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;

    }

 

}