acdeream Matrix Multiplication

D - Matrix Multiplication

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

Submit Status

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

 1 /*

 2 * this code is made by 987690183

 3 * Problem: 1213

 4 * Verdict: Accepted

 5 * Submission Date: 2014-10-14 13:40:27

 6 * Time: 236MS

 7 * Memory: 1716KB

 8 */

 9 #include<iostream>

10 #include<stdio.h>

11 #include<cstring>

12 #include<cstdlib>

13 using namespace std;

14  

15 int num[10002];

16 long long get(int n,int m)/**Cn,m**/

17 {

18     long long sum = 1;

19     for(int i=1,j=n;i<=m;i++,j--)

20         sum=sum*j/i;

21     return sum;

22 }

23 int main()

24 {

25     int n,m,x,y;

26     int hxl=  0;

27     while(scanf("%d%d",&n,&m)>0)

28     {

29         memset(num,0,sizeof(num));

30         for(int i=1;i<=m;i++)

31         {

32             scanf("%d%d",&x,&y);

33             num[x]++;

34             num[y]++;

35             hxl = hxl+2;

36         }

37         long long tom = hxl;

38         for(int i=1;i<=10000;i++)

39         if(num[i]>=2)

40         {

41             tom=tom+get(num[i],2)*2;

42         }

43         printf("%lld\n",tom);

44     }

45     return 0;

46 }