请编写一个可在matlab2021运行的Dijkstra算法

好的，以下是一个基于 MATLAB 实现的 Dijkstra 算法：

function [dist, path] = dijkstra(adj_matrix, start_node, end_node)
% DIJKSTRA  Compute the shortest path between two nodes in a graph using Dijkstra algorithm.
%
% Input:
%   - adj_matrix: A n-by-n matrix represents the adjacency matrix of the graph. 
%                 adj_matrix(i, j) = the weight of the edge between node i and node j.
%                 If there is no edge between node i and node j, adj_matrix(i, j) = inf.
%   - start_node: The index of the starting node.
%   - end_node:   The index of the ending node.
%
% Output:
%   - dist: A scalar represents the shortest distance between the start_node and end_node.
%   - path: A vector represents the path from the start_node to the end_node.

n = size(adj_matrix, 1);    % Number of nodes in the graph
visited = false(n, 1);      % Visited flag
dist = inf(n, 1);           % Distance from start_node to each node
prev = zeros(n, 1);         % Previous node in the shortest path
dist(start_node) = 0;       % Distance from start_node to start_node is 0

for i = 1:n
    % Find the node with the smallest distance
    [~, u] = min(dist(~visited));
    if isempty(u)
        break;
    end
    visited(u) = true;
    if u == end_node
        break;
    end
    
    % Update the distance of the neighboring nodes
    for v = 1:n
        if ~visited(v) && adj_matrix(u, v) < inf
            alt = dist(u) + adj_matrix(u, v);
            if alt < dist(v)
                dist(v) = alt;
                prev(v) = u;
            end
        end
    end
end

% Compute the path from start_node to end_node
path = [];
u = end_node;
while prev(u) ~= 0
    path = [u, path];
    u = prev(u);
end
if ~isempty(path)
    path = [start_node, path];
end

end

使用方法：

假设我们有一个 5 个节点的图，其邻接矩阵为：

0   4   1   ∞   ∞
4   0   3   2   ∞
1   3   0   4   2
∞   2   4   0   3
∞   ∞   2   3   0

我们想要计算从节点 1 到节点 5 的最短路径，可以使用以下代码：

adj_matrix = [0   4   1   inf inf;
              4   0   3   2   inf;
              1   3   0   4   2;
              inf 2   4   0   3;
              inf inf 2   3   0];
[start_node, end_node] = deal(1, 5);
[dist, path] = dijkstra(adj_matrix, start_node, end_node);

其中 `dist` 是从起点到每个节点的最短距离，`path` 是从起点到终点的最短路径。