迪杰克斯特拉算法matlab

以下是使用Matlab实现迪杰斯特拉算法的示例代码：

function [dist, path] = dijkstra_algorithm(graph, start_node, end_node)
% Dijkstra's algorithm implementation in Matlab
% Inputs:
%   graph: a square matrix representing the graph
%   start_node: the starting node
%   end_node: the ending node
% Outputs:
%   dist: the shortest distance from start_node to end_node
%   path: the shortest path from start_node to end_node

n = size(graph, 1);
dist = inf(1, n);
path = zeros(1, n);
visited = zeros(1, n);

dist(start_node) = 0;

for i = 1:n-1
    [~, u] = min(dist .* (1 - visited));
    visited(u) = 1;
    for v = 1:n
        if graph(u, v) ~= 0 && visited(v) == 0
            if dist(u) + graph(u, v) < dist(v)
                dist(v) = dist(u) + graph(u, v);
                path(v) = u;
            end
        end
    end
end

% construct the shortest path
if dist(end_node) == inf
    path = [];
    dist = [];
else
    path_list = end_node;
    while path(path_list(1)) ~= start_node
        path_list = [path(path_list(1)), path_list];
    end
    path_list = [start_node, path_list];
    path = path_list;
end

end

这个函数接受一个方阵作为图的输入，以及起点和终点。它返回从起点到终点的最短距离和路径。该算法使用了一个距离向量和一个访问向量来跟踪每个节点的最短距离和是否已经访问过。在每次迭代中，它选择距离向量中最小的未访问节点，并更新与该节点相邻的节点的最短距离。最后，它构造了从起点到终点的最短路径。