4 Values whose Sum is 0(二分)

　　　　　　　　　　　　　　4 Values whose Sum is 0

Time Limit: 15000MS		Memory Limit: 228000K
Total Submissions: 21370		Accepted: 6428
Case Time Limit: 5000MS

Description

The SUM problem can be formulated as follows: given four lists A, B, C, D of integer values, compute how many quadruplet (a, b, c, d ) ∈ A x B x C x D are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n .

Input

The first line of the input file contains the size of the lists n (this value can be as large as 4000). We then have n lines containing four integer values (with absolute value as large as 2²⁸ ) that belong respectively to A, B, C and D .

Output

For each input file, your program has to write the number quadruplets whose sum is zero.

Sample Input

6

-45 22 42 -16

-41 -27 56 30

-36 53 -37 77

-36 30 -75 -46

26 -38 -10 62

-32 -54 -6 45

Sample Output

5

Hint

Sample Explanation: Indeed, the sum of the five following quadruplets is zero: (-45, -27, 42, 30), (26, 30, -10, -46), (-32, 22, 56, -46),(-32, 30, -75, 77), (-32, -54, 56, 30).

Source

Southwestern Europe 2005

// 题意: 比如例子 6 行，每行 4 个数，从第一，二，三，四列各选一个数，要使和为 0 ，有几种组合?

n 最大有4000，但还是可以暴力，加二分

a + b = -( c + d )

枚举 a + b ,对于 c + d ,枚举一次，用一个大数组保存和，sort ，就可以二分了。要注意的是，二分到了要对左右继续搜索一下，不同的位置代表有不同的组合

 #include <iostream>
 #include <stdio.h>
 #include <string.h>
 #include <algorithm>

 using namespace std;

 int n;
 int k;

 int num[][];
 int s[];

 int erfen(int t)
 {
     int l=,r=k-;
     while (l<=r)
     {
         int mid=(l+r)/;
         if (s[mid]==t)
         {
             int e = mid-;
             int  all=;
             while (e>=&&s[e]==t)
                 e--,all++;
             e=mid+;
             while (e<k&&s[e]==t)
                 e++,all++;
             return all;
         }
         else if (s[mid]>t)
             r=mid-;
         else
             l=mid+;
     }
     return ;
 }

 int main()
 {
     while (scanf("%d",&n)!=EOF)
     {
         for (int i=;i<n;i++)
             scanf("%d%d%d%d",&num[i][],&num[i][],&num[i][],&num[i][]);
         k=;
         for (int i=;i<n;i++)
             for (int j=;j<n;j++)
             s[k++]=-(num[i][]+num[j][]);
         sort(s,s+k);
         int total=;
         for (int i=;i<n;i++)
         {
             for (int j=;j<n;j++)
             {
                 int left=num[i][]+num[j][];
                 total+=erfen(left);
             }
         }
         printf("%d\n",total);
     }
     return ;
 }