matlab迪杰斯特拉求最短路径完整代码

以下是使用Matlab实现的迪杰斯特拉算法求最短路径的完整代码：

function [path, dist] = dijkstra(graph, start, goal)
% Dijkstra's algorithm for finding the shortest path in a graph
% represented as an adjacency matrix, with start and goal nodes specified

n = size(graph, 1);

% Initialize the distance and visited arrays
dist = Inf(1, n);
visited = false(1, n);
prev = zeros(1, n);

% Set the distance of the start node to 0
dist(start) = 0;

while ~all(visited)
    % Find the unvisited node with the smallest distance
    [~, u] = min(dist(~visited));
    if isempty(u)
        break;
    end
    % Mark the current node as visited
    visited(u) = true;
    
    % Update the distances of the neighbors of the current node
    for v = 1:n
        if graph(u,v) ~= 0 && ~visited(v)
            alt = dist(u) + graph(u,v);
            if alt < dist(v)
                dist(v) = alt;
                prev(v) = u;
            end
        end
    end
    
    % Check if we have reached the goal node
    if visited(goal)
        break;
    end
end

% Construct the shortest path from start to goal
path = [];
if prev(goal) ~= 0
    u = goal;
    while u ~= start
        path = [u path];
        u = prev(u);
    end
    path = [start path];
end

这个算法使用了一个邻接矩阵来表示图，其中每个元素表示两个节点之间的距离，0表示没有连接。算法首先初始化距离和访问数组，然后从起始节点开始，逐个更新它的邻居节点的距离，直到所有节点都被访问或者到达目标节点为止。最后，算法构造出从起始节点到目标节点的最短路径，并返回路径和距离。