迷宫问题中的启发式搜索的MATLAB代码

在MATLAB中解决迷宫问题的启发式搜索，常用的是A*算法，这是一种用于寻找两个节点之间最短路径的算法。以下是一个简单的A*算法的MATLAB实现示例：

function [path, cost] = a_star(start, goal, maze)
    % 初始化
    heuristic = @(x,y) sqrt((x-1)^2 + (y-1)^2); % Manhattan距离作为启发函数
    open_set = {start};
    closed_set = {};
    came_from = struct('parent', [], 'cost_so_far', []);
    g_score = zeros(size(maze));
    f_score = g_score(start(1), start(2)) + heuristic(start(1), start(2));

    % 主循环
    while ~isempty(open_set)
        % 选择f_score最小的节点
        current = min(f_score, [], 'all');
        if strcmp(current, start)
            break; % 找到了起点，开始回溯
        end
        open_set = setdiff(open_set, current);
        closed_set = [closed_set, current];

        % 更新相邻节点的成本
        neighbors = get_neighbors(maze, current(1), current(2));
        for i = 1:length(neighbors)
            neighbor = neighbors{i};

            % 如果邻居已经在关闭集合中，则跳过
            if ismember(neighbor, closed_set)
                continue;
            end

            tentative_g_score = g_score(current(1), current(2)) + 1; % 节点间的移动代价
            if ~ismember(neighbor, open_set) || tentative_g_score < g_score(neighbor(1), neighbor(2))
                came_from(neighbor) = current;
                g_score(neighbor(1), neighbor(2)) = tentative_g_score;
                f_score(neighbor(1), neighbor(2)) = g_score(neighbor(1), neighbor(2)) + heuristic(neighbor(1), neighbor(2));
                if strcmp(neighbor, goal)
                    path = traceback(came_from, goal);
                    return;
            end
        end
    end

    % 没有找到路径
    disp('No path found.');
end

% 辅助函数：获取邻居
function neighbors = get_neighbors(maze, x, y)
    neighbors = [];
    if x > 1 && maze(x-1, y) == 0
        neighbors = [neighbors; [x-1, y]];
    end
    % ...其他方向的检查类似
    ... % 根据实际迷宫结构添加更多的条件
end

% 辅助函数：路径追踪
function path = traceback(came_from, current)
    path = current;
    while ~isempty(came_from(path))
        path = came_from(path).parent;
    end
    path = reverse(path);
end

% 使用示例
maze = [0 0 0 0 1; 0 1 1 1 0; 0 1 0 1 0; 0 0 0 0 0]; % 用1表示墙壁，0表示通道
[path, cost] = a_star([1 1], [4 4], maze);

这个代码示例包含了基本的A*算法实现，你需要根据具体的迷宫结构（矩阵形式）调整`get_neighbors`函数。