圖論系列（六）——圖的廣度優先遍歷及應用2

1. 二分圖檢測

import java.util.LinkedList;
import java.util.Queue;

public class BipartitionDetection {

    private Graph G;

    private boolean[] visited;
    private int[] colors;		//colors[i]：節點i的顏色:0、1
    private boolean isBipartite = true;

    public BipartitionDetection(Graph G){

        this.G = G;
        visited = new boolean[G.V()];
        colors = new int[G.V()];
        for(int i = 0; i < G.V(); i ++)
            colors[i] = -1;

        for(int v = 0; v < G.V(); v ++)
            if(!visited[v])
                if(!bfs(v)){
                    isBipartite = false;
                    break;
                }
    }

    private boolean bfs(int s){

        Queue<Integer> queue = new LinkedList<>();
        queue.add(s);
        visited[s] = true;
        colors[s] = 0;

        while(!queue.isEmpty()){
            int v = queue.remove();

            for(int w: G.adj(v))
                if(!visited[w]){
                    queue.add(w);
                    visited[w] = true;
                    colors[w] = 1 - colors[v];
                }
                else if(colors[v] == colors[w])	//當前節點與訪問過的鄰接節點顏色一致
                    return false;
        }
        return true;
    }

    public boolean isBipartite(){
        return isBipartite;
    }
}

2. 無權圖的最短路徑

import java.util.ArrayList;
import java.util.Collections;
import java.util.LinkedList;
import java.util.Queue;

// Unweighted Single Source Shortest Path
public class USSSP {
    private Graph G;
    private boolean[] visited;
    private int[] pre;      //保存到達某個點的上個節點的編號
    private int s;          //source：從哪個源頭開始
    private int[] dis;      //dis[i]：源點到i節點的距離

    public USSSP(Graph g, int s){
        this.G = g;
        visited = new boolean[g.V()];
        pre = new int[g.V()];
        dis = new int[g.V()];
        for (int i = 0; i < g.V(); i++) {
            pre[i] = -1;
            dis[i] = -1;
        }
        this.s = s;

        bfs(s);
    }

    private void bfs(int s){
        Queue<Integer> queue = new LinkedList<>();
        queue.add(s);
        visited[s] = true;
        pre[s] = s;
        dis[s] = 0;

        while(!queue.isEmpty()){
            int v = queue.remove();

            for(int w:G.adj(v)){
                if(!visited[w]){
                    queue.add(w);
                    visited[w] = true;
                    pre[w] = v;
                    dis[w] = dis[v] + 1;
                }
            }
        }
    }

    public boolean isConnectedTo(int t){
        G.validateVertex(t);
        return visited[t];      //return pre[t] != -1;
                                //return dis[t] != -1;
    }

    public Iterable<Integer> path(int t){
        ArrayList<Integer> res = new ArrayList<>();
        if(!isConnectedTo(t))   return res;

        int cur = t;
        while(cur != s){
            res.add(cur);
            cur = pre[cur];
        }
        res.add(s);

        Collections.reverse(res);
        return res;
    }

    public int dis(int t){
        G.validateVertex(t);
        return dis[t];
    }

    public static void main(String[] args) {
        Graph graph = new Graph("g_5.txt");
        USSSP usssp = new USSSP(graph, 0);
        System.out.println(usssp.isConnectedTo(6));
        System.out.println(usssp.path(6));
        System.out.println(usssp.dis(6));
    }
}

3. BFS與DFS聯繫

• 注：本系列參考玩轉算法系列–圖論精講