Dijkstra算法matlab代码

以下是Dijkstra算法的Matlab代码实现：

function [dist, path] = dijkstra(adj, start, dest)
% Dijkstra's shortest path algorithm
% Input: adj - adjacency matrix representing the graph
%        start - starting node
%        dest - destination node
% Output: dist - shortest distance from start to dest
%         path - shortest path from start to dest
% Author: Jianyu Zhao

n = size(adj, 1); % number of nodes in the graph
dist = inf(1, n); % initialize distances to infinity
prev = zeros(1, n); % initialize previous node indices to zero
visited = zeros(1, n); % initialize visited nodes to zero

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

for i = 1:n-1 % loop through all nodes except the destination
    % find the node with the shortest distance that has not been visited
    [mindist, u] = min(dist .* (1 - visited)); 
    visited(u) = 1; % mark the node as visited
    
    % update the distances of adjacent nodes
    for v = 1:n
        if adj(u, v) ~= 0 % if there is an edge between u and v
            alt = dist(u) + adj(u, v); % calculate the alternate distance
            if alt < dist(v) % if the alternate distance is less than the current distance
                dist(v) = alt; % update the distance
                prev(v) = u; % update the previous node index
            end
        end
    end
end

% construct the shortest path from start to dest
path = dest;
while prev(path(1)) ~= 0 % while there are still previous nodes to add
    path = [prev(path(1)), path]; % prepend the previous node to the path
end

end

该算法使用了邻接矩阵表示图，并且返回了起点到终点的最短距离和最短路径。