blog/assets/js/5fe5d476.4c192803.js

"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[2619],{14457:(s,e,n)=>{n.r(e),n.d(e,{assets:()=>c,contentTitle:()=>t,default:()=>o,frontMatter:()=>l,metadata:()=>r,toc:()=>m});var a=n(85893),i=n(11151);const l={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")}},t=void 0,r={id:"recursion/pyramid-slide-down",title:"Introduction to dynamic programming",description:"Solving a problem in different ways.\n",source:"@site/algorithms/04-recursion/2023-08-17-pyramid-slide-down.md",sourceDirName:"04-recursion",slug:"/recursion/pyramid-slide-down",permalink:"/algorithms/recursion/pyramid-slide-down",draft:!1,unlisted:!1,editUrl:"https://github.com/mfocko/blog/tree/main/algorithms/04-recursion/2023-08-17-pyramid-slide-down.md",tags:[{label:"java",permalink:"/algorithms/tags/java"},{label:"recursion",permalink:"/algorithms/tags/recursion"},{label:"exponential",permalink:"/algorithms/tags/exponential"},{label:"greedy",permalink:"/algorithms/tags/greedy"},{label:"dynamic-programming",permalink:"/algorithms/tags/dynamic-programming"},{label:"top-down-dp",permalink:"/algorithms/tags/top-down-dp"},{label:"bottom-up-dp",permalink:"/algorithms/tags/bottom-up-dp"}],version:"current",lastUpdatedAt:1703373170,formattedLastUpdatedAt:"Dec 23, 2023",frontMatter:{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:"2023-08-17T00:00:00.000Z"}},sidebar:"autogeneratedBar",previous:{title:"Solution to the problem",permalink:"/algorithms/recursion/karel/solution"},next:{title:"Red-Black Trees",permalink:"/algorithms/category/red-black-trees"}},c={},m=[{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}];function h(s){const e={a:"a",admonition:"admonition",annotation:"annotation",code:"code",em:"em",h2:"h2",h3:"h3",hr:"hr",li:"li",math:"math",mdxAdmonitionTitle:"mdxAdmonitionTitle",mi:"mi",mn:"mn",mo:"mo",mrow:"mrow",mspace:"mspace",mstyle:"mstyle",msub:"msub",msup:"msup",mtable:"mtable",mtd:"mtd",mtext:"mtext",mtr:"mtr",munderover:"munderover",ol:"ol",p:"p",pre:"pre",section:"section",semantics:"semantics",span:"span",strong:"strong",sup:"sup",...(0,i.a)(),...s.components};return(0,a.jsxs)(a.Fragment,{children:[(0,a.jsx)(e.p,{children:"In this post we will try to solve one problem in different ways."}),"\n",(0,a.jsx)(e.h2,{id:"problem",children:"Problem"}),"\n",(0,a.jsxs)(e.p,{children:["The problem we are going to solve is one of ",(0,a.jsx)(e.em,{children:"CodeWars"})," katas and is called\n",(0,a.jsx)(e.a,{href:"https://www.codewars.com/kata/551f23362ff852e2ab000037",children:"Pyramid Slide Down"}),"."]}),"\n",(0,a.jsxs)(e.p,{children:["We are given a 2D array of integers and we are to find the ",(0,a.jsx)(e.em,{children:"slide down"}),".\n",(0,a.jsx)(e.em,{children:"Slide down"})," is a maximum sum of consecutive numbers from the top to the bottom."]}),"\n",(0,a.jsx)(e.p,{children:"Let's have a look at few examples. Consider the following pyramid:"}),"\n",(0,a.jsx)(e.pre,{children:(0,a.jsx)(e.code,{children:"   3\n  7 4\n 2 4 6\n8