tsp问题matlab代码动态规划

以下是一个简单的TSP问题的动态规划实现的 MATLAB 代码：

function [minDist, route] = tsp_dp(dist)
% TSP_DP  Travelling Salesman Problem (TSP) solver using dynamic programming
% 
% [minDist, route] = tsp_dp(dist) returns the minimum distance and the optimal
% route for the TSP problem defined by the distance matrix 'dist'.
%
% Example usage:
%     dist = [0 10 15 20; 10 0 35 25; 15 35 0 30; 20 25 30 0];
%     [minDist, route] = tsp_dp(dist);

n = size(dist,1);
p = 2^n;
C = inf(n,p);
C(1,1) = 0;

for m = 2:n
    for S = 1:p-1
        if bitand(S,2^(m-1)) == 0
            continue;
        end
        
        for j = 1:n
            if j == m
                continue;
            end
            
            Sj = bitand(S,bitcmp(2^(j-1),'uint32'));
            
            if C(m-1,Sj) + dist(j,m) < C(m,S)
                C(m,S) = C(m-1,Sj) + dist(j,m);
                P(m,S) = j;
            end
        end
    end
end

route = zeros(n,1);
route(1) = 1;
S = p-1;
for m = n:-1:2
    route(n-m+2) = P(m,S);
    S = bitand(S,bitcmp(2^(P(m,S)-1),'uint32'));
end
route(n) = 1;

minDist = C(n,p-1);
end

其中，`dist` 是一个 $n \times n$ 的距离矩阵，`minDist` 是最短路径的长度，`route` 是最短路径的顶点序列。