java迷宫算法的理解(递归分割,递归回溯,深搜,广搜)

介绍

Java迷宫算法旨在通过编程形成一个迷宫的图形，让计算机自动地创建和解决迷宫。本文将会介绍常见的四种Java迷宫算法：递归分割算法、递归回溯算法、深度优先搜索(DFS)和广度优先搜索(BFS)算法。

递归分割算法

递归分割算法首先创建一个空的网格表示迷宫。网格中的每个单元格都代表迷宫的一个位置。分割过程会对这些位置进行标记，就像把它们铺上拼图一样。该算法会首先把整个迷宫划分成一个大的正方形，接着用随机的方法选中并划分这个正方形，直至整个网格被完全划分为止。

Java代码实现

void recursiveDivision(int x, int y, int width, int height) {
    if (width < 2 || height < 2) {
        return;
    }

    // 横线或竖线
    boolean horizontal = (width > height);

    // 随机数选择线的位置
    int max = (horizontal ? height : width) - 1;
    int line = (int) (random.nextDouble() * max);

    // 创建一堵墙和两个门
    if (horizontal) {
        // 横线
        int passage = x + line + 1;
        createWall(x, y + line, width, true);
        createPassage(passage, y + line, height);
        recursiveDivision(x, y, width, line + 1);
        recursiveDivision(x, y + line + 1, width, height - line - 1);
    } else {
        // 竖线
        int passage = y + line + 1;
        createWall(x + line, y, height, false);
        createPassage(x + line, passage, width);
        recursiveDivision(x, y, line + 1, height);
        recursiveDivision(x + line + 1, y, width - line - 1, height);
    }
}

示例

下面是一个运行递归分割算法生成的迷宫的示例图：

#############################
#   #   #   #   #   #   #   #
#   #   #   #   #   #   #   #
#   #   #   #   #   #   #   #
#   # # #   #   #   #   #   #
#   #       # # # #   #   # #
#   #   # # #       # # # # #
#   #   # # #   # # # #   # #
#   #   # # #   # #       # #
#           #   # # # #   # #
#   # # #   #   # # # #   # #
#   #     # # # #       # # #
#   # #   # # #   # # # #   #
# # # #   # # #   # #   #   #
# # # #   # # # # #     #   #
# # #     # # # # # # # #   #
# # #########################

递归回溯算法

递归回溯算法先在随机位置选择一个起点，然后在迷宫中递归回溯，尝试找到一个特定位置的解。这种算法先在节点上打标记，指示它们的访问状态，并在需要时回溯。回溯是指程序回到先前遇到的节点，并从那里开始搜索其余的路径。

Java代码实现

void recursiveBacktracking(Node node) {
    node.visited = true;

    for (Direction direction : shuffle(getDirections())) {
        Node neighbor = node.getNeighbor(direction);

        if (neighbor != null && !neighbor.visited) {
            node.open(direction);
            recursiveBacktracking(neighbor);
        }
    }
}

示例

下面是一个运行递归回溯算法生成的迷宫的示例图：

#####################
# #   #           # #
# # # # # # # # # # #
# #               # #
# # # # # # # # # # #
# #   # #     #   # #
# # # # # # # # # # #
# #       #       # #
# # # # # # # # # # #
# #   #   # # # #   #
# # # # # #     # # #
# #           # #   #
# # # # # # # # # # #
# #           # #   #
# # # # # # # # # # #

深度优先搜索算法(DFS)

深度优先搜索算法从外围上的位置开始，尽可能往迷宫的核心走；比如使用下面的二维数组表示迷宫，从左上角走到右下角：

1 1 1 1 1
1 0 1 0 1
1 0 1 0 1
1 0 0 0 1
1 1 1 1 1

从左上角走到右下角，DFS算法会按照下面的顺序搜索：

1 1 1 1 1
1 0 1 0 1
1 0 1 0 1
1 0 0 0 1
1 1 1 1 1

Java代码实现

void depthFirstSearch(Node start, Node target) {
    Stack<Node> stack = new Stack<>();
    stack.push(start);

    while (!stack.isEmpty()) {
        Node node = stack.pop();
        node.visited = true;

        if (node == target) {
            return;
        }

        for (Direction direction : shuffle(getDirections())) {
            Node neighbor = node.getNeighbor(direction);

            if (neighbor != null && !neighbor.visited && node.hasOpening(direction)) {
                neighbor.parent = node;
                stack.push(neighbor);
            }
        }
    }
}

示例

下面是一个运行深度优先搜索算法生成的迷宫的示例图：

#########################
#       #       # #     #
# # # # # # # # # # # # #
#         #           # #
# # #     # # # # # # # #
# #   #   #           # #
# # # #   # # # # # # # #
#     #               # #
# # # # # # # # # # # # #
# #   #     #         # #
# # # # # # # # # # # # #
# #             #     # #
# # # # # # # # # # # # #
#           #       #   #
# # # # # # # # # # # # #
#                       #
#########################

广度优先搜索算法(BFS)

广度优先搜索算法从迷宫外围的位置开始，先搜索距离起点最近的一圈，然后再访问次近的圈，依次搜索，直到搜索到终点，或者搜索完全部。

Java代码实现

void breadthFirstSearch(Node start, Node target) {
    Deque<Node> deque = new ArrayDeque<>();
    deque.add(start);

    while (!deque.isEmpty()) {
        Node node = deque.removeFirst();
        node.visited = true;

        if (node == target) {
            return;
        }

        for (Direction direction : shuffle(getDirections())) {
            Node neighbor = node.getNeighbor(direction);

            if (neighbor != null && !neighbor.visited && node.hasOpening(direction)) {
                neighbor.parent = node;
                deque.addLast(neighbor);
            }
        }
    }
}

示例

下面是一个运行广度优先搜索算法生成的迷宫的示例图：

#############################
#   #   #   # # # #     #   #
#   # # # # # #   # # # # # #
#   # # # # # #     # # #   #
#                   # #   # #
# # # # # # # # # # # #   # #
# #         #     # # # #   #
# # # # # # # # # # # # # # #
# #           # # #       # #
#   # # #   # # # # # # # # #
# # # # # # # # # #   #   # #
# # # # # # # # #     #     #
#   # # # # # #   # # # # # #
#   # # # # # # # # # # #   #
#           # # # # # # # # #
# # # # # # # # # # # # # # #

总结

本文介绍并且演示了四种常见的Java迷宫算法。递归分割算法、递归回溯算法、深度优先搜索算法和广度优先搜索算法，每种算法各有其优点和缺点。了解这些算法对于解决问题和实现其他有用应用程序是非常有益的。