Java实现One-way traffic（单向交通）

One-way traffic

In a certain town there are n intersections connected by two- and one-way streets. The town is very

modern so a lot of streets run through tunnels or viaducts. Of course it is possible to travel between

any two intersections in both ways, i.e. it is possible to travel from an intersection a to an intersection

b as well as from b to a without violating traffic rules. Because one-way streets are safer, it has been

decided to create as much one-way traffic as possible. In order not to make too much confusion it has

also been decided that the direction of traffic in already existing one-way streets should not be changed.

Your job is to create a new traffic system in the town. You have to determine the direction of

traffic for as many two-way streets as possible and make sure that it is still possible to travel both ways

between any two intersections.

Write a program that:

• reads a description of the street system in the town from the standard input,

• for each two-way street determines one direction of traffic or decides that the street must remain

two-way,

• writes the answer to the standard output.

Input

The first line of the input contains two integers n and m, where 2 ≤ n ≤ 2000 and n−1 ≤ m ≤ n(n−1)/2.

Integer n is the number of intersections in the town and integer m is the number of streets.

Each of the next m lines contains three integers a, b and c, where 1 ≤ a ≤ n, 1 ≤ b ≤ n, a ̸= b and

c belongs to {1, 2}. If c = 1 then intersections a and b are connected by an one-way street from a to

b. If c = 2 then intersections a and b are connected by a two-way street. There is at most one street

connecting any two intersections.

Output

The output contains exactly the same number of lines as the number of two-way streets in the input.

For each such street (in any order) the program should write three integers a, b and c meaning, the new

direction of the street from a to b (c = 1) or that the street connecting a and b remains two-way (c = 2).

If there are more than one solution with maximal number of one-way streets then your program should

output any of them but just one.

Sample Input

4

1 1

2 2

2 1

3 2

Sample Output

4 1

1 2

中文说明

单向交通

在某个城镇，有n个交叉口由双向和单向街道连接。这个城镇非常

现代，许多街道穿过隧道或高架桥。当然可以在

双向的任意两个交叉口，即可以从交叉口A行驶到交叉口

以及从B到A，不违反交通规则。因为单行道比较安全，

决定创造尽可能多的单向交通。为了不造成太多的混乱

还决定不应改变现有单向街道的交通方向。

你的工作是在城里建立一个新的交通系统。你必须确定

尽可能多的双向街道的交通，并确保双向行驶仍然可能

在任何两个交叉口之间。

编写一个程序：

•从标准输入中读取城镇街道系统的描述，

•对于每条双向街道，确定一个交通方向或决定街道必须保持

双向，

•将答案写入标准输出。

输入

输入的第一行包含两个整数n和m，其中2≤n≤2000和n−1≤m≤n（n−1）/2。

整数n为城镇交叉口数，整数m为街道数。

接下来的m行中的每一行包含三个整数a、b和c，其中1≤a≤n、1≤b≤n、a=b和

C属于1，2。如果c=1，则交叉口A和B通过从A到B的单向街道连接。

B.如果c=2，则交叉口A和B通过双向街道连接。最多有一条街道

连接任何两个交叉点。

输出

输出包含的行数与输入中的双向街道数完全相同。

对于每一条这样的街道（以任何顺序），程序应写入三个整数a、b和c，表示新的

从A到B的街道方向（c=1）或连接A和B的街道保持双向（c=2）。

如果有多个解决方案具有最大单向街道数，那么您的程序应该

只输出其中一个。

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1.割点：若删掉某点后，原连通图分裂为多个子图，则称该点为割点。

2.割点集合：在一个无向连通图中，如果有一个顶点集合，删除这个顶点集合，以及这个集合中所有顶点相关联的边以后，原图变成多个连通块，就称这个点集为割点集合。

3.点连通度：最小割点集合中的顶点数。

4.割边(桥)：删掉它之后，图必然会分裂为两个或两个以上的子图。

5.割边集合：如果有一个边集合，删除这个边集合以后，原图变成多个连通块，就称这个点集为割边集合。

6.边连通度：一个图的边连通度的定义为，最小割边集合中的边数。

7.缩点：把没有割边的连通子图缩为一个点，此时满足任意两点之间都有两条路径可达。

注：求块<>求缩点。缩点后变成一棵k个点k-1条割边连接成的树。而割点可以存在于多个块中。

8.双连通分量：分为点双连通和边双连通。它的标准定义为：点连通度大于1的图称为点双连通图，边连通度大于1的图称为边双连通图。通俗地讲，满足任意两点之间，能通过两条或两条以上没有任何重复边的路到达的图称为双连通图。无向图G的极大双连通子图称为双连通分量。

package com.liuzhen.practice;

import java.util.ArrayList;
import java.util.Scanner;
import java.util.Stack;

public class Main {
    public static int n;  //给定图的顶点数
    public static int count;  //记录遍历次序
    public static int[] DFN;
    public static int[] Low;
    public static int[] parent;   //parent[i] = j，表示顶点i的直接父母顶点为j
    public static Stack<Integer> stack;
    public static ArrayList<edge>[] map;
    public static ArrayList<edge> ans;  //存储最终输出结果

    static class edge {
        public int a;  //边的起点
        public int b;  //边的终点
        public int c;  //c = 1表示单向边，c = 2表示双向边

        public edge(int a, int b, int c) {
            this.a = a;
            this.b = b;
            this.c = c;
        }
    }

    @SuppressWarnings("unchecked")
    public void init() {
        count = 0;
        DFN = new int[n + 1];
        Low = new int[n + 1];
        parent = new int[n + 1];
        stack = new Stack<Integer>();
        map = new ArrayList[n + 1];
        ans = new ArrayList<edge>();
        for(int i = 1;i <= n;i++) {
            DFN[i] = -1;
            Low[i] = -1;
            parent[i] = -1;
            map[i] = new ArrayList<edge>();
        }
    }

    public void TarJan(int start, int father) {
        DFN[start] = count++;
        Low[start] = DFN[start];
        parent[start] = father;
        stack.push(start);
        for(int i = 0;i < map[start].size();i++) {
            edge temp = map[start].get(i);
            int j = temp.b;
            if(DFN[j] == -1) {
                TarJan(j, start);
                Low[start] = Math.min(Low[start], Low[j]);
                if(temp.c == 2) {
                    if(Low[j] > DFN[start]) {   //当边temp为割边(或者桥)时
                        ans.add(temp);
                    } else {
                        ans.add(new edge(temp.a, temp.b, 1));
                    }
                }
            } else if(j != parent[start]) {  //当j不是start的直接父母节点时
                Low[start] = Math.min(Low[start], DFN[j]);
                if(temp.c == 2) {
                    ans.add(new edge(temp.a, temp.b, 1));
                }
            }
        }
    }

    public void getResult() {
        for(int i = 1;i <= n;i++) {
            if(parent[i] == -1)
                TarJan(i, 0);
        }
        for(int i = 0;i < ans.size();i++)
            System.out.println(ans.get(i).a+" "+ans.get(i).b+" "+ans.get(i).c);
    }

    public static void main(String[] args) {
        Main test = new Main();
        Scanner in = new Scanner(System.in);
        n = in.nextInt();
        int k = in.nextInt();
        test.init();
        for(int i = 0;i < k;i++) {
            int a = in.nextInt();
            int b = in.nextInt();
            int c = in.nextInt();
            map[a].add(new edge(a, b, c));
            if(c == 2)
                map[b].add(new edge(b, a, c));
        }
        test.getResult();
    }
}

运行结果：

4
1 1
2 2
2 1
3 2
4 1
3 2