4 Values whose Sum is 0
Time Limit: 15000MS   Memory Limit: 228000K
Total Submissions: 18221   Accepted: 5363
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).

题意是给出4列数,从每一列中挑选一个数字,问有多少种方法使这四个数的和为0。

求出每两列的数的和,再二分查找。

代码:

#include <iostream>
#include <algorithm>
#include <cmath>
#include <vector>
#include <string>
#include <cstring>
#include <map>
#pragma warning(disable:4996)
using namespace std; int a[4005],b[4005],c[4005],d[4005];
int sum1[4005*4005],sum2[4005*4005];
int n; int main()
{
//freopen("i.txt","r",stdin);
//freopen("o.txt","w",stdout); int i,j; scanf("%d",&n); for(i=1;i<=n;i++)
{
scanf("%d%d%d%d",a+i,b+i,c+i,d+i);
} int num1=0;
for(i=1;i<=n;i++)
{
for(j=1;j<=n;j++)
{
sum1[++num1] = -(a[i]+b[j]);
sum2[num1] = (c[i]+d[j]);
}
}
sort(sum1+1,sum1+1+num1);
sort(sum2+1,sum2+1+num1); int ans=0;
sum1[0]= -268435456*2 - 1;
sum1[num1+1] = 268435456*2 + 1;
for(i=1;i<=num1;i++)
{
int left = 0;
int right = num1+1;
int mid;
while(left<right)
{
mid=(left+right)/2;
if(sum2[i]<=sum1[mid])
{
right=mid;
}
else
{
left= mid+1;
}
}
while(sum2[i]==sum1[right]&&right<=num1)
{
ans++;
right++;
}
} printf("%d\n",ans);
//system("pause");
return 0;
}

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