【p5.js】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。

let maze1;

function setup() {
  maze1 = new Maze(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();
}

class Maze {
  constructor(width, height, seed=0) {
    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.from(new Array(this.height), () => new Array(this.width).fill(this.PATH));
    this.dist = Array.from(new Array(this.height), () => new Array(this.width).fill(-1));
    this.start = [1, 1];
    this.goal = [this.width-2, this.height-2];
    randomSeed(seed);
  }

  set_outer_wall() {
    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() {
    for (let y = 2; y < this.height-1; y+=2) {
      for (let x = 2; x < this.width-1; x+=2) {
        this.maze[y][x] = this.WALL;
      }
    }
    return this.maze;
  }
  
  set_maze_boutaoshi() {
    let wall_x;
    let wall_y;
    let direction;
    this.set_outer_wall();
  this.set_inner_wall();
  for (let y = 2; y < this.height-1; y+=2) {
      for (let x = 2; x < this.width-1; x+=2) {
        while (true) {
          wall_x = x;
          wall_y = y;
          if (y == 2) {
            direction = floor(random(4));
          } else {
            direction = floor(random(3));
          }
          if (direction == 0) {
            wall_x += 1;
          } else if (direction == 1) {
            wall_y += 1;
          } else if (direction == 2) {
            wall_x -= 1;
          } else if (direction == 3) {
            wall_y -= 1;
          }
          if (this.maze[wall_y][wall_x] != this.WALL) {
            this.maze[wall_y][wall_x] = this.WALL;
            break;
          }
        }
      }
    }
    return this.maze;
  }
  
  set_start_goal(start, goal) {
    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=false) {
    let queue = [];
    this.dist[this.start[1]][this.start[0]] = 0;
    queue.push(this.start);
    while (queue.length > 0) {
      let 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) {
          if (point[0]+x[0] == this.goal[0] && point[1]+x[1] == this.goal[1]) {
            queue = [];
            break;
          }
        }
      }
    }
    return this.dist;
  }

  set_shortest_path() {
    let point = this.goal;
    let x = [[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() {
    this.maze[this.start[1]][this.start[0]] = 'S';
    this.maze[this.goal[1]][this.goal[0]] = 'G';
    for (let col of this.maze) {
      let arr = '';
      for(let cell of col) {
        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);
    }
  }
}

今回は、以下のように出力される。

###############
#     #  *****#
# ### ###*###*#
#   #*****#  *#
# # #*# #####*#
# # #*# #S****#
# ###*##### ###
# #  ***#     #
# # # #*# # ###
# # # #*# #   #
# #####*# ### #
#     #G#   # #
# ### ### # # #
#   # #   # # #
###############
p5.js Web Editor
A web editor for p5.js, a JavaScript library with the goal of making coding accessible to artists, designers, educators, and beginners.

参考

幅優先探索 - Algoful
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[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…
BFS (幅優先探索) 超入門! 〜 キューを鮮やかに使いこなす 〜 - Qiita
0. はじめに メジャーなグラフ探索手法には深さ優先探索 (depth-first search, DFS) と幅優先探索 (breadth-first search, BFS) とがあります1。このうち DFS については ...

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