POJ2785 4 Values whose Sum is 0 【枚举】

4 Values whose Sum is 0

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

/*
** Problem: POJ2785
** Status: Accepted
** Running Time: 6766ms
** Author: Changmu
**
** 题解：将解空间分成两部分分别枚举。
*/

#include <cstdio>
#include <cstring>
#include <algorithm>

#define maxn 4010
typedef __int64 LL;
using namespace std;

int A[4][maxn], CD[maxn * maxn];

int main() {
    LL ret = 0;
    int i, j, n, id = 0, tmp;
    scanf("%d", &n);
    for(i = 0; i < n; ++i) {
        for(j = 0; j < 4; ++j)
            scanf("%d", &A[j][i]);
    }
    for(i = 0; i < n; ++i)
        for(j = 0; j < n; ++j)
            CD[id++] = A[2][i] + A[3][j];
    sort(CD, CD + id);

    for(i = 0; i < n; ++i)
        for(j = 0; j < n; ++j) {
            tmp = A[0][i] + A[1][j];
            ret += upper_bound(CD, CD + id, -tmp) - lower_bound(CD, CD + id, -tmp);
        }
    printf("%I64d\n", ret);
}