matlab中dijkstra算法代码
时间: 2023-11-02 11:13:22 浏览: 37
以下是matlab中的Dijkstra算法代码实现:
```
function [dist,path] = dijkstra(graph, start, dest)
% Dijkstra's shortest path algorithm
% graph: adjacency matrix of the graph, where graph(i,j) is the weight of the edge from i to j
% start: starting node
% dest: destination node
% dist: array of shortest distances from start to all nodes
% path: array of previous nodes on the shortest path from start to each node
n = size(graph,1); % number of nodes
dist = inf(1,n); % initialize distances to infinity
dist(start) = 0; % distance from start to start is 0
path = zeros(1,n); % initialize previous nodes to 0
visited = zeros(1,n); % initialize visited nodes to 0
for i=1:n-1
% find node with minimum distance that has not been visited
[~, u] = min(dist .* (1 - visited));
visited(u) = 1;
% update distances and previous nodes
for v=1:n
if graph(u,v) ~= 0 && dist(u) + graph(u,v) < dist(v)
dist(v) = dist(u) + graph(u,v);
path(v) = u;
end
end
end
% construct path from start to dest by following previous nodes
if dist(dest) == inf
path = [];
else
p = dest;
while p ~= start
path = [p path];
p = path(p);
end
path = [start path];
end
```
在这个实现中,我们首先初始化距离数组dist和前一个节点数组path,然后将所有节点标记为未访问。接下来,我们将从起点开始,找到最小的未访问节点,并将其标记为已访问。然后我们更新与此节点相邻的所有节点的距离和前一个节点,如果找到了更短的路径。我们重复这个过程,直到所有节点都被访问为止。最后,我们可以通过跟随前一个节点数组从起点到目标节点构建最短路径。