# 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.

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

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 )

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

using namespace std;

int n;
int k;

][];
];

int erfen(int t)
{
,r=k-;
while (l<=r)
{
;
if (s[mid]==t)
{
;
;
&&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+;
}
;
}

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

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