图的最短路径 java

以下是使用Java实现图的最短路径的示例代码：

1. 使用Dijkstra算法求某一个顶点到其他各顶点的最短路径：

import java.util.*;

public class DijkstraAlgorithm {
    private static final int INF = Integer.MAX_VALUE;

    public static void dijkstra(int[][] graph, int start) {
        int n = graph.length;
        int[] dist = new int[n];
        boolean[] visited = new boolean[n];

        Arrays.fill(dist, INF);
        dist[start] = 0;

        for (int i = 0; i < n - 1; i++) {
            int u = -1;
            for (int j = 0; j < n; j++) {
                if (!visited[j] && (u == -1 || dist[j] < dist[u])) {
                    u = j;
                }
            }

            visited[u] = true;

            for (int v = 0; v < n; v++) {
                if (!visited[v] && graph[u][v] != 0 && dist[u] != INF && dist[u] + graph[u][v] < dist[v]) {
                    dist[v] = dist[u] + graph[u][v];
                }
            }
        }

        System.out.println("Shortest paths from vertex " + start + ":");
        for (int i = 0; i < n; i++) {
            if (dist[i] == INF) {
                System.out.println("Vertex " + i + ": No path");
            } else {
                System.out.println("Vertex " + i + ": " + dist[i]);
            }
        }
    }

    public static void main(String[] args) {
        int[][] graph = {
            {0, 4, 0, 0, 0, 0, 0, 8, 0},
            {4, 0, 8, 0, 0, 0, 0, 11, 0},
            {0, 8, 0, 7, 0, 4, 0, 0, 2},
            {0, 0, 7, 0, 9, 14, 0, 0, 0},
            {0, 0, 0, 9, 0, 10, 0, 0, 0},
            {0, 0, 4, 14, 10, 0, 2, 0, 0},
            {0, 0, 0, 0, 0, 2, 0, 1, 6},
            {8, 11, 0, 0, 0, 0, 1, 0, 7},
            {0, 0, 2, 0, 0, 0, 6, 7, 0}
        };

        dijkstra(graph, 0);
    }
}

2. 使用Floyd算法求图中任意两个顶点的最短路径：

import java.util.*;

public class FloydAlgorithm {
    private static final int INF = Integer.MAX_VALUE;

    public static void floyd(int[][] graph) {
        int n = graph.length;
        int[][] dist = new int[n][n];

        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                dist[i][j] = graph[i][j];
            }
        }

        for (int k = 0; k < n; k++) {
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < n; j++) {
                    if (dist[i][k] != INF && dist[k][j] != INF && dist[i][k] + dist[k][j] < dist[i][j]) {
                        dist[i][j] = dist[i][k] + dist[k][j];
                    }
                }
            }
        }

        System.out.println("Shortest paths between all pairs of vertices:");
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < n; j++) {
                if (dist[i][j] == INF) {
                    System.out.print("INF ");
                } else {
                    System.out.print(dist[i][j] + " ");
                }
            }
            System.out.println();
        }
    }

    public static void main(String[] args) {
        int[][] graph = {
            {0, 4, INF, INF, INF, INF, INF, 8, INF},
            {4, 0, 8, INF, INF, INF, INF, 11, INF},
            {INF, 8, 0, 7, INF, 4, INF, INF, 2},
            {INF, INF, 7, 0, 9, 14, INF, INF, INF},
            {INF, INF, INF, 9, 0, 10, INF, INF, INF},
            {INF, INF, 4, 14, 10, 0, 2, INF, INF},
            {INF, INF, INF, INF, INF, 2, 0, 1, 6},
            {8, 11, INF, INF, INF, INF, 1, 0, 7},
            {INF, INF, 2, INF, INF, INF, 6, 7, 0}
        };

        floyd(graph);
    }
}