迪杰斯特拉算法matlab代码寻找最短路径

迪杰斯特拉算法（Dijkstra's algorithm）是一种用于寻找带权图中单源最短路径的算法。其基本思想是从源点开始，不断地确定离源点距离最短的顶点，直到到达终点为止。

下面是迪杰斯特拉算法的 MATLAB 代码实现：

function [dist, path] = dijkstra(graph, start, dest)
% DIJKSTRA Find the shortest path in a weighted graph using Dijkstra's algorithm
%    [DIST, PATH] = DIJKSTRA(GRAPH, START, DEST) finds the shortest path from
%    START to DEST in the weighted graph represented by the adjacency matrix GRAPH.
%    The output DIST is the length of the shortest path and PATH is a vector of
%    node indices representing the path.

n = size(graph, 1); % number of nodes in the graph

dist = inf(1, n); % initialize distance vector to infinity
dist(start) = 0; % distance to start node is zero

visited = false(1, n); % initialize visited vector to false

prev = zeros(1, n); % initialize previous node vector to zero

for i = 1:n-1
    % find the node with the shortest distance that has not been visited
    [mindist, u] = min(dist .* ~visited);
    if isinf(mindist)
        break; % all remaining nodes are inaccessible
    end
    
    visited(u) = true; % mark the node as visited
    
    % update distances to neighboring nodes
    for v = find(graph(u, :))
        alt = dist(u) + graph(u, v);
        if alt < dist(v)
            dist(v) = alt;
            prev(v) = u;
        end
    end
end

% construct path vector
if isinf(dist(dest))
    path = [];
else
    path = dest;
    while path(1) ~= start
        path = [prev(path(1)), path];
    end
end

end

上述代码中，`graph` 是一个邻接矩阵，`start` 是起点的索引，`dest` 是终点的索引。函数返回两个输出参数，`dist` 是起点到终点的最短距离，`path` 是最短路径上经过的节点索引。如果起点与终点不连通，则 `dist` 为无穷大，`path` 为空。

相关问题：
1. 什么是带权图？
2. 迪杰斯特拉算法的时间复杂度是多少？
3. 迪杰斯特拉算法与贪心算法有什么联系？