Floyd算法

算法简介：

Floyd算法又称为弗洛伊德算法，插点法，是一种用于寻找给定的加权图中顶点间最短路径的算法。

算法过程：

1.从任意一条单边路径开始。所有两点之间的距离是边的权，如果两点之间没有边相连，则权为无穷大。

2.对于每一对顶点 i 和 j，看看是否存在一个顶点 k 使得从 i 到 k 再到 j 比已知的路径更短。如果是更新它。

代码说明：

dist[i][j] : 记录从顶点i到顶点j的最短路径长度，初始化为INF

path[i][j] : 记录从顶点i到顶点j的最短路径所经过的顶点k，初始化为0

时间复杂度：O(n^3)；

空间复杂度：O(n^2)；

代码：

package Algorithm;

import java.util.Scanner;

public class Floyd {
    public static final int INF = 100000;
    
    public Graph initGraph() {

        @SuppressWarnings("resource")
        Scanner scanner = new Scanner(System.in);
        System.out.println("Please input the number of the vertex: ");
        int vertexNum = scanner.nextInt();
        System.out.println("Please input the number of the edge: ");
        int edgeNum = scanner.nextInt();
        
        Graph graph = new Graph(vertexNum, edgeNum);
        
        for(int i = 1; i <= vertexNum; i++) {
            for(int j = 1; j <= vertexNum; j++) {
                int w = (i == j) ? 0 : INF;
                graph.addEdge(i, j, w);
                graph.addPath(i, j);
            }            
        }
        
        for(int i = 1; i <= edgeNum; i++) {
            System.out.println("Please input the vertexs and weight of the edge " + i);
            int v1 = scanner.nextInt();
            int v2 = scanner.nextInt();
            int weight = scanner.nextInt();
            graph.addEdge(v1, v2, weight);
        }
        return graph;
    }
    
    public void floyd(Graph graph) {
        int vertexNum = graph.getVertexNum();
        int dist[][] = graph.getDist();
        int path[][] = graph.getPath();
        for(int i = 1; i <= vertexNum; i++) {
            for(int j = 1; j <= vertexNum; j++) {
                for(int k = 1; k <= vertexNum; k++) {
                    if(dist[i][k] + dist[k][j] < dist[i][j]) {
                        dist[i][j] = dist[i][k] + dist[k][j];
                        path[i][j] = k;
                    }
                }
            }
        }
    }
    
    private void printPath(int i, int j, int path[][]) {
        int k = path[i][j];
        if(k == 0) return;
        printPath(i, k, path);
        System.out.print(" " + k);
        printPath(k, j, path);
    }
    
    public void showAllPath(Graph graph) {
        System.out.println("Print all path:");
        int vertexNum = graph.getVertexNum();
        int dist[][] = graph.getDist();
        int path[][] = graph.getPath();
        for(int i = 1; i <= vertexNum; i++) {
            for(int j = 1; j <= vertexNum; j++) {
                System.out.print("From vertex " + i + " to " + j + " --- Length: "
            + dist[i][j] + " Path: " + i);
                printPath(i, j, path);
                System.out.println(" " + j);
            }            
        }
    }
    
    public static void main(String args[]) {
        Floyd floyd = new Floyd();
        Graph graph = floyd.initGraph();
        floyd.floyd(graph);
        floyd.showAllPath(graph);
    }
    
}

package Algorithm;

public class Graph {
    private int vertexNum;
    private int edgeNum;
    private int[][] dist;
    private int[][] path;
    
    public Graph(int vertexNum, int edgeNum) {
        this.vertexNum = vertexNum;
        this.edgeNum = edgeNum;
        int i = vertexNum + 1;
        dist = new int[i][i];
        path = new int[i][i];
    }
    
    public void addEdge(int i, int j, int w) {
        dist[i][j] = w;
    }
    
    public void addPath(int i, int j) {
        path[i][j] = 0;
    }
    
    public int getVertexNum() {
        return vertexNum;
    }
    public void setVertexNum(int vertexNum) {
        this.vertexNum = vertexNum;
    }
    public int getEdgeNum() {
        return edgeNum;
    }
    public void setEdgeNum(int edgeNum) {
        this.edgeNum = edgeNum;
    }

    public int[][] getDist() {
        return dist;
    }

    public void setDist(int[][] dist) {
        this.dist = dist;
    }

    public int[][] getPath() {
        return path;
    }

    public void setPath(int[][] path) {
        this.path = path;
    }
 
}