acdeream Matrix Multiplication

D - Matrix Multiplication

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

SubmitStatus

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

/*
* this code is made by 987690183
* Problem: 1213
* Verdict: Accepted
* Submission Date: 2014-10-14 13:40:27
* Time: 236MS
* Memory: 1716KB
*/
#include<iostream>
#include<stdio.h>
#include<cstring>
#include<cstdlib>
using namespace std;
 
int num[10002];
long long get(int n,int m)/**Cn,m**/
{
    long long sum = 1;
    for(int i=1,j=n;i<=m;i++,j--)
        sum=sum*j/i;
    return sum;
}
int main()
{
    int n,m,x,y;
    int hxl=  0;
    while(scanf("%d%d",&n,&m)>0)
    {
        memset(num,0,sizeof(num));
        for(int i=1;i<=m;i++)
        {
            scanf("%d%d",&x,&y);
            num[x]++;
            num[y]++;
            hxl = hxl+2;
        }
        long long tom = hxl;
        for(int i=1;i<=10000;i++)
        if(num[i]>=2)
        {
            tom=tom+get(num[i],2)*2;
        }
        printf("%lld\n",tom);
    }
    return 0;
}