algorithm for estimating traveling salesman problem in matlab

main.m
function optDist = tsp_dp(dist, start)
% Inputs:
%    dist: distance matrix between cities
%    start: starting city
% Output:
%    optDist: optimized distance for the TSP

n = size(dist, 1);
dp = Inf(n, n);

% Initialize dp table
dp(start, 1) = 0;

% Compute dynamic programming table
for j = 2:n
    for k = 1:n-1
        if k == start
            continue;
        end
        
        for S = combnk([1:n], j)
            if ~ismember(start, S) || ~ismember(k, S)
                continue;
            end
            
            for m = S
                if m == k
                    continue;
                end
                
                dp(S, j) = min(dp(setdiff(S, k), j-1) + dist(k, m));
            end
        end
    end
end

% Compute optimized distance
optDist = min(dp(setdiff([1:n], start), n) + dist(k, start));
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