最短哈密顿回路 matlab
时间: 2023-05-28 20:06:42 浏览: 62
由于哈密顿回路问题是一个NP完全问题,目前没有已知的多项式时间算法可以解决它。因此,我们需要使用一些近似算法来解决这个问题。
以下是一个使用最近邻算法的MATLAB代码,它可以在给定的点集中找到最短的哈密顿回路。
```matlab
function [path, dist] = tsp_nearest_neighbor(nodes)
% TSP_NEAREST_NEIGHBOR - Find the shortest Hamiltonian cycle using the nearest neighbor algorithm
% NODES: a matrix of node coordinates, where each row represents a node
% PATH: the sequence of nodes in the shortest Hamiltonian cycle
% DIST: the length of the shortest Hamiltonian cycle
n = size(nodes, 1);
visited = false(1, n);
visited(1) = true;
path = [1];
dist = 0;
while length(path) < n
current = path(end);
nearest = inf;
index = -1;
for i = 1:n
if ~visited(i)
d = norm(nodes(current, :) - nodes(i, :));
if d < nearest
nearest = d;
index = i;
end
end
end
path = [path index];
visited(index) = true;
dist = dist + nearest;
end
dist = dist + norm(nodes(path(end), :) - nodes(1, :));
end
```
该代码首先将起始点添加到路径中,然后在每个步骤中找到最近的未访问节点并将其添加到路径中。最后,它将最后一个节点与起始节点相连,形成一个哈密顿回路。