UVa10596 - Morning Walk(并查集)

Kamal is a Motashota guy. He has got a new job in Chittagong. So, he has moved to Chittagong from Dinajpur. He was getting fatter inDinajpur as he had no work in his hand there. So, moving to Chittagong has turned to be a blessing for him. Every morning he takes a walk through the hilly roads of charming city Chittagong. He is enjoying this city very much. There are so many roads in Chittagong and every morning he takes different paths for his walking. But while choosing a path he makes sure he does not visit a road twice not even in his way back home. An intersection point of a road is not considered as the part of the road. In a sunny morning, he was thinking about how it would be if he could visit all the roads of the city in a single walk. Your task is to help Kamal in determining whether it is possible for him or not.

 

Input

Input will consist of several test cases. Each test case will start with a line containing two numbers. The first number indicates the number of road intersections and is denoted by N (2 ≤ N ≤ 200). The road intersections are assumed to be numbered from 0 to N-1. The second number Rdenotes the number of roads (0 ≤ R ≤ 10000). Then there will be R lines each containing two numbers c₁ and c₂ indicating the intersections connecting a road.

 

Output

Print a single line containing the text “Possible” without quotes if it is possible for Kamal to visit all the roads exactly once in a single walk otherwise print “Not Possible”.

 

Sample Input	Output for Sample Input
2 2 0 1 1 0 2 1 0 1	Possible Not Possible

import java.io.FileInputStream;
import java.io.InputStreamReader;
import java.io.BufferedReader;
import java.io.PrintWriter;
import java.io.OutputStreamWriter;
import java.io.StreamTokenizer;

class Main
{
	public static final boolean DEBUG = false;
	public static int N = 30;
	public BufferedReader cin;
	public PrintWriter cout;
	public StreamTokenizer tokenizer;
	public int n, r;
	public int[] p, d;
	
	public void init()
	{
		try {
			if (DEBUG) {
				cin = new BufferedReader(new InputStreamReader(
						new FileInputStream("d:\\OJ\\uva_in.txt")));
			} else {
				cin = new BufferedReader(new InputStreamReader(System.in));
			}
			
			cout = new PrintWriter(new OutputStreamWriter(System.out));
			tokenizer = new StreamTokenizer(cin);
		} catch (Exception e) {
			e.printStackTrace();
		}
	}
	
	public String next()
	{
		try {
			tokenizer.nextToken();
			if (tokenizer.ttype == StreamTokenizer.TT_EOF)
				return null;
			else if (tokenizer.ttype == StreamTokenizer.TT_NUMBER) {
				return String.valueOf((int) tokenizer.nval);
			}

			return null;
		} catch (Exception e) {
			e.printStackTrace();
			return null;
		}
	}
	
	public int find(int x)
	{
		return p[x] == x ? x : (p[x] = find(p[x]));
	}
	
	public boolean input()
	{
		String s = next();
		if (s == null) return false;
		
		n = Integer.parseInt(s);
		s = next();
		r = Integer.parseInt(s);
		
		p = new int[n];
		d =new int[n];
		for (int i = 0; i < n; i++) {
			p[i] = i;
			d[i] = 0;
		}
		
		for (int i = 0; i < r; i++) {
			s = next();
			int a = Integer.parseInt(s);
			s = next();
			int b = Integer.parseInt(s);
			p[find(b)] = find(a);
			d[a]++;
			d[b]++;
		}
		
		return true;
	}
	
	
	public void solve()
	{
		boolean ok = true;
		
		if (n == 0 || r <= 1) ok = false;
		
		int root = find(0);
		for (int i = 0; i < n && ok; i++) {
			if (d[i] != 0) {
				if (find(i) != root || d[i] % 2 != 0) {
					ok = false;
					break;
				}
			}
		}
		
		if (ok) {
			cout.println("Possible");
		} else {
			cout.println("Not Possible");
		}
		
		cout.flush();
	}
	
	public static void main(String[] args)
	{
		Main solver = new Main();
		solver.init();
		
		while (solver.input()) {
			solver.solve();
		}
	}
}