blog/assets/js/70a4540f.312c2807.js

"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[9249],{44493:(e,s,n)=>{n.r(s),n.d(s,{assets:()=>m,contentTitle:()=>l,default:()=>h,frontMatter:()=>i,metadata:()=>r,toc:()=>c});var a=n(85893),t=n(11151);const i={id:"naive",slug:"/recursion/pyramid-slide-down/naive",title:"Na\xefve solution",description:"Na\xefve solution of the Pyramid Slide Down.\n",tags:["java","recursion","exponential"],last_update:{date:new Date("2023-08-17T00:00:00.000Z")}},l=void 0,r={id:"recursion/2023-08-17-pyramid-slide-down/naive",title:"Na\xefve solution",description:"Na\xefve solution of the Pyramid Slide Down.\n",source:"@site/algorithms/04-recursion/2023-08-17-pyramid-slide-down/01-naive.md",sourceDirName:"04-recursion/2023-08-17-pyramid-slide-down",slug:"/recursion/pyramid-slide-down/naive",permalink:"/algorithms/recursion/pyramid-slide-down/naive",draft:!1,unlisted:!1,editUrl:"https://github.com/mfocko/blog/tree/main/algorithms/04-recursion/2023-08-17-pyramid-slide-down/01-naive.md",tags:[{label:"java",permalink:"/algorithms/tags/java"},{label:"recursion",permalink:"/algorithms/tags/recursion"},{label:"exponential",permalink:"/algorithms/tags/exponential"}],version:"current",lastUpdatedAt:1692230400,formattedLastUpdatedAt:"Aug 17, 2023",sidebarPosition:1,frontMatter:{id:"naive",slug:"/recursion/pyramid-slide-down/naive",title:"Na\xefve solution",description:"Na\xefve solution of the Pyramid Slide Down.\n",tags:["java","recursion","exponential"],last_update:{date:"2023-08-17T00:00:00.000Z"}},sidebar:"autogeneratedBar",previous:{title:"Introduction to dynamic programming",permalink:"/algorithms/recursion/pyramid-slide-down"},next:{title:"Greedy solution",permalink:"/algorithms/recursion/pyramid-slide-down/greedy"}},m={},c=[{value:"Time complexity",id:"time-complexity",level:2}];function o(e){const s={admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",li:"li",math:"math",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",mstyle:"mstyle",msup:"msup",mtable:"mtable",mtd:"mtd",mtext:"mtext",mtr:"mtr",ol:"ol",p:"p",pre:"pre",semantics:"semantics",span:"span",strong:"strong",...(0,t.a)(),...e.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsx)(s.p,{children:"Our na\xefve solution consists of trying out all the possible slides and finding\nthe one with maximum sum."}),"\n",(0,a.jsx)(s.pre,{children:(0,a.jsx)(s.code,{className:"language-java",children:"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"})}),"\n",(0,a.jsx)(s.p,{children:"As you can see, we have 2 overloads:"}),"\n",(0,a.jsx)(s.pre,{children:(0,a.jsx)(s.code,{className:"language-java",children:"int longestSlideDown(int[][] pyramid);\nint longestSlideDown(int[][] pyramid, int row, int col);\n"})}),"\n",(0,a.jsxs)(s.p,{children:["First one is used as a ",(0,a.jsx)(s.em,{children:"public interface"})," to the solution, you just pass in the\npyramid itself. Second one is the recursive \u201calgorithm\u201d that finds the slide\ndown."]}),"\n",(0,a.jsxs)(s.p,{children:["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,