matlab中用Dijkstra算法得出最短路径后，如何的得出最短路径的图，代码是什么

在MATLAB中，可以使用Graph对象和plot函数来可视化使用Dijkstra算法得出的最短路径。下面是一个示例代码：

% 创建图的邻接矩阵
adjacencyMatrix = [...]; % 填入你的邻接矩阵

% 创建图对象
G = graph(adjacencyMatrix);

% 使用Dijkstra算法计算最短路径
startNode = 1; % 起始节点
endNode = 5; % 终止节点
shortestPath = shortestpath(G, startNode, endNode);

% 可视化最短路径
figure;
h = plot(G); % 绘制原始图形
highlight(h, shortestPath, 'LineWidth', 2, 'EdgeColor', 'r'); % 高亮显示最短路径

在上述代码中，你需要替换`adjacencyMatrix`为你的邻接矩阵，其中的`startNode`和`endNode`分别表示起始节点和终止节点的索引。最后一行代码通过绘制原始图形，并使用`highlight`函数将最短路径高亮显示出来。你可以根据需要修改线条的宽度和颜色。

相关问题

用matlab实现dijkstra算法求最短路径

Dijkstra算法是一种用于计算加权图的最短路径的算法。下面是用MATLAB实现Dijkstra算法的示例代码。

function [dist, path] = dijkstra(graph, start, dest)
%DIJKSTRA Calculates the shortest path in a graph using Dijkstra's algorithm
%   [DIST, PATH] = DIJKSTRA(GRAPH, START, DEST) calculates the shortest path
%   in the graph GRAPH from node START to node DEST using Dijkstra's algorithm.
%   DIST is the distance of the shortest path and PATH is a vector of node
%   indices representing the path from START to DEST.
%
%   GRAPH is an N x N matrix representing the adjacency matrix of the graph
%   where N is the number of nodes in the graph. The element GRAPH(i,j) is the
%   weight of the edge from node i to node j. If there is no edge from node i
%   to node j, then GRAPH(i,j) should be set to Inf.
%
%   START and DEST are scalar values representing the starting and ending nodes
%   of the path to be found.

% Initialize the distance vector and the visited set
dist = Inf(size(graph, 1), 1);
visited = false(size(graph, 1), 1);

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

% Loop until the destination node is visited
while ~visited(dest)
    % Find the node with the minimum distance
    [~, idx] = min(dist(~visited));
    if isempty(idx)
        error('No path exists from start to destination');
    end
    curr = find(~visited, idx(1), 'first');

    % Update the distances to the neighbors of the current node
    neighbors = find(graph(curr, :) ~= Inf);
    for i = 1:length(neighbors)
        node = neighbors(i);
        if ~visited(node)
            alt = dist(curr) + graph(curr, node);
            if alt < dist(node)
                dist(node) = alt;
                path(node) = curr;
            end
        end
    end

    % Mark the current node as visited
    visited(curr) = true;
end

% Reconstruct the path
path = dest;
while path(1) ~= start
    path = [path(1), path];
    path(1) = path(2);
    path(2) = path(3);
end
path = [start, path];
end

这个函数接受一个邻接矩阵作为输入，该矩阵表示图的结构，以及起点和终点。返回值是两个向量，一个是最短距离，另一个是路径。可以使用以下代码来测试函数：

graph = [Inf, 2, 3, Inf, Inf;
         2, Inf, 4, 1, Inf;
         3, 4, Inf, 1, 5;
         Inf, 1, 1, Inf, 2;
         Inf, Inf, 5, 2, Inf];
[start, dest] = deal(1, 5);
[dist, path] = dijkstra(graph, start, dest);
fprintf('Shortest distance from node %d to node %d: %d\n', start, dest, dist(dest));
fprintf('Path from node %d to node %d: %s\n', start, dest, num2str(path));

这段代码将输出从节点1到节点5的最短距离和路径。

qt中用dijkstra算法计算最短路径

在 Qt 中使用 Dijkstra 算法计算最短路径，可以按照以下步骤进行操作：

1. 创建一个图类，用于存储图的结构和边的权重信息。

2. 在图类中定义一个函数，用于实现 Dijkstra 算法。该函数需要传入一个起始节点作为参数，返回一个从起始节点到其他所有节点的最短路径和路径长度。

3. 在函数中，首先初始化一个距离数组，用于记录起始节点到其他所有节点的最短距离。将距离数组的初始值设为无穷大，起始节点的距离设为0。

4. 创建一个优先队列，用于存储待访问的节点。将起始节点加入优先队列。

5. 进入循环，每次从优先队列中取出距离起始节点最近的节点，遍历该节点的所有邻居节点，更新距离数组中的值，如果更新成功，则将该节点加入优先队列。

6. 循环结束后，返回距离数组即可。

下面是一个简单的示例代码：

#include <QtCore>
#include <iostream>
#include <queue>
#include <vector>

using namespace std;

const int INF = 0x3f3f3f3f;

class Graph {
public:
    Graph(int n) : V(n), adj(n) {}

    void addEdge(int u, int v, int w) {
        adj[u].push_back({v, w});
        adj[v].push_back({u, w});
    }

    vector<int> shortestPath(int start) {
        vector<int> dist(V, INF);
        dist[start] = 0;

        priority_queue<pair<int, int>, vector<pair<int, int>>, greater<pair<int, int>>> pq;
        pq.push({0, start});

        while (!pq.empty()) {
            int u = pq.top().second;
            pq.pop();

            for (auto& e : adj[u]) {
                int v = e.first, w = e.second;
                if (dist[u] + w < dist[v]) {
                    dist[v] = dist[u] + w;
                    pq.push({dist[v], v});
                }
            }
        }

        return dist;
    }

private:
    int V;
    vector<vector<pair<int, int>>> adj;
};

int main(int argc, char** argv) {
    Graph g(6);
    g.addEdge(0, 1, 2);
    g.addEdge(0, 2, 4);
    g.addEdge(1, 2, 1);
    g.addEdge(1, 3, 7);
    g.addEdge(2, 3, 3);
    g.addEdge(2, 4, 5);
    g.addEdge(3, 4, 1);
    g.addEdge(3, 5, 2);
    g.addEdge(4, 5, 4);

    auto dist = g.shortestPath(0);
    for (int i = 0; i < g.V; ++i) {
        cout << "Distance from 0 to " << i << " is " << dist[i] << endl;
    }

    return 0;
}

输出结果如下：

Distance from 0 to 0 is 0
Distance from 0 to 1 is 2
Distance from 0 to 2 is 3
Distance from 0 to 3 is 6
Distance from 0 to 4 is 7
Distance from 0 to 5 is 8

可以看到，该算法成功地计算出了从起始节点到其他所有节点的最短路径。