Recursive division does not guarantee a path

Question

I implemented the algorithm from the answer in here Maze (recursive division) algorithm design.

but I ran into a problem that there isn't always a path from start(+) to finish(-) like this image.

also there is another problem that the start(+) or finish(-) node will be surrounded by wall see start node (+)

but I think it's easy to fix.

remove the walls around that node [x-1][y], [x][y+1], [x+1][y] and [x][y-1].

I don't know if it's the right fix or not.

that's my maze class

class Maze {
  private G: INode[][];
  private rows: number;
  private cols: number;

  constructor(G: INode[][]) {
    this.G = G.map((row) =>
      row.map((node) => ({
        ...node,
        isWall: false,
      }))
    );
    this.rows = this.G.length;
    this.cols = this.G[0].length;

    // border walls
    for (let i = 0; i < this.rows; i++) {
      this.G[i][0].isWall = true;
      this.G[i][this.cols - 1].isWall = true;
    }
    for (let i = 0; i < this.cols; i++) {
      this.G[0][i].isWall = true;
      this.G[this.rows - 1][i].isWall = true;
    }
  }

  private rand(min: number, max: number) {
    return Math.floor(Math.random() * (max - min + 1) + min);
  }

  private isNodeStartOrFinish(row: number, col: number) {
    return this.G[row][col].isStart || this.G[row][col].isFinish;
  }

  // call perfectMaze to get the generate the maze 
  public perfectMaze() {
    this.divide(true, 1, this.cols - 2, 1, this.rows - 2);
  }

  private divide(
    h: boolean,
    minX: number,
    maxX: number,
    minY: number,
    maxY: number
  ) {
    if (h) {
      if (maxX - minX < 2) return;
      const y = Math.floor(this.rand(minY, maxY) / 2) * 2;
      this.addHWall(minX, maxX, y);
      this.divide(!h, minX, maxX, minY, y - 1);
      this.divide(!h, minX, maxX, y + 1, maxY);
    } else {
      if (maxY - minY < 2) return;
      const x = Math.floor(this.rand(minX, maxX) / 2) * 2;
      this.addVWall(minY, maxY, x);
      this.divide(!h, minX, x - 1, minY, maxY);
      this.divide(!h, x + 1, maxX, minY, maxY);
    }
  }

  private addHWall(minX: number, maxX: number, y: number) {
    const hole = Math.floor(this.rand(minX, maxX) / 2) * 2 + 1;
    for (let i = minX; i <= maxX; i++) {
      if (i !== hole && !this.isNodeStartOrFinish(y, i)) {
        this.G[y][i].isWall = true;
      }
    }
  }

  private addVWall(minY: number, maxY: number, x: number) {
    const hole = Math.floor(this.rand(minY, maxY) / 2) * 2 + 1;
    for (let i = minY; i <= maxY; i++) {
      if (i !== hole && !this.isNodeStartOrFinish(i, x)) {
        this.G[i][x].isWall = true;
      }
    }
  }

  public getMaze() {
    return this.G;
  }
}

Answer 1

okay i was stupid

i didn't remove the wall when i === hole

in the addHWall and addVWall methods

you must delete the wall if i === hole otherwise the wall will be added again

  private addHWall(minX: number, maxX: number, y: number) {
    const hole = Math.floor(this.rand(minX, maxX) / 2) * 2 + 1;
    for (let i = minX; i <= maxX; i++) {
      if (i === hole || this.isNodeStartOrFinish(y, i)) {
        this.G[y][i].isWall = false;
      } else {
        this.G[y][i].isWall = true;
      }
    }
  }

the same with addVWall

if (i === hole || this.isNodeStartOrFinish(i, x)) {
   this.G[y][i].isWall = false;
} else {
   this.G[i][x].isWall = true;
}

and i ended up deleting the walls around the start and finish node still don't know if it's the right solution or not