of steps:"),(0,r.kt)("ol",null,(0,r.kt)("li",{parentName:"ol"},"Try to reproduce the bug."),(0,r.kt)("li",{parentName:"ol"},"Create a test that proves the presence of the bug."),(0,r.kt)("li",{parentName:"ol"},"Fix the bug.")),(0,r.kt)("p",null,"In case you are submitting the bonus via GitLab, it is helpful to commit tests\nbefore commiting the fixes, so that it is apparent that the bug is manifested.\nExample of ",(0,r.kt)("inlineCode",{parentName:"p"},"git log")," (notice that the first line represents latest commit):"),(0,r.kt)("pre",null,(0,r.kt)("code",{parentName:"pre"},"feat: Implement fizz_buzzer\ntest: Add tests for fizz_buzzer\nfix: Fix NULL-check in print_name\ntest: Add test for NULL in print_name\n")),(0,r.kt)("h2",{id:"tasks"},"Tasks"),(0,r.kt)("p",null,"As to your tasks, there are multiple things wrong in this project."),(0,r.kt)("ol",null,(0,r.kt)("li",{parentName:"ol"},(0,r.kt)("p",{parentName:"li"},'There are 2 "bugs" that cannot be detected via tests, i.e. they are not bugs\nthat affect functionality of the game.')),(0,r.kt)("li",{parentName:"ol"},(0,r.kt)("p",{parentName:"li"},"There is one evil bug in ",(0,r.kt)("inlineCode",{parentName:"p"},"get_word"),". 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Please try to figure it out, so you have green\ntests for the rest :)")),(0,r.kt)("li",{parentName:"ol"},(0,r.kt)("p",{parentName:"li"},"We have gotten a bug report for ",(0,r.kt)("inlineCode",{parentName:"p"},"word_guessed"),", all we got is"),(0,r.kt)("blockquote",{parentName:"li"},(0,r.kt)("p",{parentName:"blockquote"},"doesn't work when there are too many ",(0,r.kt)("inlineCode",{parentName:"p"},"a"),"s")),(0,r.kt)("p",{parentName:"li"},"Please try to replicate the bug and create a tests, so we don't get any\nregression later on.")),(0,r.kt)("li",{parentName:"ol"},(0,r.kt)("p",{parentName:"li"},"One hidden bug :) Closely non-specified, we cannot reproduce it and we were\ndrunk while playing the game, so we don't remember a thing. :/")),(0,r.kt)("li",{parentName:"ol"},(0,r.kt)("p",{parentName:"li"},"Try to cover as much code via the tests as possible. 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Your\ntask is to try the game, in case you find any bugs point them out and cover as\nmuch of the game as possible with tests."),(0,r.kt)("p",null,"For this bonus you can get at maximum 2 K\u20a1."),(0,r.kt)("table",null,(0,r.kt)("thead",{parentName:"table"},(0,r.kt)("tr",{parentName:"thead"},(0,r.kt)("th",{parentName:"tr",align:null},"Item"),(0,r.kt)("th",{parentName:"tr",align:null},"Bonus"))),(0,r.kt)("tbody",{parentName:"table"},(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Fixing bugs from failing tests"),(0,r.kt)("td",{parentName:"tr",align:null},"0.25")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},(0,r.kt)("inlineCode",{parentName:"td"},"word_guessed")),(0,r.kt)("td",{parentName:"tr",align:null},"0.50")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Hidden bug"),(0,r.kt)("td",{parentName:"tr",align:null},"0.50")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Extending tests, undetectable bugs or evil bug"),(0,r.kt)("td",{parentName:"tr",align:null},"0.37")),(0,r.kt)("tr",{parentName:"tbody"},(0,r.kt)("td",{parentName:"tr",align:null},"Refactor"),(0,r.kt)("td",{parentName:"tr",align:null},"0.38")))),(0,r.kt)("h2",{id:"project"},"Project"),(0,r.kt)("p",null,"Project consists of 2 source files - ",(0,r.kt)("inlineCode",{parentName:"p"},"hangman.c")," and ",(0,r.kt)("inlineCode",{parentName:"p"},"main.c"),"."),(0,r.kt)("p",null,(0,r.kt)("inlineCode",{parentName:"p"},"main.c")," is quite short and concise, there is nothing for you to do."),(0,r.kt)("p",null,(0,r.kt)("inlineCode",{parentName:"p"},"hangman.c")," contains implementation of the game. 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We are not going to look\nat the metrics, but DRY is violated a lot, so as a last task try to remove as\nmuch of the duplicit code as possible."),(0,r.kt)("p",{parentName:"li"},"Tests should help you a lot in case there are some regressions."))),(0,r.kt)("hr",null),(0,r.kt)("p",null,"In case you wonder why there are always 3 same words in the file with words, it\nis because of the ",(0,r.kt)("inlineCode",{parentName:"p"},"get_word")," bug. It is not a bug that can be easily fixed, so\nit is a not requirement at all and you can still get all points for the bonus ;)"),(0,r.kt)("h2",{id:"dictionary"},"Dictionary"),(0,r.kt)("ul",null,(0,r.kt)("li",{parentName:"ul"},(0,r.kt)("a",{parentName:"li",href:"https://en.wikipedia.org/wiki/Functional_testing"},"Functional tests")),(0,r.kt)("li",{parentName:"ul"},(0,r.kt)("a",{parentName:"li",href:"https://en.wikipedia.org/wiki/Smoke_testing_%28software%29"},"Smoke test")),(0,r.kt)("li",{parentName:"ul"},(0,r.kt)("a",{parentName:"li",href:"https://en.wikipedia.org/wiki/Don%27t_repeat_yourself"},"DRY"))),(0,r.kt)("h2",{id:"submitting"},"Submitting"),(0,r.kt)("p",null,"In case you have any questions, feel free to reach out to me."),(0,r.kt)("hr",null))}c.isMDXComponent=!0},1530:(e,t,n)=>{n.d(t,{Z:()=>a});const a=n.p+"assets/images/tdd_lifecycle-327ad9ee0ed8318ed11e19a28e02b2cc.png"}}]); \ No newline at end of file diff --git a/assets/js/7d580cdb.efd242f7.js 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m={id:"pyramid-slide-down",title:"Introduction to dynamic programming",description:"Solving a problem in different ways.\n",tags:["java","recursion","exponential","greedy","dynamic-programming","top-down-dp","bottom-up-dp"],last_updated:{date:new Date("2023-08-17T00:00:00.000Z")}},p=void 0,r={unversionedId:"recursion/pyramid-slide-down",id:"recursion/pyramid-slide-down",title:"Introduction to dynamic programming",description:"Solving a problem in different 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complexity",id:"time-complexity-3",level:3},{value:"Memory complexity",id:"memory-complexity-1",level:3},{value:"Summary",id:"summary",level:2}],o={toc:l},N="wrapper";function c(a){let{components:e,...t}=a;return(0,s.kt)(N,(0,n.Z)({},o,t,{components:e,mdxType:"MDXLayout"}),(0,s.kt)("p",null,"In this post we will try to solve one problem in different ways."),(0,s.kt)("h2",{id:"problem"},"Problem"),(0,s.kt)("p",null,"The problem we are going to solve is one of ",(0,s.kt)("em",{parentName:"p"},"CodeWars")," katas and is called\n",(0,s.kt)("a",{parentName:"p",href:"https://www.codewars.com/kata/551f23362ff852e2ab000037"},"Pyramid Slide Down"),"."),(0,s.kt)("p",null,"We are given a 2D array of integers and we are to find the ",(0,s.kt)("em",{parentName:"p"},"slide down"),".\n",(0,s.kt)("em",{parentName:"p"},"Slide down")," is a maximum sum of consecutive numbers from the top to the bottom."),(0,s.kt)("p",null,"Let's have a look at few examples. Consider the following pyramid:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 3\n 7 4\n 2 4 6\n8 5 9 3\n")),(0,s.kt)("p",null,"This pyramid has following slide down:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," *3\n *7 4\n 2 *4 6\n8 5 *9 3\n")),(0,s.kt)("p",null,"And its value is ",(0,s.kt)("inlineCode",{parentName:"p"},"23"),"."),(0,s.kt)("p",null,"We can also have a look at a ",(0,s.kt)("em",{parentName:"p"},"bigger")," example:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 75\n 95 64\n 17 47 82\n 18 35 87 10\n 20 4 82 47 65\n 19 1 23 3 34\n 88 2 77 73 7 63 67\n 99 65 4 28 6 16 70 92\n 41 41 26 56 83 40 80 70 33\n 41 48 72 33 47 32 37 16 94 29\n 53 71 44 65 25 43 91 52 97 51 14\n 70 11 33 28 77 73 17 78 39 68 17 57\n 91 71 52 38 17 14 91 43 58 50 27 29 48\n 63 66 4 68 89 53 67 30 73 16 69 87 40 31\n 4 62 98 27 23 9 70 98 73 93 38 53 60 4 23\n")),(0,s.kt)("p",null,"Slide down in this case is equal to ",(0,s.kt)("inlineCode",{parentName:"p"},"1074"),"."),(0,s.kt)("h2",{id:"solving-the-problem"},"Solving the problem"),(0,s.kt)("admonition",{type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"I will describe the following ways you can approach this problem and implement\nthem in ",(0,s.kt)("em",{parentName:"p"},"Java"),(0,s.kt)("sup",{parentName:"p",id:"fnref-1"},(0,s.kt)("a",{parentName:"sup",href:"#fn-1",className:"footnote-ref"},"1")),".")),(0,s.kt)("p",null,"For all of the following solutions I will be using basic ",(0,s.kt)("inlineCode",{parentName:"p"},"main")," function that\nwill output ",(0,s.kt)("inlineCode",{parentName:"p"},"true"),"/",(0,s.kt)("inlineCode",{parentName:"p"},"false")," based on the expected output of our algorithm. Any\nother differences will lie only in the solutions of the problem. You can see the\n",(0,s.kt)("inlineCode",{parentName:"p"},"main")," here:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},'public static void main(String[] args) {\n System.out.print("Test #1: ");\n System.out.println(longestSlideDown(new int[][] {\n { 3 },\n { 7, 4 },\n { 2, 4, 6 },\n { 8, 5, 9, 3 }\n }) == 23 ? "passed" : "failed");\n\n System.out.print("Test #2: ");\n System.out.println(longestSlideDown(new int[][] {\n { 75 },\n { 95, 64 },\n { 17, 47, 82 },\n { 18, 35, 87, 10 },\n { 20, 4, 82, 47, 65 },\n { 19, 1, 23, 75, 3, 34 },\n { 88, 2, 77, 73, 7, 63, 67 },\n { 99, 65, 4, 28, 6, 16, 70, 92 },\n { 41, 41, 26, 56, 83, 40, 80, 70, 33 },\n { 41, 48, 72, 33, 47, 32, 37, 16, 94, 29 },\n { 53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14 },\n { 70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57 },\n { 91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48 },\n { 63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31 },\n { 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23 },\n }) == 1074 ? "passed" : "failed");\n}\n')),(0,s.kt)("h2",{id:"na\xefve-solution"},"Na\xefve solution"),(0,s.kt)("p",null,"Our na\xefve solution consists of trying out all the possible slides and finding\nthe one with maximum sum."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: We have gotten out of bounds, there's no reasonable value to\n // return, so we just return the \u2039MIN_VALUE\u203a to ensure that it cannot\n // be maximum.\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: Bottom of the pyramid, we just return the value, there's\n // nowhere to slide anymore.\n return pyramid[row][col];\n }\n\n // Otherwise we account for the current position and return maximum of the\n // available \u201cslides\u201d.\n return pyramid[row][col] + Math.max(\n longestSlideDown(pyramid, row + 1, col),\n longestSlideDown(pyramid, row + 1, col + 1));\n}\n\npublic static int longestSlideDown(int[][] pyramid) {\n // We start the slide in the top cell of the pyramid.\n return longestSlideDown(pyramid, 0, 0);\n}\n")),(0,s.kt)("p",null,"As you can see, we have 2 overloads:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"int longestSlideDown(int[][] pyramid);\nint longestSlideDown(int[][] pyramid, int row, int col);\n")),(0,s.kt)("p",null,"First one is used as a ",(0,s.kt)("em",{parentName:"p"},"public interface")," to the solution, you just pass in the\npyramid itself. Second one is the recursive \u201calgorithm\u201d that finds the slide\ndown."),(0,s.kt)("p",null,"It is a relatively simple solution\u2026 There's nothing to do at the bottom of the\npyramid, so we just return the value in the ",(0,s.kt)("em",{parentName:"p"},"cell"),". Otherwise we add it and try\nto slide down the available cells below the current row."),(0,s.kt)("h3",{id:"time-complexity"},"Time complexity"),(0,s.kt)("p",null,"If you get the source code and run it yourself, it runs rather fine\u2026 I hope you\nare wondering about the time complexity of the proposed solution and, since it\nreally is a na\xefve solution, the time complexity is pretty bad. Let's find the\nworst case scenario."),(0,s.kt)("p",null,"Let's start with the first overload:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid) {\n return longestSlideDown(pyramid, 0, 0);\n}\n")),(0,s.kt)("p",null,"There's not much to do here, so we can safely say that the time complexity of\nthis function is bounded by ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"))))),", where ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T")))))," is our second overload. This\ndoesn't tell us anything, so let's move on to the second overload where we are\ngoing to define the ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))," function."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: We have gotten out of bounds, there's no reasonable value to\n // return, so we just return the \u2039MIN_VALUE\u203a to ensure that it cannot\n // be maximum.\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: Bottom of the pyramid, we just return the value, there's\n // nowhere to slide anymore.\n return pyramid[row][col];\n }\n\n // Otherwise we account for the current position and return maximum of the\n // available \u201cslides\u201d.\n return pyramid[row][col] + Math.max(\n longestSlideDown(pyramid, row + 1, col),\n longestSlideDown(pyramid, row + 1, col + 1));\n}\n")),(0,s.kt)("p",null,"Fun fact is that the whole \u201calgorithm\u201d consists of just 2 ",(0,s.kt)("inlineCode",{parentName:"p"},"return")," statements\nand nothing else. Let's dissect them!"),(0,s.kt)("p",null,"First ",(0,s.kt)("inlineCode",{parentName:"p"},"return")," statement is the base case, so it has a constant time complexity."),(0,s.kt)("p",null,"Second one a bit tricky. We add two numbers together, which we'll consider as\nconstant, but for the right part of the expression we take maximum from the left\nand right paths. OK\u2026 So what happens? We evaluate the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown")," while\nchoosing the under and right both. They are separate computations though, so we\nare branching from each call of ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown"),", unless it's a base case."),(0,s.kt)("p",null,"What does that mean for us then? 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= \\begin{cases} 1 & \\text{, if } y = rows \\\\ 1 + 2 \\cdot T(y + 1) & \\text{, otherwise} \\end{cases}")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord 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mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"y"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"1"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))),(0,s.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.19em"}},(0,s.kt)("span",{parentName:"span"}))))),(0,s.kt)("span",{parentName:"span",className:"arraycolsep",style:{width:"1em"}}),(0,s.kt)("span",{parentName:"span",className:"col-align-l"},(0,s.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.69em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-3.69em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3.008em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},",\xa0if\xa0")),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"y"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"="),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"))),(0,s.kt)("span",{parentName:"span",style:{top:"-2.25em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3.008em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},",\xa0otherwise"))))),(0,s.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.19em"}},(0,s.kt)("span",{parentName:"span"}))))))),(0,s.kt)("span",{parentName:"span",className:"mclose nulldelimiter"}))))))),(0,s.kt)("p",null,"That looks rather easy to compute, isn't it? If you sum it up, you'll get:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")"),(0,s.kt)("mo",{parentName:"mrow"},"\u2208"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("msup",{parentName:"mrow"},(0,s.kt)("mn",{parentName:"msup"},"2"),(0,s.kt)("mrow",{parentName:"msup"},(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"))),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(rows) \\in \\mathcal{O}(2^{rows})")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"\u2208"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord"},"2"),(0,s.kt)("span",{parentName:"span",className:"msupsub"},(0,s.kt)("span",{parentName:"span",className:"vlist-t"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7144em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-3.113em",marginRight:"0.05em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,s.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight"},"s"))))))))),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("p",null,"If you wonder why, I'll try to describe it intuitively:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"In each call to ",(0,s.kt)("inlineCode",{parentName:"li"},"longestSlideDown")," we do some work in constant time,\nregardless of being in the base case. Those are the ",(0,s.kt)("inlineCode",{parentName:"li"},"1"),"s in both cases."),(0,s.kt)("li",{parentName:"ol"},"If we are not in the base case, we move one row down ",(0,s.kt)("strong",{parentName:"li"},"twice"),". That's how we\nobtained ",(0,s.kt)("inlineCode",{parentName:"li"},"2 *")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"y + 1")," in the ",(0,s.kt)("em",{parentName:"li"},"otherwise")," case."),(0,s.kt)("li",{parentName:"ol"},"We move row-by-row, so we move down ",(0,s.kt)("inlineCode",{parentName:"li"},"y"),"-times and each call splits to two\nsubtrees."),(0,s.kt)("li",{parentName:"ol"},"Overall, if we were to represent the calls as a tree, we would get a full\nbinary tree of height ",(0,s.kt)("inlineCode",{parentName:"li"},"y"),", in each node we do some work in constant time,\ntherefore we can just sum the ones.")),(0,s.kt)("admonition",{type:"warning"},(0,s.kt)("p",{parentName:"admonition"},"It would've been more complicated to get an exact result. In the equation above\nwe are assuming that the width of the pyramid is bound by the height.")),(0,s.kt)("p",null,"Hopefully we can agree that this is not the best we can do. \ud83d\ude09"),(0,s.kt)("h2",{id:"greedy-solution"},"Greedy solution"),(0,s.kt)("p",null,"We will try to optimize it a bit. Let's start with a relatively simple ",(0,s.kt)("em",{parentName:"p"},"greedy"),"\napproach."),(0,s.kt)("admonition",{title:"Greedy algorithms",type:"info"},(0,s.kt)("p",{parentName:"admonition"},(0,s.kt)("em",{parentName:"p"},"Greedy algorithms")," can be described as algorithms that decide the action on the\noptimal option at the moment.")),(0,s.kt)("p",null,"We can try to adjust the na\xefve solution. The most problematic part are the\nrecursive calls. Let's apply the greedy approach there:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row == pyramid.length - 1) {\n // BASE: We're at the bottom\n return pyramid[row][col];\n }\n\n if (col + 1 >= pyramid[row + 1].length\n || pyramid[row + 1][col] > pyramid[row + 1][col + 1]) {\n // If we cannot go right or it's not feasible, we continue to the left.\n return pyramid[row][col] + longestSlideDown(pyramid, row + 1, col);\n }\n\n // Otherwise we just move to the right.\n return pyramid[row][col] + longestSlideDown(pyramid, row + 1, col + 1);\n}\n")),(0,s.kt)("p",null,"OK, if we cannot go right ",(0,s.kt)("strong",{parentName:"p"},"or")," the right path adds smaller value to the sum,\nwe simply go left."),(0,s.kt)("h3",{id:"time-complexity-1"},"Time complexity"),(0,s.kt)("p",null,"We have switched from ",(0,s.kt)("em",{parentName:"p"},"adding the maximum")," to ",(0,s.kt)("em",{parentName:"p"},"following the \u201cbigger\u201d path"),", so\nwe improved the time complexity tremendously. We just go down the pyramid all\nthe way to the bottom. Therefore we are getting:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(rows)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("p",null,"We have managed to convert our exponential solution into a linear one."),(0,s.kt)("h3",{id:"running-the-tests"},"Running the tests"),(0,s.kt)("p",null,"However, if we run the tests, we notice that the second test failed:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"},"Test #1: passed\nTest #2: failed\n")),(0,s.kt)("p",null,"What's going on? Well, we have improved the time complexity, but greedy\nalgorithms are not the ideal solution to ",(0,s.kt)("strong",{parentName:"p"},"all")," problems. In this case there\nmay be a solution that is bigger than the one found using the greedy algorithm."),(0,s.kt)("p",null,"Imagine the following pyramid:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 1\n 2 3\n 5 6 7\n 8 9 10 11\n99 13 14 15 16\n")),(0,s.kt)("p",null,"We start at the top:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"1"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"2")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"3"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"3")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"3"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"6")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"7"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"7")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"7"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"10")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"11"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"11")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"11"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"15")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"16"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"16")," looks better, so\nwe choose it.")),(0,s.kt)("p",null,"Our final sum is: ",(0,s.kt)("inlineCode",{parentName:"p"},"1 + 3 + 7 + 11 + 16 = 38"),", but in the bottom left cell we\nhave a ",(0,s.kt)("inlineCode",{parentName:"p"},"99")," that is bigger than our whole sum."),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"Dijkstra's algorithm is a greedy algorithm too, try to think why it is correct.")),(0,s.kt)("h2",{id:"top-down-dp"},"Top-down DP"),(0,s.kt)("p",null,(0,s.kt)("em",{parentName:"p"},"Top-down dynamic programming")," is probably the most common approach, since (at\nleast looks like) is the easiest to implement. The whole point is avoiding the\nunnecessary computations that we have already done."),(0,s.kt)("p",null,"In our case, we can use our na\xefve solution and put a ",(0,s.kt)("em",{parentName:"p"},"cache")," on top of it that\nwill make sure, we don't do unnecessary calculations."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"// This \u201cstructure\u201d is required, since I have decided to use \u2039TreeMap\u203a which\n// requires the ordering on the keys. It represents one position in the pyramid.\nrecord Position(int row, int col) implements Comparable {\n public int compareTo(Position r) {\n if (row != r.row) {\n return Integer.valueOf(row).compareTo(r.row);\n }\n\n if (col != r.col) {\n return Integer.valueOf(col).compareTo(r.col);\n }\n\n return 0;\n }\n}\n\npublic static int longestSlideDown(\n int[][] pyramid,\n TreeMap cache,\n Position position) {\n int row = position.row;\n int col = position.col;\n\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: out of bounds\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: bottom of the pyramid\n return pyramid[position.row][position.col];\n }\n\n if (!cache.containsKey(position)) {\n // We haven't computed the position yet, so we run the same \u201cformula\u201d as\n // in the na\xefve version \xbband\xab we put calculated slide into the cache.\n // Next time we want the slide down from given position, it will be just\n // retrieved from the cache.\n int slideDown = Math.max(\n longestSlideDown(pyramid, cache, new Position(row + 1, col)),\n longestSlideDown(pyramid, cache, new Position(row + 1, col + 1)));\n cache.put(position, pyramid[row][col] + slideDown);\n }\n\n return cache.get(position);\n}\n\npublic static int longestSlideDown(int[][] pyramid) {\n // At the beginning we need to create a cache and share it across the calls.\n TreeMap cache = new TreeMap<>();\n return longestSlideDown(pyramid, cache, new Position(0, 0));\n}\n")),(0,s.kt)("p",null,"You have probably noticed that ",(0,s.kt)("inlineCode",{parentName:"p"},"record Position")," have appeared. Since we are\ncaching the already computed values, we need a \u201creasonable\u201d key. In this case we\nshare the cache only for one ",(0,s.kt)("em",{parentName:"p"},"run")," (i.e. pyramid) of the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown"),", so\nwe can cache just with the indices within the pyramid, i.e. the ",(0,s.kt)("inlineCode",{parentName:"p"},"Position"),"."),(0,s.kt)("admonition",{title:"Record",type:"tip"},(0,s.kt)("p",{parentName:"admonition"},(0,s.kt)("em",{parentName:"p"},"Record")," is relatively new addition to the Java language. It is basically an\nimmutable structure with implicitly defined ",(0,s.kt)("inlineCode",{parentName:"p"},".equals()"),", ",(0,s.kt)("inlineCode",{parentName:"p"},".hashCode()"),",\n",(0,s.kt)("inlineCode",{parentName:"p"},".toString()")," and getters for the attributes.")),(0,s.kt)("p",null,"Because of the choice of ",(0,s.kt)("inlineCode",{parentName:"p"},"TreeMap"),", we had to additionally define the ordering\non it."),(0,s.kt)("p",null,"In the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown")," you can notice that the computation which used to be\nat the end of the na\xefve version above, is now wrapped in an ",(0,s.kt)("inlineCode",{parentName:"p"},"if")," statement that\nchecks for the presence of the position in the cache and computes the slide down\njust when it's needed."),(0,s.kt)("h3",{id:"time-complexity-2"},"Time complexity"),(0,s.kt)("p",null,"If you think that evaluating time complexity for this approach is a bit more\ntricky, you are right. Keeping the cache in mind, it is not the easiest thing\nto do. However there are some observations that might help us figure this out:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"Slide down from each position is calculated only once."),(0,s.kt)("li",{parentName:"ol"},"Once calculated, we use the result from the cache.")),(0,s.kt)("p",null,"Knowing this, we still cannot, at least easily, describe the time complexity of\nfinding the best slide down from a specific position, ",(0,s.kt)("strong",{parentName:"p"},"but")," we can bound it\nfrom above for the ",(0,s.kt)("strong",{parentName:"p"},"whole")," run from the top. Now the question is how we can do\nthat!"),(0,s.kt)("p",null,"Overall we are doing the same things for almost",(0,s.kt)("sup",{parentName:"p",id:"fnref-2"},(0,s.kt)("a",{parentName:"sup",href:"#fn-2",className:"footnote-ref"},"2"))," all of the positions within\nthe pyramid:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},(0,s.kt)("p",{parentName:"li"},"We calculate and store it (using the partial results stored in cache). This\nis done only once."),(0,s.kt)("p",{parentName:"li"},"For each calculation we take 2 values from the cache and insert one value.\nBecause we have chosen ",(0,s.kt)("inlineCode",{parentName:"p"},"TreeMap"),", these 3 operations have logarithmic time\ncomplexity and therefore this step is equivalent to ",(0,s.kt)("span",{parentName:"p",className:"math 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to account only for the\ninsertion, the reason is rather simple, if we include the 2 retrievals here,\nit will be interleaved with the next step, therefore it is easier to keep the\nretrievals in the following point."),(0,s.kt)("admonition",{parentName:"li",type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"You might have noticed it's still not that easy, cause we're not having full\ncache right from the beginning, but the sum of those logarithms cannot be\nexpressed in a nice way, so taking the upper bound, i.e. expecting the cache\nto be full at all times, is the best option for nice and readable complexity\nof the whole approach.")),(0,s.kt)("p",{parentName:"li"},"Our final upper bound of this work is therefore ",(0,s.kt)("span",{parentName:"p",className:"math 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"),(0,s.kt)("admonition",{parentName:"li",type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"It's done twice because of the ",(0,s.kt)("inlineCode",{parentName:"p"},".containsKey()")," in the ",(0,s.kt)("inlineCode",{parentName:"p"},"if")," condition.")))),(0,s.kt)("p",null,"Okay, we have evaluated work done for each of the cells in the pyramid and now\nwe need to put it together."),(0,s.kt)("p",null,"Let's split the time complexity of our solution into two operands:"),(0,s.kt)("div",{className:"math 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However we are expressing the complexity in the\nBachmann-Landau notation, so we care about the ",(0,s.kt)("strong",{parentName:"p"},"upper bound"),", not the exact\nnumber.")),(0,s.kt)("admonition",{title:"Can this be optimized?",type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"Yes, it can! Try to think about a way, how can you minimize the memory\ncomplexity of this approach. I'll give you a hint:"),(0,s.kt)("div",{parentName:"admonition",className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(rows)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"))))))),(0,s.kt)("h2",{id:"bottom-up-dp"},"Bottom-up DP"),(0,s.kt)("p",null,"If you try to think in depth about the top-down DP solution, you might notice\nthat the ",(0,s.kt)("em",{parentName:"p"},"core")," of it stands on caching the calculations that have been already\ndone on the lower \u201clevels\u201d of the pyramid. Our bottom-up implementation will be\nusing this fact!"),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"As I have said in the ",(0,s.kt)("em",{parentName:"p"},"top-down DP")," section, it is the easiest way to implement\nDP (unless the cached function has complicated parameters, in that case it might\nget messy)."),(0,s.kt)("p",{parentName:"admonition"},"Bottom-up dynamic programming can be more effective, but may be more complicated\nto implement right from the beginning.")),(0,s.kt)("p",null,"Let's see how we can implement it:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid) {\n // In the beginning we declare new array. At this point it is easier to just\n // work with the one dimension, i.e. just allocating the space for the rows.\n int[][] slideDowns = new int[pyramid.length][];\n\n // Bottom row gets just copied, there's nothing else to do\u2026 It's the base\n // case.\n slideDowns[pyramid.length - 1] = Arrays.copyOf(pyramid[pyramid.length - 1],\n pyramid[pyramid.length - 1].length);\n\n // Then we need to propagate the found slide downs for each of the levels\n // above.\n for (int y = pyramid.length - 2; y >= 0; --y) {\n // We start by copying the values lying in the row we're processing.\n // They get included in the final sum and we need to allocate the space\n // for the precalculated slide downs anyways.\n int[] row = Arrays.copyOf(pyramid[y], pyramid[y].length);\n\n // At this we just need to \u201cfetch\u201d the partial results from \u201cneighbours\u201d\n for (int x = 0; x < row.length; ++x) {\n // We look under our position, since we expect the rows to get\n // shorter, we can safely assume such position exists.\n int under = slideDowns[y + 1][x];\n\n // Then we have a look to the right, such position doesn't have to\n // exist, e.g. on the right edge, so we validate the index, and if\n // it doesn't exist, we just assign minimum of the \u2039int\u203a which makes\n // sure that it doesn't get picked in the \u2039Math.max()\u203a call.\n int toRight = x + 1 < slideDowns[y + 1].length\n ? slideDowns[y + 1][x + 1]\n : Integer.MIN_VALUE;\n\n // Finally we add the best choice at this point.\n row[x] += Math.max(under, toRight);\n }\n\n // And save the row we've just calculated partial results for to the\n // \u201ctable\u201d.\n slideDowns[y] = row;\n }\n\n // At the end we can find our seeked slide down at the top cell.\n return slideDowns[0][0];\n}\n")),(0,s.kt)("p",null,"I've tried to explain the code as much as possible within the comments, since it\nmight be more beneficial to see right next to the \u201coffending\u201d lines."),(0,s.kt)("p",null,"As you can see, in this approach we go from the other side",(0,s.kt)("sup",{parentName:"p",id:"fnref-3"},(0,s.kt)("a",{parentName:"sup",href:"#fn-3",className:"footnote-ref"},"3")),", the bottom of\nthe pyramid and propagate the partial results up."),(0,s.kt)("admonition",{type:"info"},(0,s.kt)("mdxAdmonitionTitle",{parentName:"admonition"},"How is this different from the ",(0,s.kt)("em",{parentName:"mdxAdmonitionTitle"},"greedy")," solution???"),(0,s.kt)("p",{parentName:"admonition"},"If you try to compare them, you might find a very noticable difference. The\ngreedy approach is going from the top to the bottom without ",(0,s.kt)("strong",{parentName:"p"},"any")," knowledge of\nwhat's going on below. On the other hand, bottom-up DP is going from the bottom\n(",(0,s.kt)("em",{parentName:"p"},"DUH\u2026"),") and ",(0,s.kt)("strong",{parentName:"p"},"propagates")," the partial results to the top. The propagation is\nwhat makes sure that at the top I don't choose the best ",(0,s.kt)("strong",{parentName:"p"},"local")," choice, but\nthe best ",(0,s.kt)("strong",{parentName:"p"},"overall")," result I can achieve.")),(0,s.kt)("h3",{id:"time-complexity-3"},"Time complexity"),(0,s.kt)("p",null,"Time complexity of this solution is rather simple. We allocate an array for the\nrows and then for each row, we copy it and adjust the partial results. Doing\nthis we get:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow"},"+"),(0,s.kt)("mn",{parentName:"mrow"},"2"),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(rows + 2n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"2"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("p",null,"Of course, this is an upper bound, since we iterate through the bottom row only\nonce."),(0,s.kt)("h3",{id:"memory-complexity-1"},"Memory complexity"),(0,s.kt)("p",null,"We're allocating an array for the pyramid ",(0,s.kt)("strong",{parentName:"p"},"again")," for our partial results, so\nwe get:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"If we were writing this in C++ or Rust, we could've avoided that, but not\nreally."),(0,s.kt)("p",{parentName:"admonition"},"C++ would allow us to ",(0,s.kt)("strong",{parentName:"p"},"copy")," the pyramid rightaway into the parameter, so we\nwould be able to directly change it. However it's still a copy, even though we\ndon't need to allocate anything ourselves. It's just implicitly done for us."),(0,s.kt)("p",{parentName:"admonition"},"Rust is more funny in this case. If the pyramids weren't used after the call of\n",(0,s.kt)("inlineCode",{parentName:"p"},"longest_slide_down"),", it would simply ",(0,s.kt)("strong",{parentName:"p"},"move")," them into the functions. If they\nwere used afterwards, the compiler would force you to either borrow it, or\n",(0,s.kt)("em",{parentName:"p"},"clone-and-move")," for the function."),(0,s.kt)("hr",{parentName:"admonition"}),(0,s.kt)("p",{parentName:"admonition"},"Since we're doing it in Java, we get a reference to the ",(0,s.kt)("em",{parentName:"p"},"original")," array and we\ncan't do whatever we want with it.")),(0,s.kt)("h2",{id:"summary"},"Summary"),(0,s.kt)("p",null,"And we've finally reached the end. We have seen 4 different \u201csolutions\u201d",(0,s.kt)("sup",{parentName:"p",id:"fnref-4"},(0,s.kt)("a",{parentName:"sup",href:"#fn-4",className:"footnote-ref"},"4"))," of\nthe same problem using different approaches. Different approaches follow the\norder in which you might come up with them, each approach influences its\nsuccessor and represents the way we can enhance the existing implementation."),(0,s.kt)("hr",null),(0,s.kt)("admonition",{title:"source",type:"info"},(0,s.kt)("p",{parentName:"admonition"},"You can find source code referenced in the text\n",(0,s.kt)("a",{parentName:"p",href:"pathname:///files/ib002/recursion/pyramid-slide-down.tar.gz"},"here"),".")),(0,s.kt)("div",{className:"footnotes"},(0,s.kt)("hr",{parentName:"div"}),(0,s.kt)("ol",{parentName:"div"},(0,s.kt)("li",{parentName:"ol",id:"fn-1"},"cause why not, right!?",(0,s.kt)("a",{parentName:"li",href:"#fnref-1",className:"footnote-backref"},"\u21a9")),(0,s.kt)("li",{parentName:"ol",id:"fn-2"},"except the bottom row",(0,s.kt)("a",{parentName:"li",href:"#fnref-2",className:"footnote-backref"},"\u21a9")),(0,s.kt)("li",{parentName:"ol",id:"fn-3"},"definitely not an RHCP reference \ud83d\ude09",(0,s.kt)("a",{parentName:"li",href:"#fnref-3",className:"footnote-backref"},"\u21a9")),(0,s.kt)("li",{parentName:"ol",id:"fn-4"},"one was not correct, thus the quotes",(0,s.kt)("a",{parentName:"li",href:"#fnref-4",className:"footnote-backref"},"\u21a9")))))}c.isMDXComponent=!0}}]); \ No newline at end of file +"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[8442],{3905:(a,e,t)=>{t.d(e,{Zo:()=>o,kt:()=>h});var n=t(7294);function s(a,e,t){return e in a?Object.defineProperty(a,e,{value:t,enumerable:!0,configurable:!0,writable:!0}):a[e]=t,a}function m(a,e){var t=Object.keys(a);if(Object.getOwnPropertySymbols){var n=Object.getOwnPropertySymbols(a);e&&(n=n.filter((function(e){return Object.getOwnPropertyDescriptor(a,e).enumerable}))),t.push.apply(t,n)}return t}function p(a){for(var e=1;e=0||(s[t]=a[t]);return s}(a,e);if(Object.getOwnPropertySymbols){var 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l=2;l{t.r(e),t.d(e,{assets:()=>i,contentTitle:()=>p,default:()=>c,frontMatter:()=>m,metadata:()=>r,toc:()=>l});var n=t(7462),s=(t(7294),t(3905));const m={id:"pyramid-slide-down",title:"Introduction to dynamic programming",description:"Solving a problem in different ways.\n",tags:["java","recursion","exponential","greedy","dynamic-programming","top-down-dp","bottom-up-dp"],last_updated:{date:new Date("2023-08-17T00:00:00.000Z")}},p=void 0,r={unversionedId:"recursion/pyramid-slide-down",id:"recursion/pyramid-slide-down",title:"Introduction to dynamic programming",description:"Solving a problem in different 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ways.\n",tags:["java","recursion","exponential","greedy","dynamic-programming","top-down-dp","bottom-up-dp"],last_updated:{date:"2023-08-17T00:00:00.000Z"}},sidebar:"autogeneratedBar",previous:{title:"Recursion and backtracking with Robot Karel",permalink:"/ib002/recursion/karel-1"},next:{title:"Red-Black Trees",permalink:"/ib002/category/red-black-trees"}},i={},l=[{value:"Problem",id:"problem",level:2},{value:"Solving the problem",id:"solving-the-problem",level:2},{value:"Na\xefve solution",id:"na\xefve-solution",level:2},{value:"Time complexity",id:"time-complexity",level:3},{value:"Greedy solution",id:"greedy-solution",level:2},{value:"Time complexity",id:"time-complexity-1",level:3},{value:"Running the tests",id:"running-the-tests",level:3},{value:"Top-down DP",id:"top-down-dp",level:2},{value:"Time complexity",id:"time-complexity-2",level:3},{value:"Memory complexity",id:"memory-complexity",level:3},{value:"Bottom-up DP",id:"bottom-up-dp",level:2},{value:"Time complexity",id:"time-complexity-3",level:3},{value:"Memory complexity",id:"memory-complexity-1",level:3},{value:"Summary",id:"summary",level:2}],o={toc:l},N="wrapper";function c(a){let{components:e,...t}=a;return(0,s.kt)(N,(0,n.Z)({},o,t,{components:e,mdxType:"MDXLayout"}),(0,s.kt)("p",null,"In this post we will try to solve one problem in different ways."),(0,s.kt)("h2",{id:"problem"},"Problem"),(0,s.kt)("p",null,"The problem we are going to solve is one of ",(0,s.kt)("em",{parentName:"p"},"CodeWars")," katas and is called\n",(0,s.kt)("a",{parentName:"p",href:"https://www.codewars.com/kata/551f23362ff852e2ab000037"},"Pyramid Slide Down"),"."),(0,s.kt)("p",null,"We are given a 2D array of integers and we are to find the ",(0,s.kt)("em",{parentName:"p"},"slide down"),".\n",(0,s.kt)("em",{parentName:"p"},"Slide down")," is a maximum sum of consecutive numbers from the top to the bottom."),(0,s.kt)("p",null,"Let's have a look at few examples. Consider the following pyramid:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 3\n 7 4\n 2 4 6\n8 5 9 3\n")),(0,s.kt)("p",null,"This pyramid has following slide down:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," *3\n *7 4\n 2 *4 6\n8 5 *9 3\n")),(0,s.kt)("p",null,"And its value is ",(0,s.kt)("inlineCode",{parentName:"p"},"23"),"."),(0,s.kt)("p",null,"We can also have a look at a ",(0,s.kt)("em",{parentName:"p"},"bigger")," example:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 75\n 95 64\n 17 47 82\n 18 35 87 10\n 20 4 82 47 65\n 19 1 23 3 34\n 88 2 77 73 7 63 67\n 99 65 4 28 6 16 70 92\n 41 41 26 56 83 40 80 70 33\n 41 48 72 33 47 32 37 16 94 29\n 53 71 44 65 25 43 91 52 97 51 14\n 70 11 33 28 77 73 17 78 39 68 17 57\n 91 71 52 38 17 14 91 43 58 50 27 29 48\n 63 66 4 68 89 53 67 30 73 16 69 87 40 31\n 4 62 98 27 23 9 70 98 73 93 38 53 60 4 23\n")),(0,s.kt)("p",null,"Slide down in this case is equal to ",(0,s.kt)("inlineCode",{parentName:"p"},"1074"),"."),(0,s.kt)("h2",{id:"solving-the-problem"},"Solving the problem"),(0,s.kt)("admonition",{type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"I will describe the following ways you can approach this problem and implement\nthem in ",(0,s.kt)("em",{parentName:"p"},"Java"),(0,s.kt)("sup",{parentName:"p",id:"fnref-1"},(0,s.kt)("a",{parentName:"sup",href:"#fn-1",className:"footnote-ref"},"1")),".")),(0,s.kt)("p",null,"For all of the following solutions I will be using basic ",(0,s.kt)("inlineCode",{parentName:"p"},"main")," function that\nwill output ",(0,s.kt)("inlineCode",{parentName:"p"},"true"),"/",(0,s.kt)("inlineCode",{parentName:"p"},"false")," based on the expected output of our algorithm. Any\nother differences will lie only in the solutions of the problem. You can see the\n",(0,s.kt)("inlineCode",{parentName:"p"},"main")," here:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},'public static void main(String[] args) {\n System.out.print("Test #1: ");\n System.out.println(longestSlideDown(new int[][] {\n { 3 },\n { 7, 4 },\n { 2, 4, 6 },\n { 8, 5, 9, 3 }\n }) == 23 ? "passed" : "failed");\n\n System.out.print("Test #2: ");\n System.out.println(longestSlideDown(new int[][] {\n { 75 },\n { 95, 64 },\n { 17, 47, 82 },\n { 18, 35, 87, 10 },\n { 20, 4, 82, 47, 65 },\n { 19, 1, 23, 75, 3, 34 },\n { 88, 2, 77, 73, 7, 63, 67 },\n { 99, 65, 4, 28, 6, 16, 70, 92 },\n { 41, 41, 26, 56, 83, 40, 80, 70, 33 },\n { 41, 48, 72, 33, 47, 32, 37, 16, 94, 29 },\n { 53, 71, 44, 65, 25, 43, 91, 52, 97, 51, 14 },\n { 70, 11, 33, 28, 77, 73, 17, 78, 39, 68, 17, 57 },\n { 91, 71, 52, 38, 17, 14, 91, 43, 58, 50, 27, 29, 48 },\n { 63, 66, 4, 68, 89, 53, 67, 30, 73, 16, 69, 87, 40, 31 },\n { 4, 62, 98, 27, 23, 9, 70, 98, 73, 93, 38, 53, 60, 4, 23 },\n }) == 1074 ? "passed" : "failed");\n}\n')),(0,s.kt)("h2",{id:"na\xefve-solution"},"Na\xefve solution"),(0,s.kt)("p",null,"Our na\xefve solution consists of trying out all the possible slides and finding\nthe one with maximum sum."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: We have gotten out of bounds, there's no reasonable value to\n // return, so we just return the \u2039MIN_VALUE\u203a to ensure that it cannot\n // be maximum.\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: Bottom of the pyramid, we just return the value, there's\n // nowhere to slide anymore.\n return pyramid[row][col];\n }\n\n // Otherwise we account for the current position and return maximum of the\n // available \u201cslides\u201d.\n return pyramid[row][col] + Math.max(\n longestSlideDown(pyramid, row + 1, col),\n longestSlideDown(pyramid, row + 1, col + 1));\n}\n\npublic static int longestSlideDown(int[][] pyramid) {\n // We start the slide in the top cell of the pyramid.\n return longestSlideDown(pyramid, 0, 0);\n}\n")),(0,s.kt)("p",null,"As you can see, we have 2 overloads:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"int longestSlideDown(int[][] pyramid);\nint longestSlideDown(int[][] pyramid, int row, int col);\n")),(0,s.kt)("p",null,"First one is used as a ",(0,s.kt)("em",{parentName:"p"},"public interface")," to the solution, you just pass in the\npyramid itself. Second one is the recursive \u201calgorithm\u201d that finds the slide\ndown."),(0,s.kt)("p",null,"It is a relatively simple solution\u2026 There's nothing to do at the bottom of the\npyramid, so we just return the value in the ",(0,s.kt)("em",{parentName:"p"},"cell"),". Otherwise we add it and try\nto slide down the available cells below the current row."),(0,s.kt)("h3",{id:"time-complexity"},"Time complexity"),(0,s.kt)("p",null,"If you get the source code and run it yourself, it runs rather fine\u2026 I hope you\nare wondering about the time complexity of the proposed solution and, since it\nreally is a na\xefve solution, the time complexity is pretty bad. Let's find the\nworst case scenario."),(0,s.kt)("p",null,"Let's start with the first overload:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid) {\n return longestSlideDown(pyramid, 0, 0);\n}\n")),(0,s.kt)("p",null,"There's not much to do here, so we can safely say that the time complexity of\nthis function is bounded by ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"))))),", where ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6833em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T")))))," is our second overload. This\ndoesn't tell us anything, so let's move on to the second overload where we are\ngoing to define the ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"n"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(n)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))," function."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: We have gotten out of bounds, there's no reasonable value to\n // return, so we just return the \u2039MIN_VALUE\u203a to ensure that it cannot\n // be maximum.\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: Bottom of the pyramid, we just return the value, there's\n // nowhere to slide anymore.\n return pyramid[row][col];\n }\n\n // Otherwise we account for the current position and return maximum of the\n // available \u201cslides\u201d.\n return pyramid[row][col] + Math.max(\n longestSlideDown(pyramid, row + 1, col),\n longestSlideDown(pyramid, row + 1, col + 1));\n}\n")),(0,s.kt)("p",null,"Fun fact is that the whole \u201calgorithm\u201d consists of just 2 ",(0,s.kt)("inlineCode",{parentName:"p"},"return")," statements\nand nothing else. Let's dissect them!"),(0,s.kt)("p",null,"First ",(0,s.kt)("inlineCode",{parentName:"p"},"return")," statement is the base case, so it has a constant time complexity."),(0,s.kt)("p",null,"Second one a bit tricky. We add two numbers together, which we'll consider as\nconstant, but for the right part of the expression we take maximum from the left\nand right paths. OK\u2026 So what happens? We evaluate the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown")," while\nchoosing the under and right both. They are separate computations though, so we\nare branching from each call of ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown"),", unless it's a base case."),(0,s.kt)("p",null,"What does that mean for us then? We basically get"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"y"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mrow",{parentName:"mrow"},(0,s.kt)("mo",{parentName:"mrow",fence:"true"},"{"),(0,s.kt)("mtable",{parentName:"mrow",rowspacing:"0.36em",columnalign:"left left",columnspacing:"1em"},(0,s.kt)("mtr",{parentName:"mtable"},(0,s.kt)("mtd",{parentName:"mtr"},(0,s.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"false"},(0,s.kt)("mn",{parentName:"mstyle"},"1"))),(0,s.kt)("mtd",{parentName:"mtr"},(0,s.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"false"},(0,s.kt)("mrow",{parentName:"mstyle"},(0,s.kt)("mtext",{parentName:"mrow"},",\xa0if\xa0"),(0,s.kt)("mi",{parentName:"mrow"},"y"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"))))),(0,s.kt)("mtr",{parentName:"mtable"},(0,s.kt)("mtd",{parentName:"mtr"},(0,s.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"false"},(0,s.kt)("mrow",{parentName:"mstyle"},(0,s.kt)("mn",{parentName:"mrow"},"1"),(0,s.kt)("mo",{parentName:"mrow"},"+"),(0,s.kt)("mn",{parentName:"mrow"},"2"),(0,s.kt)("mo",{parentName:"mrow"},"\u22c5"),(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"y"),(0,s.kt)("mo",{parentName:"mrow"},"+"),(0,s.kt)("mn",{parentName:"mrow"},"1"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")))),(0,s.kt)("mtd",{parentName:"mtr"},(0,s.kt)("mstyle",{parentName:"mtd",scriptlevel:"0",displaystyle:"false"},(0,s.kt)("mtext",{parentName:"mstyle"},",\xa0otherwise"))))))),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(y) = \\begin{cases} 1 & \\text{, if } y = rows \\\\ 1 + 2 \\cdot T(y + 1) & \\text{, otherwise} \\end{cases}")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord 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vlist-t2"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.69em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-3.69em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3.008em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},",\xa0if\xa0")),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.03588em"}},"y"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"="),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"))),(0,s.kt)("span",{parentName:"span",style:{top:"-2.25em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"3.008em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord text"},(0,s.kt)("span",{parentName:"span",className:"mord"},",\xa0otherwise"))))),(0,s.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"1.19em"}},(0,s.kt)("span",{parentName:"span"}))))))),(0,s.kt)("span",{parentName:"span",className:"mclose nulldelimiter"}))))))),(0,s.kt)("p",null,"That looks rather easy to compute, isn't it? If you sum it up, you'll get:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"T"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")"),(0,s.kt)("mo",{parentName:"mrow"},"\u2208"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("msup",{parentName:"mrow"},(0,s.kt)("mn",{parentName:"msup"},"2"),(0,s.kt)("mrow",{parentName:"msup"},(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"))),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"T(rows) \\in \\mathcal{O}(2^{rows})")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.13889em"}},"T"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}}),(0,s.kt)("span",{parentName:"span",className:"mrel"},"\u2208"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2778em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord"},"2"),(0,s.kt)("span",{parentName:"span",className:"msupsub"},(0,s.kt)("span",{parentName:"span",className:"vlist-t"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.7144em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-3.113em",marginRight:"0.05em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,s.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal mtight"},"s"))))))))),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("p",null,"If you wonder why, I'll try to describe it intuitively:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"In each call to ",(0,s.kt)("inlineCode",{parentName:"li"},"longestSlideDown")," we do some work in constant time,\nregardless of being in the base case. Those are the ",(0,s.kt)("inlineCode",{parentName:"li"},"1"),"s in both cases."),(0,s.kt)("li",{parentName:"ol"},"If we are not in the base case, we move one row down ",(0,s.kt)("strong",{parentName:"li"},"twice"),". That's how we\nobtained ",(0,s.kt)("inlineCode",{parentName:"li"},"2 *")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"y + 1")," in the ",(0,s.kt)("em",{parentName:"li"},"otherwise")," case."),(0,s.kt)("li",{parentName:"ol"},"We move row-by-row, so we move down ",(0,s.kt)("inlineCode",{parentName:"li"},"y"),"-times and each call splits to two\nsubtrees."),(0,s.kt)("li",{parentName:"ol"},"Overall, if we were to represent the calls as a tree, we would get a full\nbinary tree of height ",(0,s.kt)("inlineCode",{parentName:"li"},"y"),", in each node we do some work in constant time,\ntherefore we can just sum the ones.")),(0,s.kt)("admonition",{type:"warning"},(0,s.kt)("p",{parentName:"admonition"},"It would've been more complicated to get an exact result. In the equation above\nwe are assuming that the width of the pyramid is bound by the height.")),(0,s.kt)("p",null,"Hopefully we can agree that this is not the best we can do. \ud83d\ude09"),(0,s.kt)("h2",{id:"greedy-solution"},"Greedy solution"),(0,s.kt)("p",null,"We will try to optimize it a bit. Let's start with a relatively simple ",(0,s.kt)("em",{parentName:"p"},"greedy"),"\napproach."),(0,s.kt)("admonition",{title:"Greedy algorithms",type:"info"},(0,s.kt)("p",{parentName:"admonition"},(0,s.kt)("em",{parentName:"p"},"Greedy algorithms")," can be described as algorithms that decide the action on the\noptimal option at the moment.")),(0,s.kt)("p",null,"We can try to adjust the na\xefve solution. The most problematic part are the\nrecursive calls. Let's apply the greedy approach there:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid, int row, int col) {\n if (row == pyramid.length - 1) {\n // BASE: We're at the bottom\n return pyramid[row][col];\n }\n\n if (col + 1 >= pyramid[row + 1].length\n || pyramid[row + 1][col] > pyramid[row + 1][col + 1]) {\n // If we cannot go right or it's not feasible, we continue to the left.\n return pyramid[row][col] + longestSlideDown(pyramid, row + 1, col);\n }\n\n // Otherwise we just move to the right.\n return pyramid[row][col] + longestSlideDown(pyramid, row + 1, col + 1);\n}\n")),(0,s.kt)("p",null,"OK, if we cannot go right ",(0,s.kt)("strong",{parentName:"p"},"or")," the right path adds smaller value to the sum,\nwe simply go left."),(0,s.kt)("h3",{id:"time-complexity-1"},"Time complexity"),(0,s.kt)("p",null,"We have switched from ",(0,s.kt)("em",{parentName:"p"},"adding the maximum")," to ",(0,s.kt)("em",{parentName:"p"},"following the \u201cbigger\u201d path"),", so\nwe improved the time complexity tremendously. We just go down the pyramid all\nthe way to the bottom. Therefore we are getting:"),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(rows)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")")))))),(0,s.kt)("p",null,"We have managed to convert our exponential solution into a linear one."),(0,s.kt)("h3",{id:"running-the-tests"},"Running the tests"),(0,s.kt)("p",null,"However, if we run the tests, we notice that the second test failed:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"},"Test #1: passed\nTest #2: failed\n")),(0,s.kt)("p",null,"What's going on? Well, we have improved the time complexity, but greedy\nalgorithms are not the ideal solution to ",(0,s.kt)("strong",{parentName:"p"},"all")," problems. In this case there\nmay be a solution that is bigger than the one found using the greedy algorithm."),(0,s.kt)("p",null,"Imagine the following pyramid:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre"}," 1\n 2 3\n 5 6 7\n 8 9 10 11\n99 13 14 15 16\n")),(0,s.kt)("p",null,"We start at the top:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"1"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"2")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"3"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"3")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"3"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"6")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"7"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"7")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"7"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"10")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"11"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"11")," looks better, so we\nchoose it."),(0,s.kt)("li",{parentName:"ol"},"Current cell: ",(0,s.kt)("inlineCode",{parentName:"li"},"11"),", we can choose from ",(0,s.kt)("inlineCode",{parentName:"li"},"15")," and ",(0,s.kt)("inlineCode",{parentName:"li"},"16"),", ",(0,s.kt)("inlineCode",{parentName:"li"},"16")," looks better, so\nwe choose it.")),(0,s.kt)("p",null,"Our final sum is: ",(0,s.kt)("inlineCode",{parentName:"p"},"1 + 3 + 7 + 11 + 16 = 38"),", but in the bottom left cell we\nhave a ",(0,s.kt)("inlineCode",{parentName:"p"},"99")," that is bigger than our whole sum."),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"Dijkstra's algorithm is a greedy algorithm too, try to think why it is correct.")),(0,s.kt)("h2",{id:"top-down-dp"},"Top-down DP"),(0,s.kt)("p",null,(0,s.kt)("em",{parentName:"p"},"Top-down dynamic programming")," is probably the most common approach, since (at\nleast looks like) is the easiest to implement. The whole point is avoiding the\nunnecessary computations that we have already done."),(0,s.kt)("p",null,"In our case, we can use our na\xefve solution and put a ",(0,s.kt)("em",{parentName:"p"},"cache")," on top of it that\nwill make sure, we don't do unnecessary calculations."),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"// This \u201cstructure\u201d is required, since I have decided to use \u2039TreeMap\u203a which\n// requires the ordering on the keys. It represents one position in the pyramid.\nrecord Position(int row, int col) implements Comparable {\n public int compareTo(Position r) {\n if (row != r.row) {\n return Integer.valueOf(row).compareTo(r.row);\n }\n\n if (col != r.col) {\n return Integer.valueOf(col).compareTo(r.col);\n }\n\n return 0;\n }\n}\n\npublic static int longestSlideDown(\n int[][] pyramid,\n TreeMap cache,\n Position position) {\n int row = position.row;\n int col = position.col;\n\n if (row >= pyramid.length || col < 0 || col >= pyramid[row].length) {\n // BASE: out of bounds\n return Integer.MIN_VALUE;\n }\n\n if (row == pyramid.length - 1) {\n // BASE: bottom of the pyramid\n return pyramid[position.row][position.col];\n }\n\n if (!cache.containsKey(position)) {\n // We haven't computed the position yet, so we run the same \u201cformula\u201d as\n // in the na\xefve version \xbband\xab we put calculated slide into the cache.\n // Next time we want the slide down from given position, it will be just\n // retrieved from the cache.\n int slideDown = Math.max(\n longestSlideDown(pyramid, cache, new Position(row + 1, col)),\n longestSlideDown(pyramid, cache, new Position(row + 1, col + 1)));\n cache.put(position, pyramid[row][col] + slideDown);\n }\n\n return cache.get(position);\n}\n\npublic static int longestSlideDown(int[][] pyramid) {\n // At the beginning we need to create a cache and share it across the calls.\n TreeMap cache = new TreeMap<>();\n return longestSlideDown(pyramid, cache, new Position(0, 0));\n}\n")),(0,s.kt)("p",null,"You have probably noticed that ",(0,s.kt)("inlineCode",{parentName:"p"},"record Position")," have appeared. Since we are\ncaching the already computed values, we need a \u201creasonable\u201d key. In this case we\nshare the cache only for one ",(0,s.kt)("em",{parentName:"p"},"run")," (i.e. pyramid) of the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown"),", so\nwe can cache just with the indices within the pyramid, i.e. the ",(0,s.kt)("inlineCode",{parentName:"p"},"Position"),"."),(0,s.kt)("admonition",{title:"Record",type:"tip"},(0,s.kt)("p",{parentName:"admonition"},(0,s.kt)("em",{parentName:"p"},"Record")," is relatively new addition to the Java language. It is basically an\nimmutable structure with implicitly defined ",(0,s.kt)("inlineCode",{parentName:"p"},".equals()"),", ",(0,s.kt)("inlineCode",{parentName:"p"},".hashCode()"),",\n",(0,s.kt)("inlineCode",{parentName:"p"},".toString()")," and getters for the attributes.")),(0,s.kt)("p",null,"Because of the choice of ",(0,s.kt)("inlineCode",{parentName:"p"},"TreeMap"),", we had to additionally define the ordering\non it."),(0,s.kt)("p",null,"In the ",(0,s.kt)("inlineCode",{parentName:"p"},"longestSlideDown")," you can notice that the computation which used to be\nat the end of the na\xefve version above, is now wrapped in an ",(0,s.kt)("inlineCode",{parentName:"p"},"if")," statement that\nchecks for the presence of the position in the cache and computes the slide down\njust when it's needed."),(0,s.kt)("h3",{id:"time-complexity-2"},"Time complexity"),(0,s.kt)("p",null,"If you think that evaluating time complexity for this approach is a bit more\ntricky, you are right. Keeping the cache in mind, it is not the easiest thing\nto do. However there are some observations that might help us figure this out:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},"Slide down from each position is calculated only once."),(0,s.kt)("li",{parentName:"ol"},"Once calculated, we use the result from the cache.")),(0,s.kt)("p",null,"Knowing this, we still cannot, at least easily, describe the time complexity of\nfinding the best slide down from a specific position, ",(0,s.kt)("strong",{parentName:"p"},"but")," we can bound it\nfrom above for the ",(0,s.kt)("strong",{parentName:"p"},"whole")," run from the top. Now the question is how we can do\nthat!"),(0,s.kt)("p",null,"Overall we are doing the same things for almost",(0,s.kt)("sup",{parentName:"p",id:"fnref-2"},(0,s.kt)("a",{parentName:"sup",href:"#fn-2",className:"footnote-ref"},"2"))," all of the positions within\nthe pyramid:"),(0,s.kt)("ol",null,(0,s.kt)("li",{parentName:"ol"},(0,s.kt)("p",{parentName:"li"},"We calculate and store it (using the partial results stored in cache). This\nis done only once."),(0,s.kt)("p",{parentName:"li"},"For each calculation we take 2 values from the cache and insert one value.\nBecause we have chosen ",(0,s.kt)("inlineCode",{parentName:"p"},"TreeMap"),", these 3 operations have logarithmic time\ncomplexity and therefore this step is equivalent to ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"3"),(0,s.kt)("mo",{parentName:"mrow"},"\u22c5"),(0,s.kt)("msub",{parentName:"mrow"},(0,s.kt)("mrow",{parentName:"msub"},(0,s.kt)("mi",{parentName:"mrow"},"log"),(0,s.kt)("mo",{parentName:"mrow"},"\u2061")),(0,s.kt)("mn",{parentName:"msub"},"2")),(0,s.kt)("mi",{parentName:"mrow"},"n")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"3 \\cdot \\log_2{n}")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"3"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mbin"},"\u22c5"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.9386em",verticalAlign:"-0.2441em"}}),(0,s.kt)("span",{parentName:"span",className:"mop"},(0,s.kt)("span",{parentName:"span",className:"mop"},"lo",(0,s.kt)("span",{parentName:"span",style:{marginRight:"0.01389em"}},"g")),(0,s.kt)("span",{parentName:"span",className:"msupsub"},(0,s.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.207em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-2.4559em",marginRight:"0.05em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,s.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mtight"},"2")))),(0,s.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.2441em"}},(0,s.kt)("span",{parentName:"span"})))))),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),"."),(0,s.kt)("p",{parentName:"li"},"However for the sake of simplicity, we are going to account only for the\ninsertion, the reason is rather simple, if we include the 2 retrievals here,\nit will be interleaved with the next step, therefore it is easier to keep the\nretrievals in the following point."),(0,s.kt)("admonition",{parentName:"li",type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"You might have noticed it's still not that easy, cause we're not having full\ncache right from the beginning, but the sum of those logarithms cannot be\nexpressed in a nice way, so taking the upper bound, i.e. expecting the cache\nto be full at all times, is the best option for nice and readable complexity\nof the whole approach.")),(0,s.kt)("p",{parentName:"li"},"Our final upper bound of this work is therefore ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("msub",{parentName:"mrow"},(0,s.kt)("mrow",{parentName:"msub"},(0,s.kt)("mi",{parentName:"mrow"},"log"),(0,s.kt)("mo",{parentName:"mrow"},"\u2061")),(0,s.kt)("mn",{parentName:"msub"},"2")),(0,s.kt)("mi",{parentName:"mrow"},"n")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\log_2{n}")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.9386em",verticalAlign:"-0.2441em"}}),(0,s.kt)("span",{parentName:"span",className:"mop"},(0,s.kt)("span",{parentName:"span",className:"mop"},"lo",(0,s.kt)("span",{parentName:"span",style:{marginRight:"0.01389em"}},"g")),(0,s.kt)("span",{parentName:"span",className:"msupsub"},(0,s.kt)("span",{parentName:"span",className:"vlist-t 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from the cache. Same as in first point, but only twice, so we\nget ",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mn",{parentName:"mrow"},"2"),(0,s.kt)("mo",{parentName:"mrow"},"\u22c5"),(0,s.kt)("msub",{parentName:"mrow"},(0,s.kt)("mrow",{parentName:"msub"},(0,s.kt)("mi",{parentName:"mrow"},"log"),(0,s.kt)("mo",{parentName:"mrow"},"\u2061")),(0,s.kt)("mn",{parentName:"msub"},"2")),(0,s.kt)("mi",{parentName:"mrow"},"n")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"2 \\cdot \\log_2{n}")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.6444em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},"2"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mbin"},"\u22c5"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.9386em",verticalAlign:"-0.2441em"}}),(0,s.kt)("span",{parentName:"span",className:"mop"},(0,s.kt)("span",{parentName:"span",className:"mop"},"lo",(0,s.kt)("span",{parentName:"span",style:{marginRight:"0.01389em"}},"g")),(0,s.kt)("span",{parentName:"span",className:"msupsub"},(0,s.kt)("span",{parentName:"span",className:"vlist-t vlist-t2"},(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.207em"}},(0,s.kt)("span",{parentName:"span",style:{top:"-2.4559em",marginRight:"0.05em"}},(0,s.kt)("span",{parentName:"span",className:"pstrut",style:{height:"2.7em"}}),(0,s.kt)("span",{parentName:"span",className:"sizing reset-size6 size3 mtight"},(0,s.kt)("span",{parentName:"span",className:"mord mtight"},"2")))),(0,s.kt)("span",{parentName:"span",className:"vlist-s"},"\u200b")),(0,s.kt)("span",{parentName:"span",className:"vlist-r"},(0,s.kt)("span",{parentName:"span",className:"vlist",style:{height:"0.2441em"}},(0,s.kt)("span",{parentName:"span"})))))),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"n")))))),". "),(0,s.kt)("admonition",{parentName:"li",type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"It's done twice because of the ",(0,s.kt)("inlineCode",{parentName:"p"},".containsKey()")," in the ",(0,s.kt)("inlineCode",{parentName:"p"},"if")," condition.")))),(0,s.kt)("p",null,"Okay, we have evaluated work done for each of the cells in the pyramid and now\nwe need to put it together."),(0,s.kt)("p",null,"Let's split the time complexity of our solution into two operands:"),(0,s.kt)("div",{className:"math 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s)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02778em"}},"r"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}}),(0,s.kt)("span",{parentName:"span",className:"mbin"},"+"),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.2222em"}})),(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord 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",(0,s.kt)("span",{parentName:"p",className:"math math-inline"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow"},"s")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"s")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"0.4306em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s")))))," will represent\nthe additional retrievals on top of the calculation."),(0,s.kt)("p",null,"We calculate the values only ",(0,s.kt)("strong",{parentName:"p"},"once"),", therefore we can safely agree on:"),(0,s.kt)("div",{className:"math 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",(0,s.kt)("em",{parentName:"p"},"na\xefve")," one."),(0,s.kt)("h3",{id:"memory-complexity"},"Memory complexity"),(0,s.kt)("p",null,"With this approach we need to talk about the memory complexity too, because we\nhave introduced cache. If you think that the memory complexity is linear to the\ninput, you are right. We start at the top and try to find each and every slide\ndown. At the end we get the final result for ",(0,s.kt)("inlineCode",{parentName:"p"},"new Position(0, 0)"),", so we need to\ncompute everything below."),(0,s.kt)("p",null,"That's how we obtain:"),(0,s.kt)("div",{className:"math 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mathnormal"},"n")))))," represents the total amount of cells in the pyramid, i.e."),(0,s.kt)("div",{className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("munderover",{parentName:"mrow"},(0,s.kt)("mo",{parentName:"munderover"},"\u2211"),(0,s.kt)("mrow",{parentName:"munderover"},(0,s.kt)("mi",{parentName:"mrow"},"y"),(0,s.kt)("mo",{parentName:"mrow"},"="),(0,s.kt)("mn",{parentName:"mrow"},"0")),(0,s.kt)("mrow",{parentName:"munderover"},(0,s.kt)("mrow",{parentName:"mrow"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"p"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"y"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"r"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"a"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"m"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"i"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"d"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"."),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"l"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"e"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"n"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"g"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"t"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"h")),(0,s.kt)("mo",{parentName:"mrow"},"\u2212"),(0,s.kt)("mn",{parentName:"mrow"},"1"))),(0,s.kt)("mrow",{parentName:"mrow"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"p"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"y"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"r"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"a"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"m"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"i"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"d")),(0,s.kt)("mrow",{parentName:"mrow"},(0,s.kt)("mo",{parentName:"mrow",fence:"true"},"["),(0,s.kt)("mi",{parentName:"mrow"},"y"),(0,s.kt)("mo",{parentName:"mrow",fence:"true"},"]")),(0,s.kt)("mrow",{parentName:"mrow"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"."),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"l"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"e"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"n"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"g"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"t"),(0,s.kt)("mi",{parentName:"mrow",mathvariant:"monospace"},"h"))),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\sum_{y=0}^{\\mathtt{pyramid.length} 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delimcenter",style:{top:"0em"}},"]")),(0,s.kt)("span",{parentName:"span",className:"mspace",style:{marginRight:"0.1667em"}}),(0,s.kt)("span",{parentName:"span",className:"mord"},(0,s.kt)("span",{parentName:"span",className:"mord mathtt"},".length"))))))),(0,s.kt)("admonition",{type:"caution"},(0,s.kt)("p",{parentName:"admonition"},"If you're wondering whether it's correct because of the second ",(0,s.kt)("inlineCode",{parentName:"p"},"if")," in our\nfunction, your guess is right. However we are expressing the complexity in the\nBachmann-Landau notation, so we care about the ",(0,s.kt)("strong",{parentName:"p"},"upper bound"),", not the exact\nnumber.")),(0,s.kt)("admonition",{title:"Can this be optimized?",type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"Yes, it can! Try to think about a way, how can you minimize the memory\ncomplexity of this approach. I'll give you a hint:"),(0,s.kt)("div",{parentName:"admonition",className:"math math-display"},(0,s.kt)("span",{parentName:"div",className:"katex-display"},(0,s.kt)("span",{parentName:"span",className:"katex"},(0,s.kt)("span",{parentName:"span",className:"katex-mathml"},(0,s.kt)("math",{parentName:"span",xmlns:"http://www.w3.org/1998/Math/MathML",display:"block"},(0,s.kt)("semantics",{parentName:"math"},(0,s.kt)("mrow",{parentName:"semantics"},(0,s.kt)("mi",{parentName:"mrow",mathvariant:"script"},"O"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},"("),(0,s.kt)("mi",{parentName:"mrow"},"r"),(0,s.kt)("mi",{parentName:"mrow"},"o"),(0,s.kt)("mi",{parentName:"mrow"},"w"),(0,s.kt)("mi",{parentName:"mrow"},"s"),(0,s.kt)("mo",{parentName:"mrow",stretchy:"false"},")")),(0,s.kt)("annotation",{parentName:"semantics",encoding:"application/x-tex"},"\\mathcal{O}(rows)")))),(0,s.kt)("span",{parentName:"span",className:"katex-html","aria-hidden":"true"},(0,s.kt)("span",{parentName:"span",className:"base"},(0,s.kt)("span",{parentName:"span",className:"strut",style:{height:"1em",verticalAlign:"-0.25em"}}),(0,s.kt)("span",{parentName:"span",className:"mord mathcal",style:{marginRight:"0.02778em"}},"O"),(0,s.kt)("span",{parentName:"span",className:"mopen"},"("),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"ro"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal",style:{marginRight:"0.02691em"}},"w"),(0,s.kt)("span",{parentName:"span",className:"mord mathnormal"},"s"),(0,s.kt)("span",{parentName:"span",className:"mclose"},")"))))))),(0,s.kt)("h2",{id:"bottom-up-dp"},"Bottom-up DP"),(0,s.kt)("p",null,"If you try to think in depth about the top-down DP solution, you might notice\nthat the ",(0,s.kt)("em",{parentName:"p"},"core")," of it stands on caching the calculations that have been already\ndone on the lower \u201clevels\u201d of the pyramid. Our bottom-up implementation will be\nusing this fact!"),(0,s.kt)("admonition",{type:"tip"},(0,s.kt)("p",{parentName:"admonition"},"As I have said in the ",(0,s.kt)("em",{parentName:"p"},"top-down DP")," section, it is the easiest way to implement\nDP (unless the cached function has complicated parameters, in that case it might\nget messy)."),(0,s.kt)("p",{parentName:"admonition"},"Bottom-up dynamic programming can be more effective, but may be more complicated\nto implement right from the beginning.")),(0,s.kt)("p",null,"Let's see how we can implement it:"),(0,s.kt)("pre",null,(0,s.kt)("code",{parentName:"pre",className:"language-java"},"public static int longestSlideDown(int[][] pyramid) {\n // In the beginning we declare new array. At this point it is easier to just\n // work with the one dimension, i.e. just allocating the space for the rows.\n int[][] slideDowns = new int[pyramid.length][];\n\n // Bottom row gets just copied, there's nothing else to do\u2026 It's the base\n // case.\n slideDowns[pyramid.length - 1] = Arrays.copyOf(pyramid[pyramid.length - 1],\n pyramid[pyramid.length - 1].length);\n\n // Then we need to propagate the found slide downs for each of the levels\n // above.\n for (int y = pyramid.length - 2; y >= 0; --y) {\n // We start by copying the values lying in the row we're processing.\n // They get included in the final sum and we need to allocate the space\n // for the precalculated slide downs anyways.\n int[] row = Arrays.copyOf(pyramid[y], pyramid[y].length);\n\n // At this we just need to \u201cfetch\u201d the partial results from \u201cneighbours\u201d\n for (int x = 0; x < row.length; ++x) {\n // We look under our position, since we expect the rows to get\n // shorter, we can safely assume such position exists.\n int under = slideDowns[y + 1][x];\n\n // Then we have a look to the right, such position doesn't have to\n // exist, e.g. on the right edge, so we validate the index, and if\n // it doesn't exist, we just assign minimum of the \u2039int\u203a which makes\n // sure that it doesn't get picked in the \u2039Math.max()\u203a call.\n int toRight = x + 1 < slideDowns[y + 1].length\n ? slideDowns[y + 1][x + 1]\n : Integer.MIN_VALUE;\n\n // Finally we add the best choice at this point.\n row[x] += Math.max(under, toRight);\n }\n\n // And save the row we've just calculated partial results for to the\n // \u201ctable\u201d.\n slideDowns[y] = row;\n }\n\n // At the end we can find our seeked slide down at the top cell.\n return slideDowns[0][0];\n}\n")),(0,s.kt)("p",null,"I've tried to explain the code as much as possible within the comments, since it\nmight be more beneficial to see right next to the \u201coffending\u201d lines."),(0,s.kt)("p",null,"As you can see, in this approach we go from the other side",(0,s.kt)("sup",{parentName:"p",id:"fnref-3"},(0,s.kt)("a",{parentName:"sup",href:"#fn-3",className:"footnote-ref"},"3")),", the bottom of\nthe pyramid and propagate the partial results up."),(0,s.kt)("admonition",{type:"info"},(0,s.kt)("mdxAdmonitionTitle",{parentName:"admonition"},"How is this different from the ",(0,s.kt)("em",{parentName:"mdxAdmonitionTitle"},"greedy")," solution???"),(0,s.kt)("p",{parentName:"admonition"},"If you try to compare them, you might find a very noticable difference. The\ngreedy approach is going from the top to the bottom without ",(0,s.kt)("strong",{parentName:"p"},"any")," knowledge of\nwhat's going on below. On the other hand, bottom-up DP is going from the bottom\n(",(0,s.kt)("em",{parentName:"p"},"DUH\u2026"),") and ",(0,s.kt)("strong",{parentName:"p"},"propagates")," the partial results to the top. The propagation is\nwhat makes sure that at the top I don't choose the best ",(0,s.kt)("strong",{parentName:"p"},"local")," choice, but\nthe best ",(0,s.kt)("strong",{parentName:"p"},"overall")," result I can achieve.")),(0,s.kt)("h3",{id:"time-complexity-3"},"Time complexity"),(0,s.kt)("p",null,"Time complexity of this solution is rather simple. We allocate an array for the\nrows and then for each row, we copy it and adjust the partial results. 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If you do not know what your default branch is, it is probably ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),"\nand you should not be on any other branch."),(0,a.kt)("p",null,"Output of the command should look like this:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git status\nOn branch master # Or main or trunk.\nYour branch is up to date with 'origin/master'.\n\nnothing to commit, working tree clean\n")),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"In case you are on different branch or there are uncommitted changes,\n",(0,a.kt)("strong",{parentName:"p"},"do not continue!!!")," Clean your repository (commit the changes or discard\nthem), before you continue.")),(0,a.kt)("h3",{id:"step-2---create-new-branch"},"Step #2 - Create new branch"),(0,a.kt)("p",null,"In your repository write command:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git checkout -b BRANCH\nSwitched to a new branch 'BRANCH'\n")),(0,a.kt)("p",null,"Instead of ",(0,a.kt)("inlineCode",{parentName:"p"},"BRANCH")," use some reasonable name for the branch. For example if you\nare working on the seminar from 3rd week, name the branch ",(0,a.kt)("inlineCode",{parentName:"p"},"seminar-03"),"."),(0,a.kt)("h3",{id:"step-3---do-the-assignment"},"Step #3 - Do the assignment"),(0,a.kt)("p",null,"Download the skeleton for the seminar assignment, extract and program. For example\nif you are working on 3rd seminar, you can do so by:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ wget https://www.fi.muni.cz/pb071/seminars/seminar-03/pb071-seminar-03.zip\naisa$ unzip pb071-seminar-03.zip\n# Now you should have directory 'seminar-03'.\naisa$ rm pb071-seminar-03.zip\naisa$ cd seminar-03\n# You can work on the assignment.\n")),(0,a.kt)("h3",{id:"step-4---commit-and-upload-the-changes-to-gitlab"},"Step #4 - Commit and upload the changes to GitLab"),(0,a.kt)("p",null,"The same way you ",(0,a.kt)("em",{parentName:"p"},"add")," and ",(0,a.kt)("em",{parentName:"p"},"commit")," files for the homework assignments, you do for\nthe seminar."),(0,a.kt)("p",null,"Now you can upload the changes to GitLab. ",(0,a.kt)("inlineCode",{parentName:"p"},"git push")," is not enough, since repository\non GitLab does not know your new branch. You can solve this by adding arguments:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git push origin BRANCH\n...\nremote: To create a merge request for BRANCH, visit:\nremote: https://gitlab.fi.muni.cz/login/pb071/merge_requests/new?merge_request%5Bsource_branch%5D=BRANCH\n...\n")),(0,a.kt)("p",null,"In the output you should have a link for creating a merge request. If you see this\nlink, open it and skip next step."),(0,a.kt)("h3",{id:"step-5---creating-a-merge-request-manually"},"Step #5 - Creating a merge request manually"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Open your repository on GitLab."),(0,a.kt)("li",{parentName:"ol"},"On the left panel click on ",(0,a.kt)("em",{parentName:"li"},"Merge Requests"),"."),(0,a.kt)("li",{parentName:"ol"},"Click on ",(0,a.kt)("em",{parentName:"li"},"New Merge Request"),"."),(0,a.kt)("li",{parentName:"ol"},"In ",(0,a.kt)("em",{parentName:"li"},"Source branch")," select ",(0,a.kt)("inlineCode",{parentName:"li"},"login/pb071")," and ",(0,a.kt)("inlineCode",{parentName:"li"},"BRANCH"),", which you created."),(0,a.kt)("li",{parentName:"ol"},"In ",(0,a.kt)("em",{parentName:"li"},"Target branch")," select ",(0,a.kt)("inlineCode",{parentName:"li"},"login/pb071")," and your default branch you have seen\nin the output of the first command. (most likely ",(0,a.kt)("inlineCode",{parentName:"li"},"master"),")"),(0,a.kt)("li",{parentName:"ol"},"Click on ",(0,a.kt)("em",{parentName:"li"},"Compare branches and continue"),".")),(0,a.kt)("h3",{id:"step-6---set-assignees"},"Step #6 - Set assignees"),(0,a.kt)("p",null,"On the page that is opened, please check at the top that you are creating merge\nrequest ",(0,a.kt)("strong",{parentName:"p"},"from")," your new branch ",(0,a.kt)("strong",{parentName:"p"},"to")," your default branch (one of ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),", ",(0,a.kt)("inlineCode",{parentName:"p"},"main"),"\nor ",(0,a.kt)("inlineCode",{parentName:"p"},"trunk"),")."),(0,a.kt)("p",null,"Then in the field ",(0,a.kt)("em",{parentName:"p"},"Assignees")," set your tutors based on the seminar group. You can\nuse login for a quick look up."),(0,a.kt)("p",null,"In the end click on ",(0,a.kt)("em",{parentName:"p"},"Submit merge request"),"."),(0,a.kt)("h3",{id:"step-7---return-to-default-branch"},"Step #7 - Return to default branch"),(0,a.kt)("p",null,"Homework assignments can be submitted only from branches specified in the rules\nfor the course. Because of that, before you do anything else, you should switch\nback to your default branch."),(0,a.kt)("p",null,"First of all, same as in step #1, check that your repository is clean with ",(0,a.kt)("inlineCode",{parentName:"p"},"git status"),".\nFor the sake of safety, do not continue without clean repository. Then with command\n",(0,a.kt)("inlineCode",{parentName:"p"},"git checkout BRANCH")," switch to your default branch ",(0,a.kt)("inlineCode",{parentName:"p"},"BRANCH"),"."),(0,a.kt)("p",null,"If you do not know which branch is your default, try ",(0,a.kt)("inlineCode",{parentName:"p"},"git branch")," that outputs all branches in your repository. Default branch is typically ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),", but can\nbe ",(0,a.kt)("inlineCode",{parentName:"p"},"main")," or ",(0,a.kt)("inlineCode",{parentName:"p"},"trunk"),"."),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git status\n# Check if repository is clean\n\n# If you know, what is your default branch, you can skip next command.\naisa$ git branch\n# Find the default branch in the list; should be one of the `master`, `main` or\n# `trunk` and you should not have more than one of those.\n# In case the list clears the terminal and you cannot see shell prompt, you can\n# press `q` to quit the pager.\n\naisa$ git checkout master\n")),(0,a.kt)("hr",null),(0,a.kt)("p",null,"Adapted from: ",(0,a.kt)("a",{parentName:"p",href:"https://www.fi.muni.cz/~xlacko1/pb071/mr.html"},"https://www.fi.muni.cz/~xlacko1/pb071/mr.html")))}c.isMDXComponent=!0}}]); \ No newline at end of file +"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[7823],{3905:(e,t,n)=>{n.d(t,{Zo:()=>u,kt:()=>d});var r=n(7294);function a(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function o(e,t){var n=Object.keys(e);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(e);t&&(r=r.filter((function(t){return Object.getOwnPropertyDescriptor(e,t).enumerable}))),n.push.apply(n,r)}return n}function i(e){for(var t=1;t=0||(a[n]=e[n]);return a}(e,t);if(Object.getOwnPropertySymbols){var o=Object.getOwnPropertySymbols(e);for(r=0;r=0||Object.prototype.propertyIsEnumerable.call(e,n)&&(a[n]=e[n])}return a}var l=r.createContext({}),p=function(e){var t=r.useContext(l),n=t;return e&&(n="function"==typeof e?e(t):i(i({},t),e)),n},u=function(e){var t=p(e.components);return r.createElement(l.Provider,{value:t},e.children)},m="mdxType",c={inlineCode:"code",wrapper:function(e){var t=e.children;return r.createElement(r.Fragment,{},t)}},h=r.forwardRef((function(e,t){var n=e.components,a=e.mdxType,o=e.originalType,l=e.parentName,u=s(e,["components","mdxType","originalType","parentName"]),m=p(n),h=a,d=m["".concat(l,".").concat(h)]||m[h]||c[h]||o;return n?r.createElement(d,i(i({ref:t},u),{},{components:n})):r.createElement(d,i({ref:t},u))}));function d(e,t){var n=arguments,a=t&&t.mdxType;if("string"==typeof e||a){var o=n.length,i=new Array(o);i[0]=h;var s={};for(var l in t)hasOwnProperty.call(t,l)&&(s[l]=t[l]);s.originalType=e,s[m]="string"==typeof e?e:a,i[1]=s;for(var p=2;p{n.r(t),n.d(t,{assets:()=>l,contentTitle:()=>i,default:()=>c,frontMatter:()=>o,metadata:()=>s,toc:()=>p});var r=n(7462),a=(n(7294),n(3905));const o={title:"Submitting merge requests"},i="Submitting merge requests for review",s={unversionedId:"mr",id:"mr",title:"Submitting merge requests",description:"This tutorial aims to show you how to follow basic git workflow and submit changes",source:"@site/pb071/mr.md",sourceDirName:".",slug:"/mr",permalink:"/pb071/mr",draft:!1,editUrl:"https://github.com/mfocko/blog/tree/main/pb071/mr.md",tags:[],version:"current",lastUpdatedAt:1694960869,formattedLastUpdatedAt:"Sep 17, 2023",frontMatter:{title:"Submitting merge requests"},sidebar:"autogeneratedBar",previous:{title:"Practice exam C",permalink:"/pb071/pexam/cams"}},l={},p=[{value:"Tutorial",id:"tutorial",level:2},{value:"Step #1 - Starting from the clean repository",id:"step-1---starting-from-the-clean-repository",level:3},{value:"Step #2 - Create new branch",id:"step-2---create-new-branch",level:3},{value:"Step #3 - Do the assignment",id:"step-3---do-the-assignment",level:3},{value:"Step #4 - Commit and upload the changes to GitLab",id:"step-4---commit-and-upload-the-changes-to-gitlab",level:3},{value:"Step #5 - Creating a merge request manually",id:"step-5---creating-a-merge-request-manually",level:3},{value:"Step #6 - Set assignees",id:"step-6---set-assignees",level:3},{value:"Step #7 - Return to default branch",id:"step-7---return-to-default-branch",level:3}],u={toc:p},m="wrapper";function c(e){let{components:t,...n}=e;return(0,a.kt)(m,(0,r.Z)({},u,n,{components:t,mdxType:"MDXLayout"}),(0,a.kt)("h1",{id:"submitting-merge-requests-for-review"},"Submitting merge requests for review"),(0,a.kt)("p",null,"This tutorial aims to show you how to follow basic git workflow and submit changes\nthrough ",(0,a.kt)("em",{parentName:"p"},"Merge Requests")," for review."),(0,a.kt)("p",null,"The rudimentary idea behind aims for changes to be present on a separate branch\nthat is supposedly ",(0,a.kt)("em",{parentName:"p"},"merged")," into the default branch. Till then changes can be reviewed\non ",(0,a.kt)("em",{parentName:"p"},"Merge Request")," and additional changes may be made based on the reviews. Once\nthe changes satisfy requirements, the merge request is merged."),(0,a.kt)("h2",{id:"tutorial"},"Tutorial"),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"Use this tutorial only for bonus assignments ",(0,a.kt)("strong",{parentName:"p"},"made by your tutors")," or in case\nyou need to make up for the absence.")),(0,a.kt)("h3",{id:"step-1---starting-from-the-clean-repository"},"Step #1 - Starting from the clean repository"),(0,a.kt)("p",null,"In your repository (either locally or on aisa) type ",(0,a.kt)("inlineCode",{parentName:"p"},"git status")," and check if your\nrepository is clean and you are present on the main branch (",(0,a.kt)("inlineCode",{parentName:"p"},"master"),", ",(0,a.kt)("inlineCode",{parentName:"p"},"main")," or\n",(0,a.kt)("inlineCode",{parentName:"p"},"trunk"),"). If you do not know what your default branch is, it is probably ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),"\nand you should not be on any other branch."),(0,a.kt)("p",null,"Output of the command should look like this:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git status\nOn branch master # Or main or trunk.\nYour branch is up to date with 'origin/master'.\n\nnothing to commit, working tree clean\n")),(0,a.kt)("blockquote",null,(0,a.kt)("p",{parentName:"blockquote"},"In case you are on different branch or there are uncommitted changes,\n",(0,a.kt)("strong",{parentName:"p"},"do not continue!!!")," Clean your repository (commit the changes or discard\nthem), before you continue.")),(0,a.kt)("h3",{id:"step-2---create-new-branch"},"Step #2 - Create new branch"),(0,a.kt)("p",null,"In your repository write command:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git checkout -b BRANCH\nSwitched to a new branch 'BRANCH'\n")),(0,a.kt)("p",null,"Instead of ",(0,a.kt)("inlineCode",{parentName:"p"},"BRANCH")," use some reasonable name for the branch. For example if you\nare working on the seminar from 3rd week, name the branch ",(0,a.kt)("inlineCode",{parentName:"p"},"seminar-03"),"."),(0,a.kt)("h3",{id:"step-3---do-the-assignment"},"Step #3 - Do the assignment"),(0,a.kt)("p",null,"Download the skeleton for the seminar assignment, extract and program. For example\nif you are working on 3rd seminar, you can do so by:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ wget https://www.fi.muni.cz/pb071/seminars/seminar-03/pb071-seminar-03.zip\naisa$ unzip pb071-seminar-03.zip\n# Now you should have directory 'seminar-03'.\naisa$ rm pb071-seminar-03.zip\naisa$ cd seminar-03\n# You can work on the assignment.\n")),(0,a.kt)("h3",{id:"step-4---commit-and-upload-the-changes-to-gitlab"},"Step #4 - Commit and upload the changes to GitLab"),(0,a.kt)("p",null,"The same way you ",(0,a.kt)("em",{parentName:"p"},"add")," and ",(0,a.kt)("em",{parentName:"p"},"commit")," files for the homework assignments, you do for\nthe seminar."),(0,a.kt)("p",null,"Now you can upload the changes to GitLab. ",(0,a.kt)("inlineCode",{parentName:"p"},"git push")," is not enough, since repository\non GitLab does not know your new branch. You can solve this by adding arguments:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git push origin BRANCH\n...\nremote: To create a merge request for BRANCH, visit:\nremote: https://gitlab.fi.muni.cz/login/pb071/merge_requests/new?merge_request%5Bsource_branch%5D=BRANCH\n...\n")),(0,a.kt)("p",null,"In the output you should have a link for creating a merge request. If you see this\nlink, open it and skip next step."),(0,a.kt)("h3",{id:"step-5---creating-a-merge-request-manually"},"Step #5 - Creating a merge request manually"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Open your repository on GitLab."),(0,a.kt)("li",{parentName:"ol"},"On the left panel click on ",(0,a.kt)("em",{parentName:"li"},"Merge Requests"),"."),(0,a.kt)("li",{parentName:"ol"},"Click on ",(0,a.kt)("em",{parentName:"li"},"New Merge Request"),"."),(0,a.kt)("li",{parentName:"ol"},"In ",(0,a.kt)("em",{parentName:"li"},"Source branch")," select ",(0,a.kt)("inlineCode",{parentName:"li"},"login/pb071")," and ",(0,a.kt)("inlineCode",{parentName:"li"},"BRANCH"),", which you created."),(0,a.kt)("li",{parentName:"ol"},"In ",(0,a.kt)("em",{parentName:"li"},"Target branch")," select ",(0,a.kt)("inlineCode",{parentName:"li"},"login/pb071")," and your default branch you have seen\nin the output of the first command. (most likely ",(0,a.kt)("inlineCode",{parentName:"li"},"master"),")"),(0,a.kt)("li",{parentName:"ol"},"Click on ",(0,a.kt)("em",{parentName:"li"},"Compare branches and continue"),".")),(0,a.kt)("h3",{id:"step-6---set-assignees"},"Step #6 - Set assignees"),(0,a.kt)("p",null,"On the page that is opened, please check at the top that you are creating merge\nrequest ",(0,a.kt)("strong",{parentName:"p"},"from")," your new branch ",(0,a.kt)("strong",{parentName:"p"},"to")," your default branch (one of ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),", ",(0,a.kt)("inlineCode",{parentName:"p"},"main"),"\nor ",(0,a.kt)("inlineCode",{parentName:"p"},"trunk"),")."),(0,a.kt)("p",null,"Then in the field ",(0,a.kt)("em",{parentName:"p"},"Assignees")," set your tutors based on the seminar group. You can\nuse login for a quick look up."),(0,a.kt)("p",null,"In the end click on ",(0,a.kt)("em",{parentName:"p"},"Submit merge request"),"."),(0,a.kt)("h3",{id:"step-7---return-to-default-branch"},"Step #7 - Return to default branch"),(0,a.kt)("p",null,"Homework assignments can be submitted only from branches specified in the rules\nfor the course. Because of that, before you do anything else, you should switch\nback to your default branch."),(0,a.kt)("p",null,"First of all, same as in step #1, check that your repository is clean with ",(0,a.kt)("inlineCode",{parentName:"p"},"git status"),".\nFor the sake of safety, do not continue without clean repository. Then with command\n",(0,a.kt)("inlineCode",{parentName:"p"},"git checkout BRANCH")," switch to your default branch ",(0,a.kt)("inlineCode",{parentName:"p"},"BRANCH"),"."),(0,a.kt)("p",null,"If you do not know which branch is your default, try ",(0,a.kt)("inlineCode",{parentName:"p"},"git branch")," that outputs all branches in your repository. Default branch is typically ",(0,a.kt)("inlineCode",{parentName:"p"},"master"),", but can\nbe ",(0,a.kt)("inlineCode",{parentName:"p"},"main")," or ",(0,a.kt)("inlineCode",{parentName:"p"},"trunk"),"."),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre"},"aisa$ git status\n# Check if repository is clean\n\n# If you know, what is your default branch, you can skip next command.\naisa$ git branch\n# Find the default branch in the list; should be one of the `master`, `main` or\n# `trunk` and you should not have more than one of those.\n# In case the list clears the terminal and you cannot see shell prompt, you can\n# press `q` to quit the pager.\n\naisa$ git checkout master\n")),(0,a.kt)("hr",null),(0,a.kt)("p",null,"Adapted from: ",(0,a.kt)("a",{parentName:"p",href:"https://www.fi.muni.cz/~xlacko1/pb071/mr.html"},"https://www.fi.muni.cz/~xlacko1/pb071/mr.html")))}c.isMDXComponent=!0}}]); \ No newline at end of file diff --git a/assets/js/f533ef4a.4d4a423f.js b/assets/js/f533ef4a.a34c7233.js similarity index 99% rename from assets/js/f533ef4a.4d4a423f.js rename to assets/js/f533ef4a.a34c7233.js index 95d9a75..0f8a8e2 100644 --- a/assets/js/f533ef4a.4d4a423f.js +++ b/assets/js/f533ef4a.a34c7233.js @@ -1 +1 @@ -"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[2160],{3905:(e,t,n)=>{n.d(t,{Zo:()=>c,kt:()=>h});var r=n(7294);function a(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function i(e,t){var n=Object.keys(e);if(Object.getOwnPropertySymbols){var r=Object.getOwnPropertySymbols(e);t&&(r=r.filter((function(t){return Object.getOwnPropertyDescriptor(e,t).enumerable}))),n.push.apply(n,r)}return n}function o(e){for(var t=1;t=0||(a[n]=e[n]);return a}(e,t);if(Object.getOwnPropertySymbols){var i=Object.getOwnPropertySymbols(e);for(r=0;r=0||Object.prototype.propertyIsEnumerable.call(e,n)&&(a[n]=e[n])}return a}var p=r.createContext({}),s=function(e){var 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i={id:"seminar-05-06",title:"5th and 6th seminar",description:"200IQ encryption.\n"},o=void 0,l={unversionedId:"bonuses/seminar-05-06",id:"bonuses/seminar-05-06",title:"5th and 6th seminar",description:"200IQ encryption.\n",source:"@site/pb071/bonuses/05-06.md",sourceDirName:"bonuses",slug:"/bonuses/seminar-05-06",permalink:"/pb071/bonuses/seminar-05-06",draft:!1,editUrl:"https://github.com/mfocko/blog/tree/main/pb071/bonuses/05-06.md",tags:[],version:"current",lastUpdatedAt:1694959505,formattedLastUpdatedAt:"Sep 17, 2023",frontMatter:{id:"seminar-05-06",title:"5th and 6th seminar",description:"200IQ encryption.\n"},sidebar:"autogeneratedBar",previous:{title:"4th seminar",permalink:"/pb071/bonuses/seminar-04"},next:{title:"8th seminar",permalink:"/pb071/bonuses/seminar-08"}},p={},s=[{value:"Introduction",id:"introduction",level:2},{value:"Task no. 1: Reverse (0.5 K\u20a1)",id:"task-no-1-reverse-05-k",level:3},{value:"Task no. 2: Vigen\xe8re (0.5 K\u20a1)",id:"task-no-2-vigen\xe8re-05-k",level:3},{value:"Bonus part (0.5 K\u20a1)",id:"bonus-part-05-k",level:4},{value:"Task no. 3: Bit madness (0.5 K\u20a1)",id:"task-no-3-bit-madness-05-k",level:3},{value:"Task no. 4: All combined to BMP (0.5 K\u20a1)",id:"task-no-4-all-combined-to-bmp-05-k",level:3},{value:"Submitting",id:"submitting",level:2}],c={toc:s},u="wrapper";function d(e){let{components:t,...n}=e;return(0,a.kt)(u,(0,r.Z)({},c,n,{components:t,mdxType:"MDXLayout"}),(0,a.kt)("p",null,"For this bonus you can get at maximum 2.5 K\u20a1."),(0,a.kt)("p",null,(0,a.kt)("a",{parentName:"p",href:"pathname:///files/pb071/bonuses/05-06.tar.gz"},"Source")),(0,a.kt)("h2",{id:"introduction"},"Introduction"),(0,a.kt)("p",null,"In this bonus you will implement few functions that will be used together for\nimplementing a very special cipher."),(0,a.kt)("h3",{id:"task-no-1-reverse-05-k"},"Task no. 1: Reverse (0.5 K\u20a1)"),(0,a.kt)("p",null,"Write a function ",(0,a.kt)("inlineCode",{parentName:"p"},"char* reverse(const char* text)")," that returns copy of the input\nstring in reversed order (also uppercase)."),(0,a.kt)("p",null,"In case you are given ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL"),", return ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL"),"."),(0,a.kt)("p",null,"Example (more in tests):"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'char* reversed = reverse("Hello world!");\n\nprintf("%s\\n", reversed);\n// "!DLROW OLLEH"\n\nif (reversed != NULL) {\n free(reversed);\n}\n')),(0,a.kt)("h3",{id:"task-no-2-vigen\xe8re-05-k"},"Task no. 2: Vigen\xe8re (0.5 K\u20a1)"),(0,a.kt)("p",null,"Vigen\xe8re cipher is similar to the Caesar cipher, but you also have a key that is\nused for encrypting (or decrypting)."),(0,a.kt)("p",null,"Your task is to write two functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* vigenere_encrypt(const char* key, const char* text)")," for encrypting"),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* vigenere_decrypt(const char* key, const char* text)")," for decrypting")),(0,a.kt)("p",null,"In both of those you should return uppercase characters."),(0,a.kt)("p",null,"Meaning of the parameters you are given:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"key")," - String that represents key that is used for ","*","crypting. It consists of\none word and can have only characters of the alphabet. Does not matter if they\nare uppercase or lowercase."),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"text")," - String that is to be ","*","crypted.")),(0,a.kt)("p",null,"Function returns address of the encrypted (or decrypted) string. Or ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL")," in case\nerror occurs."),(0,a.kt)("p",null,"Example:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'char *encrypted = vigenere_encrypt("CoMPuTeR", "Hello world!");\n\nprintf("%s\\n", encrypted);\n// "JSXAI PSINR!"\n\nif (encrypted != NULL) {\n free(encrypted)\n}\n')),(0,a.kt)("h4",{id:"bonus-part-05-k"},"Bonus part (0.5 K\u20a1)"),(0,a.kt)("p",null,"If you can utilize helper function that would do both encrypting and decrypting,\nyou can gain 0.5 K\u20a1."),(0,a.kt)("p",null,"Usage of ",(0,a.kt)("inlineCode",{parentName:"p"},"true"),"/",(0,a.kt)("inlineCode",{parentName:"p"},"false")," to decide path in code is prohibited. It leads to merging\nof both functions into one. Point of this part is to discover a way to do this\ngenerically in such way that there are no separate paths for one or the other. One\nfunction with no branching for both of them, parametrization is your friend :)"),(0,a.kt)("h3",{id:"task-no-3-bit-madness-05-k"},"Task no. 3: Bit madness (0.5 K\u20a1)"),(0,a.kt)("p",null,"This is a state of the art crypto. Please do not share :)"),(0,a.kt)("p",null,"For encrypting:"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Split the character that is to be encrypted in halves (4 and 4 bits each)."),(0,a.kt)("li",{parentName:"ol"},"Bits in 1st half are to be split into pairs. Swap bits in those pairs."),(0,a.kt)("li",{parentName:"ol"},"Then use the 4 bits that you created in the 2nd step for ",(0,a.kt)("inlineCode",{parentName:"li"},"XOR")," with the other\n4 bits.")),(0,a.kt)("p",null,"This simple and ingenious principle will be illustrated on the following example.\nString we want to encrypt is ",(0,a.kt)("inlineCode",{parentName:"p"},"Hello world!"),". We need to encrypt each letter separately,\nso we will demonstrate on letter ",(0,a.kt)("inlineCode",{parentName:"p"},"H"),":"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"Letter ",(0,a.kt)("inlineCode",{parentName:"p"},"H")," is represented in ASCII as ",(0,a.kt)("inlineCode",{parentName:"p"},"72"),"."),(0,a.kt)("p",{parentName:"li"},(0,a.kt)("inlineCode",{parentName:"p"},"72")," represented in binary is: ",(0,a.kt)("inlineCode",{parentName:"p"},"01001000"),". So first 4 bits are: ",(0,a.kt)("inlineCode",{parentName:"p"},"0100")," and last\n4 bits are ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),".")),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"First half of bits (",(0,a.kt)("inlineCode",{parentName:"p"},"0100"),") consists of 2 pairs (",(0,a.kt)("inlineCode",{parentName:"p"},"01")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"00"),") which we swap\n(",(0,a.kt)("inlineCode",{parentName:"p"},"01 ~> 10")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"00 ~> 00"),"). That way we get ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),".")),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"That half is used for xor with the other 4 bits:"),(0,a.kt)("pre",{parentName:"li"},(0,a.kt)("code",{parentName:"pre"}," 1000 // second half\nXOR 1000 // first half after 2nd step\n--------\n 0000\n"))),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"Now we combine both halves (first one is ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),", which we got from the 2nd step\nand second one is ",(0,a.kt)("inlineCode",{parentName:"p"},"0000"),", which we got from the 3rd step) and get ",(0,a.kt)("inlineCode",{parentName:"p"},"10000000"),",\nwhich is encrypted character ",(0,a.kt)("inlineCode",{parentName:"p"},"H")," using this method."))),(0,a.kt)("p",null,"In case of decryption, reverse those steps."),(0,a.kt)("p",null,"Your task is to implement functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"unsigned char* bit_encrypt(const char* text)")),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* bit_decrypt(const unsigned char* text)"))),(0,a.kt)("p",null,"Example:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'unsigned char* encrypted = bit_encrypt("Hello world!");\n\nfor (int i = 0; i < 12;i++) {\n printf("%x ", encrypted[i]);\n //80 9c 95 95 96 11 bc 96 b9 95 9d 10\n}\n\nif (encrypted != NULL) {\n free(encrypted);\n}\n')),(0,a.kt)("h3",{id:"task-no-4-all-combined-to-bmp-05-k"},"Task no. 4: All combined to BMP (0.5 K\u20a1)"),(0,a.kt)("p",null,"Authors of the BMP cipher are non-disclosed :)"),(0,a.kt)("p",null,"Create pair of functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"unsigned char* bmp_encrypt(const char* key, const char* text)")),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* bmp_decrypt(const char* key, const unsigned char* text)"))),(0,a.kt)("p",null,"BMP cipher consists of following steps for encrypting:"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Reverse the input string"),(0,a.kt)("li",{parentName:"ol"},"Use Vigenere on the string you got from step #1"),(0,a.kt)("li",{parentName:"ol"},"Use bit madness on the string you got from step #2")),(0,a.kt)("p",null,"For decrypting, reverse the steps."),(0,a.kt)("h2",{id:"submitting"},"Submitting"),(0,a.kt)("p",null,"In case you have any questions, feel free to reach out to me."),(0,a.kt)("hr",null))}d.isMDXComponent=!0}}]); \ No newline at end of file +"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[2160],{3905:(e,t,n)=>{n.d(t,{Zo:()=>c,kt:()=>h});var r=n(7294);function a(e,t,n){return t in e?Object.defineProperty(e,t,{value:n,enumerable:!0,configurable:!0,writable:!0}):e[t]=n,e}function 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n?r.createElement(h,o(o({ref:t},c),{},{components:n})):r.createElement(h,o({ref:t},c))}));function h(e,t){var n=arguments,a=t&&t.mdxType;if("string"==typeof e||a){var i=n.length,o=new Array(i);o[0]=m;var l={};for(var p in t)hasOwnProperty.call(t,p)&&(l[p]=t[p]);l.originalType=e,l[u]="string"==typeof e?e:a,o[1]=l;for(var s=2;s{n.r(t),n.d(t,{assets:()=>p,contentTitle:()=>o,default:()=>d,frontMatter:()=>i,metadata:()=>l,toc:()=>s});var r=n(7462),a=(n(7294),n(3905));const i={id:"seminar-05-06",title:"5th and 6th seminar",description:"200IQ encryption.\n"},o=void 0,l={unversionedId:"bonuses/seminar-05-06",id:"bonuses/seminar-05-06",title:"5th and 6th seminar",description:"200IQ encryption.\n",source:"@site/pb071/bonuses/05-06.md",sourceDirName:"bonuses",slug:"/bonuses/seminar-05-06",permalink:"/pb071/bonuses/seminar-05-06",draft:!1,editUrl:"https://github.com/mfocko/blog/tree/main/pb071/bonuses/05-06.md",tags:[],version:"current",lastUpdatedAt:1694960869,formattedLastUpdatedAt:"Sep 17, 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K\u20a1."),(0,a.kt)("p",null,(0,a.kt)("a",{parentName:"p",href:"pathname:///files/pb071/bonuses/05-06.tar.gz"},"Source")),(0,a.kt)("h2",{id:"introduction"},"Introduction"),(0,a.kt)("p",null,"In this bonus you will implement few functions that will be used together for\nimplementing a very special cipher."),(0,a.kt)("h3",{id:"task-no-1-reverse-05-k"},"Task no. 1: Reverse (0.5 K\u20a1)"),(0,a.kt)("p",null,"Write a function ",(0,a.kt)("inlineCode",{parentName:"p"},"char* reverse(const char* text)")," that returns copy of the input\nstring in reversed order (also uppercase)."),(0,a.kt)("p",null,"In case you are given ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL"),", return ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL"),"."),(0,a.kt)("p",null,"Example (more in tests):"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'char* reversed = reverse("Hello world!");\n\nprintf("%s\\n", reversed);\n// "!DLROW OLLEH"\n\nif (reversed != NULL) {\n free(reversed);\n}\n')),(0,a.kt)("h3",{id:"task-no-2-vigen\xe8re-05-k"},"Task no. 2: Vigen\xe8re (0.5 K\u20a1)"),(0,a.kt)("p",null,"Vigen\xe8re cipher is similar to the Caesar cipher, but you also have a key that is\nused for encrypting (or decrypting)."),(0,a.kt)("p",null,"Your task is to write two functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* vigenere_encrypt(const char* key, const char* text)")," for encrypting"),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* vigenere_decrypt(const char* key, const char* text)")," for decrypting")),(0,a.kt)("p",null,"In both of those you should return uppercase characters."),(0,a.kt)("p",null,"Meaning of the parameters you are given:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"key")," - String that represents key that is used for ","*","crypting. It consists of\none word and can have only characters of the alphabet. Does not matter if they\nare uppercase or lowercase."),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"text")," - String that is to be ","*","crypted.")),(0,a.kt)("p",null,"Function returns address of the encrypted (or decrypted) string. Or ",(0,a.kt)("inlineCode",{parentName:"p"},"NULL")," in case\nerror occurs."),(0,a.kt)("p",null,"Example:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'char *encrypted = vigenere_encrypt("CoMPuTeR", "Hello world!");\n\nprintf("%s\\n", encrypted);\n// "JSXAI PSINR!"\n\nif (encrypted != NULL) {\n free(encrypted)\n}\n')),(0,a.kt)("h4",{id:"bonus-part-05-k"},"Bonus part (0.5 K\u20a1)"),(0,a.kt)("p",null,"If you can utilize helper function that would do both encrypting and decrypting,\nyou can gain 0.5 K\u20a1."),(0,a.kt)("p",null,"Usage of ",(0,a.kt)("inlineCode",{parentName:"p"},"true"),"/",(0,a.kt)("inlineCode",{parentName:"p"},"false")," to decide path in code is prohibited. It leads to merging\nof both functions into one. Point of this part is to discover a way to do this\ngenerically in such way that there are no separate paths for one or the other. One\nfunction with no branching for both of them, parametrization is your friend :)"),(0,a.kt)("h3",{id:"task-no-3-bit-madness-05-k"},"Task no. 3: Bit madness (0.5 K\u20a1)"),(0,a.kt)("p",null,"This is a state of the art crypto. Please do not share :)"),(0,a.kt)("p",null,"For encrypting:"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Split the character that is to be encrypted in halves (4 and 4 bits each)."),(0,a.kt)("li",{parentName:"ol"},"Bits in 1st half are to be split into pairs. Swap bits in those pairs."),(0,a.kt)("li",{parentName:"ol"},"Then use the 4 bits that you created in the 2nd step for ",(0,a.kt)("inlineCode",{parentName:"li"},"XOR")," with the other\n4 bits.")),(0,a.kt)("p",null,"This simple and ingenious principle will be illustrated on the following example.\nString we want to encrypt is ",(0,a.kt)("inlineCode",{parentName:"p"},"Hello world!"),". We need to encrypt each letter separately,\nso we will demonstrate on letter ",(0,a.kt)("inlineCode",{parentName:"p"},"H"),":"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"Letter ",(0,a.kt)("inlineCode",{parentName:"p"},"H")," is represented in ASCII as ",(0,a.kt)("inlineCode",{parentName:"p"},"72"),"."),(0,a.kt)("p",{parentName:"li"},(0,a.kt)("inlineCode",{parentName:"p"},"72")," represented in binary is: ",(0,a.kt)("inlineCode",{parentName:"p"},"01001000"),". So first 4 bits are: ",(0,a.kt)("inlineCode",{parentName:"p"},"0100")," and last\n4 bits are ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),".")),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"First half of bits (",(0,a.kt)("inlineCode",{parentName:"p"},"0100"),") consists of 2 pairs (",(0,a.kt)("inlineCode",{parentName:"p"},"01")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"00"),") which we swap\n(",(0,a.kt)("inlineCode",{parentName:"p"},"01 ~> 10")," and ",(0,a.kt)("inlineCode",{parentName:"p"},"00 ~> 00"),"). That way we get ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),".")),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"That half is used for xor with the other 4 bits:"),(0,a.kt)("pre",{parentName:"li"},(0,a.kt)("code",{parentName:"pre"}," 1000 // second half\nXOR 1000 // first half after 2nd step\n--------\n 0000\n"))),(0,a.kt)("li",{parentName:"ol"},(0,a.kt)("p",{parentName:"li"},"Now we combine both halves (first one is ",(0,a.kt)("inlineCode",{parentName:"p"},"1000"),", which we got from the 2nd step\nand second one is ",(0,a.kt)("inlineCode",{parentName:"p"},"0000"),", which we got from the 3rd step) and get ",(0,a.kt)("inlineCode",{parentName:"p"},"10000000"),",\nwhich is encrypted character ",(0,a.kt)("inlineCode",{parentName:"p"},"H")," using this method."))),(0,a.kt)("p",null,"In case of decryption, reverse those steps."),(0,a.kt)("p",null,"Your task is to implement functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"unsigned char* bit_encrypt(const char* text)")),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* bit_decrypt(const unsigned char* text)"))),(0,a.kt)("p",null,"Example:"),(0,a.kt)("pre",null,(0,a.kt)("code",{parentName:"pre",className:"language-c"},'unsigned char* encrypted = bit_encrypt("Hello world!");\n\nfor (int i = 0; i < 12;i++) {\n printf("%x ", encrypted[i]);\n //80 9c 95 95 96 11 bc 96 b9 95 9d 10\n}\n\nif (encrypted != NULL) {\n free(encrypted);\n}\n')),(0,a.kt)("h3",{id:"task-no-4-all-combined-to-bmp-05-k"},"Task no. 4: All combined to BMP (0.5 K\u20a1)"),(0,a.kt)("p",null,"Authors of the BMP cipher are non-disclosed :)"),(0,a.kt)("p",null,"Create pair of functions:"),(0,a.kt)("ul",null,(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"unsigned char* bmp_encrypt(const char* key, const char* text)")),(0,a.kt)("li",{parentName:"ul"},(0,a.kt)("inlineCode",{parentName:"li"},"char* bmp_decrypt(const char* key, const unsigned char* text)"))),(0,a.kt)("p",null,"BMP cipher consists of following steps for encrypting:"),(0,a.kt)("ol",null,(0,a.kt)("li",{parentName:"ol"},"Reverse the input string"),(0,a.kt)("li",{parentName:"ol"},"Use Vigenere on the string you got from step #1"),(0,a.kt)("li",{parentName:"ol"},"Use bit madness on the string you got from step #2")),(0,a.kt)("p",null,"For decrypting, reverse the steps."),(0,a.kt)("h2",{id:"submitting"},"Submitting"),(0,a.kt)("p",null,"In case you have any questions, feel free to reach out to me."),(0,a.kt)("hr",null))}d.isMDXComponent=!0}}]); \ No newline at end of file diff --git a/assets/js/main.a28961b3.js b/assets/js/main.9f54e33a.js similarity index 96% rename from assets/js/main.a28961b3.js rename to assets/js/main.9f54e33a.js index d38c563..f622ca8 100644 --- a/assets/js/main.a28961b3.js +++ b/assets/js/main.9f54e33a.js @@ -1,2 +1,2 @@ -/*! 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