matlab代码利用Dijkstra算法求有向图最短路代码
时间: 2023-11-12 17:03:08 浏览: 36
下面是一个简单的 Matlab 程序,用 Dijkstra 算法求解有向图的最短路径问题:
```matlab
function [dist, path] = Dijkstra(A, s)
% A - adjacency matrix of the directed graph
% s - the starting vertex
% dist - distances from the starting vertex to all other vertices
% path - shortest paths from the starting vertex to all other vertices
n = size(A, 1);
dist = inf(1, n);
dist(s) = 0;
path = cell(1, n);
for i = 1:n
path{i} = [s];
end
for i = 1:n-1
[~, u] = min(dist);
dist(u) = inf;
for v = 1:n
if A(u, v) > 0
alt = dist(u) + A(u, v);
if alt < dist(v)
dist(v) = alt;
path{v} = [path{u}, v];
end
end
end
end
```
其中,`A` 是一个邻接矩阵,表示有向图的连接情况,`s` 是起始节点的编号。程序返回两个变量:`dist` 表示起始节点到其他节点的最短距离,`path` 表示起始节点到其他节点的最短路径。