"use strict";(self.webpackChunkfi=self.webpackChunkfi||[]).push([[635],{61381:(t,e,n)=>{n.r(e),n.d(e,{assets:()=>l,contentTitle:()=>a,default:()=>d,frontMatter:()=>o,metadata:()=>i,toc:()=>h});varr=n(85893),s=n(11151);consto={id:"index",slug:"/paths/bf-to-astar",title:"From BF to A*",description:"Figuring out shortest-path problem from the BF to the A* algorithm.\n",tags:["cpp","brute force","bellman ford","dynamic programming","dijkstra","greedy","a star"],last_update:{date:newDate("2024-01-01T00:00:00.000Z")}},a=void0,i={id:"paths/2024-01-01-bf-to-astar/index",title:"From BF to A*",description:"Figuring out shortest-path problem from the BF to the A* algorithm.\n",source:"@site/algorithms/11-paths/2024-01-01-bf-to-astar/index.md",sourceDirName:"11-paths/2024-01-01-bf-to-astar",slug:"/paths/bf-to-astar",permalink:"/algorithms/paths/bf-to-astar",draft:!1,unlisted:!1,editUrl:"https://github.com/mfocko/blog/tree/main/algorithms/11-paths/2024-01-01-bf-to-astar/index.md",tags:[{label:"cpp",permalink:"/algorithms/tags/cpp"},{label:"brute force",permalink:"/algorithms/tags/brute-force"},{label:"bellman ford",permalink:"/algorithms/tags/bellman-ford"},{label:"dynamic programming",permalink:"/algorithms/tags/dynamic-programming"},{label:"dijkstra",permalink:"/algorithms/tags/dijkstra"},{label:"greedy",permalink:"/algorithms/tags/greedy"},{label:"a star",permalink:"/algorithms/tags/a-star"}],version:"current",lastUpdatedAt:1704067200,formattedLastUpdatedAt:"Jan 1, 2024",frontMatter:{id:"index",slug:"/paths/bf-to-astar",title:"From BF to A*",description:"Figuring out shortest-path problem from the BF to the A* algorithm.\n",tags:["cpp","brute force","bellman ford","dynamic programming","dijkstra","greedy","a star"],last_update:{date:"2024-01-01T00:00:00.000Z"}},sidebar:"autogeneratedBar",previous:{title:"Paths in Graphs",permalink:"/algorithms/category/paths-in-graphs"},next:{title:"BF",permalink:"/algorithms/paths/bf-to-astar/bf"}},l={},h=[{value:"Intro",id:"intro",level:2},{value:"Boilerplate",id:"boilerplate",level:2}];functionc(t){conste={a:"a",admonition:"admonition",code:"code",em:"em",h2:"h2",li:"li",ol:"ol",p:"p",pre:"pre",strong:"strong",ul:"ul",...(0,s.a)(),...t.components};return(0,r.jsxs)(r.Fragment,{children:[(0,r.jsx)(e.h2,{id:"intro",children:"Intro"}),"\n",(0,r.jsx)(e.p,{children:"We will delve into the details and ideas of the most common path-finding\nalgorithms. For the purpose of demonstrating some \u201cfeatures\u201d of the improved\nalgorithms, we will use a 2D map with some rules that will allow us to show cons\nand pros of the shown algorithms."}),"\n",(0,r.jsx)(e.p,{children:"Let's have a look at the example map:"}),"\n",(0,r.jsx)(e.pre,{children:(0,r.jsx)(e.code,{children:"#############\n#..#..*.*.**#\n##***.....**#\n#..########.#\n#...###...#.#\n#..#...##.#.#\n#..#.*.#..#.#\n#....#....#.#\n########*.*.#\n#...........#\n#############\n"})}),"\n",(0,r.jsx)(e.p,{children:"We can see three different kinds of cells:"}),"\n",(0,r.jsxs)(e.ol,{children:["\n",(0,r.jsxs)(e.li,{children:[(0,r.jsx)(e.code,{children:"#"})," which represent walls, that cannot be entered at all"]}),"\n",(0,r.jsxs)(e.li,{children:[(0,r.jsx)(e.code,{children:"*"})," which represent vortices that can be entered at the cost of 5 coins"]}),"\n",(0,r.jsxs)(e.li,{children:[(0,r.jsx)(e.code,{children:"."})," which represent normal cells that can be entered for 1 coin (which is the\nbase price of moving around the map)"]}),"\n"]}),"\n",(0,r.jsx)(e.p,{children:"Let's dissect a specific position on the map to get a better grasp of the rules:"}),"\n",(0,r.jsx)(e.pre,{children:(0,r.jsx)(e.code,{children:" .\n#S*\n .\n"})}),"\n",(0,r.jsxs)(e.p,{children:["We are standing in the cell marked with ",(0,r.jsx)(e.code,{children:"S"})," and we have the following options"]}),"\n",(0,r.jsxs)(e.ul,{children:["\n",(0,r.jsxs)(e.li,{children:["move to the north (",(0,r.jsx)(e.code,{children:"."}),") with the cost of 1 coin,"]}),"\n",(0,r.jsxs)(e.li,{children:["move to the west (",(0,r.jsx)(e.code,{children:"#"}),") ",(0,r.jsx)(e.strong,{children:"isnot
