ACdream 1213 Matrix Multiplication(矩阵相乘)

Matrix Multiplication

Time Limit: 2000/1000MS (Java/Others)  Memory Limit: 128000/64000KB (Java/Others)

Submit  Statistic  Next Problem

Problem Description

      Let us consider undirected graph G = {V; E} which has N vertices and M edges. Incidence matrix of this graph is N × M matrix A = {a i,j}, such that a i,j is 1 if i-th vertex is one of the ends of j -th edge and 0 in the other case. Your task is to find the sum of all elements of the matrix A TA.

Input

      The first line of the input file contains two integer numbers — N and M (2 ≤ N ≤ 10 000, 1 ≤ M ≤100 000). Then 2*M integer numbers follow, forming M pairs, each pair describes one edge of the graph. All edges are different and there are no loops (i.e. edge ends are distinct).

Output

      Output the only number — the sum requested.

Sample Input

4 4
1 2
1 3
2 3
2 4

Sample Output

18

其实就是一个矩阵，自己乘自己，画图可以秒懂

java:

import java.util.*;
import java.io.*;
import java.math.*;

public class Main{
	static final int MAXN = 10000 + 5;
	static int [] mp = new int[MAXN];
	public static void main(String [] agrv)
	throws IOException
	{
		//System.setIn(new FileInputStream(new File("D:" + File.separator + "imput.txt")));
		Scanner cin = new Scanner(System.in);
		int N, M, u, v;
		while(cin.hasNext()){
			N = cin.nextInt();
			M = cin.nextInt();
			Arrays.fill(mp, 1, N + 1, 0);
			for(int i = 1;i <= M ;i ++){
				u = cin.nextInt();
				v = cin.nextInt();
				if(u == v) mp[v] ++;
				else {
					mp[v] ++;
					mp[u] ++;
				}
			}
			long ans = 0;
			for(int i = 1;i <= N;i ++){
				ans += (long)mp[i] * mp[i];
			}
			System.out.println(ans);
		}
	}
}