无权图的广度优先遍历寻找单源最短路径

图的广度优先遍历寻找最短路径

直接看代码

package GraphBasics;

import java.util.LinkedList;
import java.util.Stack;
import java.util.Vector;

/**
 * @ Description: 寻找s到w的最短路径
 * @ Date: Created in 13:14 2018/8/1
 * @ Author: Anthony_Duan
 */
public class ShortestPath {
    private Graph G;
    private int s;
    private boolean[] visited;
    // 记录路径, from[i]表示查找的路径上i的上一个节点
    private int[] from;
    //记录路径中节点的次序，ord[i]表示i节点在路径中的次序。
    private int[] ord;

    // 构造函数, 寻路算法, 寻找图graph从s点到其他点的路径
    public ShortestPath(Graph graph, int s) {
        //算法初始化
        G = graph;
        assert s >= 0 && s < G.V();
        visited = new boolean[G.V()];
        from = new int[G.V()];
        ord = new int[G.V()];
        for (int i = 0; i < G.V(); i++) {
            visited[i] = false;
            from[i] = -1;
            ord[i] = -1;
        }
        this.s = s;
        //无向图最短路径算法，从s开始广度优先遍历整张图
        LinkedList q = new LinkedList<>();

        q.push(s);
        visited[s] = true;
        ord[s] = 0;
        while (!q.isEmpty()) {
            int v = q.pop();
            for (int i :
                    G.adj(v)) {
                if (!visited[i]) {
                    q.push(i);
                    visited[i] = true;
                    from[i] = v;
                    ord[i] = ord[v] + 1;
                }
            }
        }
    }


    // 查询s 到w是否有路径
    public boolean hasPath(int w) {
        assert w >= 0 && w < G.V();
        return visited[w];
    }


    //查询s到w的路径存放到vec中
    public Vector path(int w) {
        assert hasPath(w);

        // 通过from数组逆向查找到从s到w的路径, 存放到栈中
        Stack s = new Stack<>();

        int p = w;
        while (p != -1) {
            s.push(p);
            p = from[p];
        }

        // 从栈中依次取出元素, 获得顺序的从s到w的路径
        Vector res = new Vector<>();
        while (!s.empty()) {
            res.add(s.pop());
        }
        return res;
    }

    // 打印出从s点到w点的路径
    public void showPath(int w) {
        assert hasPath(w);

        Vector vec = path(w);
        for (int i = 0; i < vec.size(); i++) {
            System.out.print(vec.elementAt(i));
            if (i == vec.size() - 1) {
                System.out.println();
            } else {
                System.out.print(" -> ");
            }
        }
    }

    // 查看从s点到w点的最短路径长度
    // 若从s到w不可达，返回-1
    public int length(int w) {
        assert w >= 0 && w < G.V();
        return ord[w];
    }
}