单源最短路径dijkstral算法

手写迪杰斯特拉-Dijkstra

转自：https://www.bilibili.com/video/BV1jE411W7tT?share_source=copy_web

 

 

输入文件：(test.txt)

7
0 5 2 9999 9999 9999 9999
5 0 9999 1 6 9999 9999
2 9999 0 6 9999 8 9999
9999 1 6 0 1 2 9999
9999 6 9999 1 0 9999 7
9999 9999 8 2 9999 0 3
9999 9999 9999 9999 7 3 0

采用floyed算法计算计算出来的结果：

 

 

#include <iostream>
#include <vector>

using namespace std;

constexpr int INF = 0x3F;

vector<int> dijkstral(const vector<vector<int>> &graph, int start) {
    int n = graph.size();
    vector<int> dis(n, INF); // 初始化起点到各节点最短距离为无穷大
    vector<bool> visited(n, false); // 初始化所有节点未被选过
    dis[start] = 0; // 初始起点到起点距离为0
    for (int i = 0; i < n - 1; i++) {
        int minNode = -1;
        // 选定一个节点:
        // 1)未被选过;
        // 2)距离最短;
        for (int j = 0; j < n; j++) {
            if (!visited[j] && ((minNode == -1) || (dis[j] < dis[minNode]))) {
                minNode = j;
            }
        }
        // 对于已选择的节点作为中转站,刷新经过中转站到各节点的最短路径
        for (int j = 0; j < n; j++) {
            dis[j] = std::min(dis[j], dis[minNode] + graph[minNode][j]);
        }
        visited[minNode] = true;
    }
    return dis;
}

void buildGraph(int n, vector<vector<int>> &graph) {
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            std::cin >> graph[i][j];
        }
    }
}
void printGraph(const vector<vector<int>> &graph) {
    for (const auto &vec : graph) {
        for (const auto &val : vec) {
            std::cout << val << " ";
        }
        std::cout << endl;
    }

    std::cout << endl;
}

int main()
{
    FILE *fpIn;
    fpIn = freopen("D:\\test.txt", "r", stdin);
    if (fpIn == nullptr) {
        std::cout << "freopen fail!" << endl;
    }
    int n = 0;
    std::cin >> n;
    vector<vector<int>> graph(n, vector<int>(n));
    // 构建无向带权图
    buildGraph(n, graph);
    // 打印无向图
    printGraph(graph);
    // 遍历打印n个节点作为中转站时到各节点的最短距离数组:
    for (int i = 0; i < n; i++) {
        int start = i;
        std::cout << "start : " << start << endl;
        std::cout << "dis[" << i << "]:";
        vector<int> dis = dijkstral(graph, start);
        for (const auto &val : dis) {
            std::cout << val << " ";
        }
        std::cout << endl;
    }
    fclose(fpIn);
    system("pause");
    return 0;
}

验证结果：