用matlab实现dijsktra 算法

以下是用 Matlab 实现 Dijkstra 算法的示例代码：

function [dist, path] = dijkstra(adj, src, dest)
% DIJKSTRA Find the shortest path from a source node to a destination node
% in a graph represented by an adjacency matrix using Dijkstra's algorithm.
%   adj: adjacency matrix of the graph
%   src: source node index
%   dest: destination node index
%   dist: shortest distance from the source node to each node
%   path: shortest path from the source node to the destination node
%
% Example:
%   adj = [0 3 9 0 0;
%          3 0 1 7 0;
%          9 1 0 5 8;
%          0 7 5 0 4;
%          0 0 8 4 0];
%   [dist, path] = dijkstra(adj, 1, 5);

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

dist(src) = 0;  % distance from source to itself is zero

for i = 1:n
    % find the node with the smallest tentative distance
    [min_dist, u] = min(dist(~visited));
    if isempty(u)
        break;  % all remaining nodes are unreachable
    end
    
    % mark the selected node as visited
    visited(u) = true;
    
    % update the distances of its neighbors
    for v = 1:n
        if adj(u, v) ~= 0 && ~visited(v)
            alt = dist(u) + adj(u, v);
            if alt < dist(v)
                dist(v) = alt;
                prev(v) = u;
            end
        end
    end
    
    % check if we have reached the destination node
    if u == dest
        break;
    end
end

% construct the shortest path from the source to the destination
path = [];
u = dest;
while prev(u) ~= 0
    path = [u path];
    u = prev(u);
end
if u == src
    path = [u path];
end
end

该函数的输入参数是邻接矩阵 `adj`，源节点索引 `src` 和目标节点索引 `dest`，输出参数是最短距离数组 `dist` 和最短路径数组 `path`。该函数使用了 Dijkstra 算法来计算最短路径，其中包括了对节点距离的初始化、标记已访问的节点、更新邻居节点的距离等过程。最后，根据存储的前驱节点信息，构造从源节点到目标节点的最短路径。