算法（图论）——最短路径问题（弗洛伊德算法）

给定一个带权有向图，计算任意两结点间的最短路径。

算法思想：遍历每个点到另外点的距离。三层循环，第一层枚举中间点，第二层和第三层枚举起点和终点。

public static void main() {
    int N = 1010, M = 2000010, INF = 1000000000;


    int[][] d = new int[N][N];    // 存储两点之间的最短距离

    Scanner sc = new Scanner(System.in);
    int n = sc.nextInt();
    int m = sc.nextInt();
    for (int i = 1; i <= n; i++)
        for (int j = 1; j <= n; j++)
            d[i][j] = i == j ? 0 : INF;
    for (int i = 0; i < m; i++) {
        int a, b, c;
        a = sc.nextInt();
        b = sc.nextInt();
        c = sc.nextInt();
        d[a][b] = d[b][a] = Math.min(c, d[a][b]);
    }
    // floyd 算法核心
    for (int k = 1; k <= n; k++) {
        for (int i = 1; i <= n; i++) {
            for (int j = 1; j <= n; j++) {
                d[i][j] = Math.min(d[i][j], d[i][k] + d[k][j]);
            }
        }
    }

    System.out.println(d[1][n]);
}