迷宫（递归除法）算法设计

Question

我目前正在开发一个随机迷宫生成器，它将迷宫存储在一个名为< code>grid的二维数组中。这将随后用于生成一个真实的3D迷宫，用户可以在其中穿行。

在做了一些研究之后，我试图使用递归除法算法创建这个迷宫生成器，但是由于迷宫格式的性质，这对我来说并不是真的有效。

据我所知，递归分裂方法并不将壁视为细胞。

例如，我的网格如下所示：

  a b c d e f g h
1 - - - - - - - -
2 |   |   | |   |
3 |       |     |
4 | -   - |   - |
5 |     |     | |
6 |   - |   -   |
7 x             |
8 - - - - - - - -

我想在这里说的是，我试图创建的网格将像这样表示：

w w w w w w w w
w   w   w w   w
w       w     w
w w   w w   w w
w     w     w w
w   w w   w   w
g             w
w w w w w w w w

其中“w”是墙，“g”是入口/出口。因此，墙被放置在网格中，例如，网格[1][2]='w'

递归除法算法的问题是墙不被视为单元格的成员。所有的“单元格”基本上都包含空白，墙将被放置在它们周围。

从本质上讲，用户将从红色方块开始，必须穿过迷宫并找到可以打开门（红色方块）以逃脱的钥匙，因此迷宫中的所有空白都必须是可访问的。

有人知道我如何重写这个算法，以确保迷宫中始终有一条从红色方块到任何其他空间的路径吗？理想情况下，路径永远不会超过一个正方形宽。

var grid;

function generate(dimensions, numDoors) {
    //numDoors is unused right now

    grid = new Array();
    for (var i = 0; i < dimensions; i++) {
        grid[i] = new Array();

        for (var j = 0; j < dimensions; j++) {
            grid[i][j] = "";
        }
    }

    addOuterWalls();
    var ent = addEntrance();
    addInnerWalls(true, 1, grid.length - 2, 1, grid.length - 2, ent);
}

function addOuterWalls() {
    for (var i = 0; i < grid.length; i++) {
        if (i == 0 || i == (grid.length - 1)) {
            for (var j = 0; j < grid.length; j++) {
                grid[i][j] = "w";
            }
        } else {
            grid[i][0] = "w";
            grid[i][grid.length - 1] = "w";
        }
    }
}

function addEntrance() {
    var x = randomNumber(1, grid.length - 1);
    grid[grid.length - 1][x] = "g";
    return x;
}

function addInnerWalls(h, minX, maxX, minY, maxY, gate) {
    if (h) {

        if (maxX - minX < 2) {
            return;
        }

        var y = randomNumber(minY, maxY);
        addHWall(minX, maxX, y);

        addInnerWalls(!h, minX, maxX, minY, y-1, gate);
        addInnerWalls(!h, minX, maxX, y + 1, maxY, gate);
    } else {
        if (maxY - minY < 2) {
            return;
        }

        var x = randomNumber(minX, maxX);
        addVWall(minY, maxY, x);

        addInnerWalls(!h, minX, x-1, minY, maxY, gate);
        addInnerWalls(!h, x + 1, maxX, minY, maxY, gate);
    }
}

function addHWall(minX, maxX, y) {
    var hole = randomNumber(minX, maxX);

    for (var i = minX; i <= maxX; i++) {
        if (i == hole) grid[y][i] = "";
        else grid[y][i] = "w";
    }
}

function addVWall(minY, maxY, x) {
    var hole = randomNumber(minY, maxY);

    for (var i = minY; i <= maxY; i++) {
        if (i == hole) grid[i][x] = "";
        else grid[i][x] = "w";
    }
}

function randomNumber(min, max) {
    return Math.floor(Math.random() * (max - min + 1) + min);
}

function display() {
    document.getElementById("cnt").innerHTML = "";

    for (var i = 0; i < grid.length; i++) {
        var output = "<div>";
        for (var j = 0; j < grid.length; j++) {
            output += "<b " + grid[i][j] + "></b>";
        }
        output += "</div>";
        document.getElementById("cnt").innerHTML += output;
    }
}
generate(30, 1, 1);
display();

Answer 1

只在偶数单元格中设置墙壁，在奇数单元格中设置门，并使“维度”奇数。http://jsfiddle.net/tPm3s/1/

Code:
var grid;

function generate(dimensions, numDoors) {
    grid = new Array();
    for (var i = 0; i < dimensions; i++) {
        grid[i] = new Array();

        for (var j = 0; j < dimensions; j++) {
            grid[i][j] = "";
        }
    }

    addOuterWalls();
    var ent = addEntrance();
    addInnerWalls(true, 1, grid.length - 2, 1, grid.length - 2, ent);
}

function addOuterWalls() {
    for (var i = 0; i < grid.length; i++) {
        if (i == 0 || i == (grid.length - 1)) {
            for (var j = 0; j < grid.length; j++) {
                grid[i][j] = "w";
            }
        } else {
            grid[i][0] = "w";
            grid[i][grid.length - 1] = "w";
        }
    }
}

function addEntrance() {
    var x = randomNumber(1, grid.length - 1);
    grid[grid.length - 1][x] = "g";
    return x;
}

function addInnerWalls(h, minX, maxX, minY, maxY, gate) {
    if (h) {

        if (maxX - minX < 2) {
            return;
        }

        var y = Math.floor(randomNumber(minY, maxY)/2)*2;
        addHWall(minX, maxX, y);

        addInnerWalls(!h, minX, maxX, minY, y-1, gate);
        addInnerWalls(!h, minX, maxX, y + 1, maxY, gate);
    } else {
        if (maxY - minY < 2) {
            return;
        }

        var x = Math.floor(randomNumber(minX, maxX)/2)*2;
        addVWall(minY, maxY, x);

        addInnerWalls(!h, minX, x-1, minY, maxY, gate);
        addInnerWalls(!h, x + 1, maxX, minY, maxY, gate);
    }
}

function addHWall(minX, maxX, y) {
    var hole = Math.floor(randomNumber(minX, maxX)/2)*2+1;

    for (var i = minX; i <= maxX; i++) {
        if (i == hole) grid[y][i] = "";
        else grid[y][i] = "w";
    }
}

function addVWall(minY, maxY, x) {
    var hole = Math.floor(randomNumber(minY, maxY)/2)*2+1;

    for (var i = minY; i <= maxY; i++) {
        if (i == hole) grid[i][x] = "";
        else grid[i][x] = "w";
    }
}

function randomNumber(min, max) {
    return Math.floor(Math.random() * (max - min + 1) + min);
}

function display() {
    document.getElementById("cnt").innerHTML = "";

    for (var i = 0; i < grid.length; i++) {
        var output = "<div>";
        for (var j = 0; j < grid.length; j++) {
            output += "<b " + grid[i][j] + "></b>";
        }
        output += "</div>";
        document.getElementById("cnt").innerHTML += output;
    }
}
generate(31, 1, 1);
display();