迪杰斯特拉算法求最短路径matlab完整代码

以下是迪杰斯特拉算法求最短路径的 Matlab 完整代码：

function [dist, path] = dijkstra(graph, startNode, endNode)
% Dijkstra's algorithm to find shortest path
% Inputs:
%   graph: adjacency matrix of the graph
%   startNode: starting node
%   endNode: destination node
% Outputs:
%   dist: shortest distance from startNode to endNode
%   path: shortest path from startNode to endNode

n = size(graph, 1); % number of nodes
dist = inf(1, n); % initialize distance to all nodes as infinity
visited = zeros(1, n); % mark all nodes as unvisited
prev = zeros(1, n); % array to store previous node in optimal path

dist(startNode) = 0; % distance from start node to itself is zero

for i = 1:n-1
    % find the node with the minimum distance
    [u, minDist] = minDistance(dist, visited);
    
    visited(u) = 1; % mark the node as visited
    
    % update the distance of the adjacent nodes
    for v = 1:n
        if graph(u, v) ~= 0 && visited(v) == 0
            alt = dist(u) + graph(u, v);
            if alt < dist(v)
                dist(v) = alt;
                prev(v) = u;
            end
        end
    end
end

% compute the shortest path
path = endNode;
while path(1) ~= startNode
    path = [prev(path(1)), path];
end

end

function [u, minDist] = minDistance(dist, visited)
% helper function to find the node with the minimum distance
minDist = inf;
for i = 1:length(dist)
    if visited(i) == 0 && dist(i) < minDist
        u = i;
        minDist = dist(i);
    end
end
end

其中，`graph` 是邻接矩阵，`startNode` 是起点，`endNode` 是终点。函数返回值包括最短距离 `dist` 和最短路径 `path`。