matlab邮递员问题代码实例

以下是一个可能的 MATLAB 邮递员问题代码实例：

% 邮递员问题
% n：城市数量
% dist：距离矩阵，dist(i, j)表示从城市i到城市j的距离
% start：起点城市编号
% 返回：最短路径长度
function [min_dist] = tsp(n, dist, start)
% 记录已访问城市
visited = zeros(n, 1);
visited(start) = 1;
% 记录当前路径
path = [start];
% 记录最短路径长度
min_dist = inf;
% 递归求解
[min_dist, path] = tsp_recursive(n, dist, visited, path, start, min_dist);
end

% 递归求解
function [min_dist, min_path] = tsp_recursive(n, dist, visited, path, cur_city, min_dist)
% 所有城市已访问，返回路径长度
if sum(visited) == n
cur_dist = path_distance(path, dist);
if cur_dist < min_dist
min_dist = cur_dist;
min_path = path;
end
return;
end
% 访问未访问城市
for i = 1:n
if visited(i) == 0
visited(i) = 1;
path(end+1) = i;
% 递归访问下一个城市
[min_dist, min_path] = tsp_recursive(n, dist, visited, path, i, min_dist);
% 回溯
visited(i) = 0;
path(end) = [];
end
end
end

% 计算路径长度
function [dist] = path_distance(path, dist)
n = length(path);
dist = 0;
for i = 1:n-1
dist = dist + dist(path(i), path(i+1));
end
dist = dist + dist(path(n), path(1));
end

% 示例
n = 4;
dist = [0, 1, 2, 3;
1, 0, 4, 5;
2, 4, 0, 6;
3, 5, 6, 0];
start = 1;
[min_dist, min_path] = tsp(n, dist, start);
disp(min_dist);
disp(min_path);