【React】幅優先探索で迷路の最短経路を求める

探索していない通路を「-1」として表現して
スタートからゴールに到達するまで幅優先探索で迷路を探索し、
探索した通路はスタートからの距離に数値を置き換える。

Canvas.tsx

import React, { useEffect } from 'react';
import p5 from 'p5';
import Maze from './maze';

const sketch = (p: p5) => {
  p.setup = () => {
    const maze1 = new Maze(p, 15, 15);
    maze1.set_maze_boutaoshi();
    maze1.set_start_goal([9,5], [7,11]);
    maze1.set_dist_bfs();
    maze1.set_shortest_path();
    maze1.print_maze();
  }
}
    
const Canvas: React.FC = () => {
  useEffect(() => {
    new p5(sketch)
  })
  return (
    <React.Fragment>
    </React.Fragment>
  );
}
    
export default Canvas;

maze.ts

import p5 from 'p5';

type maze = number[][] | string[][];
type binary = 0 | 1;

class Maze {
  p: p5;
  PATH: number;
  WALL: number;
  width: number;
  height: number;
  maze: maze = [];
  dist: number[][] = [];
  start: number[] = [];
  goal: number[] = [];

  constructor(p: p5, width: number, height: number, seed: number = 0) {
    this.p = p;
    this.PATH = 0;
    this.WALL = 1;
    this.width = width;
    this.height = height;
    if (this.width < 5 || this.height < 5) {
      return;
    }
    if (this.width%2 === 0) {
      this.width++;
    }
    if (this.height%2 === 0) {
      this.height++;
    }
    this.maze = [...Array(this.height)].map(() => Array(this.width).fill(0));
    this.dist = [...Array(this.height)].map(() => Array(this.width).fill(-1));
    this.start = [1, 1];
    this.goal = [this.width-2, this.height-2];
    p.randomSeed(seed);
  }

  set_outer_wall(): maze {
    for (let y = 0; y < this.height; y++) {
      for (let x = 0; x < this.width; x++) {
        if (x === 0 || y === 0 || x === this.width-1 || y === this.height-1) {
          this.maze[y][x] = this.WALL;
        }
      }
    }
    return this.maze;
  }

  set_inner_wall(): maze {
    for (let y = 2; y <= this.height-3; y+=2) {
      for (let x = 2; x <= this.width-3; x+=2) {
        this.maze[y][x] = this.WALL;
      }
    }
    return this.maze;
  }

  set_maze_boutaoshi(): maze {
    let cell_x: number, cell_y: number, direction: number;
    this.set_outer_wall();
    this.set_inner_wall();
    for (let y = 2; y <= this.height-3; y+=2) {
      for (let x = 2; x <= this.width-3; x+=2) {
        while (true) {
          cell_x = x;
          cell_y = y;
          if (y === 2) {
            direction = this.p.floor(this.p.random(4));
          } else {
            direction = this.p.floor(this.p.random(3));
          }
          if (direction === 0) {
            cell_x += 1;
          } else if (direction === 1) {
            cell_y += 1;
          } else if (direction === 2) {
            cell_x -= 1;
          } else if (direction === 3) {
            cell_y -= 1;
          }
          if (this.maze[cell_y][cell_x] !== this.WALL) {
            this.maze[cell_y][cell_x] = this.WALL;
            break;
          }
        }
      }
    }
    return this.maze;
  }

  set_start_goal(start: number[], goal: number[]): maze {
    if (this.maze[start[1]][start[0]] === this.PATH) {
      this.start = start;
    }
    if (this.maze[goal[1]][goal[0]] === this.PATH) {
      this.goal = goal;
    }
    return this.maze;
  }

  set_dist_bfs(flag: boolean | binary = false): number[][] {
    let queue: number[][] = [], point: number[];
    this.dist[this.start[1]][this.start[0]] = 0;
    queue.push(this.start);
    while (queue.length > 0) {
      point = queue.shift()!;
      for (let x of [[0,-1],[1,0],[0,1],[-1,0]]) {
        if (this.maze[point[1]+x[1]][point[0]+x[0]] === 0 && this.dist[point[1]+x[1]][point[0]+x[0]] === -1) {
          this.dist[point[1]+x[1]][point[0]+x[0]] = this.dist[point[1]][point[0]] + 1;
          queue.push([point[0]+x[0],point[1]+x[1]]);
        }
        if (flag !== true && flag !== 1) {
          if (point[0]+x[0] === this.goal[0] && point[1]+x[1] === this.goal[1]) {
            queue = [];
            break;
          }
        }
      }
    }
    return this.dist;
  }

  set_shortest_path(): maze {
    let point: number[] = this.goal;
    const x: number[][] = [[0,-1],[1,0],[0,1],[-1,0]];
    this.maze[point[1]][point[0]] = '*';
    while (this.dist[point[1]][point[0]] > 0) {
      for (let i = 0; i < x.length; i++) {
        if (this.dist[point[1]][point[0]]-this.dist[point[1]+x[i][1]][point[0]+x[i][0]] === 1) {
          if (this.dist[point[1]][point[0]] > 0) {
            this.maze[point[1]+x[i][1]][point[0]+x[i][0]] = '*';
            point = [point[0]+x[i][0],point[1]+x[i][1]];
          }
        }
      }
    }
    return this.maze;
  }

  print_maze(): void {
    let arr: string;
    this.maze[this.start[1]][this.start[0]] = 'S';
    this.maze[this.goal[1]][this.goal[0]] = 'G';
    for (let row of this.maze) {
      arr = '';
      for (let cell of row) {
        if (cell === this.WALL) {
          arr += '#';
        } else if (cell === this.PATH) {
          arr += ' ';
        } else if (cell === 'S') {
	  arr += 'S';
	} else if (cell === 'G') {
	  arr += 'G';
	} else if (cell === '*') {
	  arr += '*';
	}
      }
      console.log(arr);
    }
  }
}

export default Maze;

今回は、以下のように出力される。

###############
#     #  *****#
# ### ###*###*#
#   #*****#  *#
# # #*# #####*#
# # #*# #S****#
# ###*##### ###
# #  ***#     #
# # # #*# # ###
# # # #*# #   #
# #####*# ### #
#     #G#   # #
# ### ### # # #
#   # #   # # #
###############

参考

幅優先探索 - Algoful
幅優先探索(BFS)とは隣接するノードを優先して&#x...
[Python] 幅優先探索で迷路を解く
幅優先探索 幅優先探索(Breadth First Search)とは、グラフを始点から近い順に1つずつ調べて…
https://qiita.com/drken/items/996d80bcae64649a6580

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