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 2 28 ) 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).
题目求a+b+c+d=0的组合数,等价于a+b=-(c+d)的组合数
upper_bound(begin,end,num)-----→找到大于num的第一个数,返回地址
lower_bound(begin,end,num)-----→找到大于等于(重点!)num的第一个数,返回地址
upper_bound(begin,end,num)-lower_bound(begin,end,num)-----→若为1,存在num;若为0,不存在
#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
const int maxn=40005;
using namespace std;
int ans=0,n;
int a[maxn],b[maxn],c[maxn],d[maxn],f[16000005];
int main()
{
scanf("%d",&n);
for(int i=1;i<=n;i++)scanf("%d %d %d %d",&a[i],&b[i],&c[i],&d[i]);
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
f[(i-1)*n+j]=c[i]+d[j];
sort(f+1,f+1+n*n);
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
{
int F=-a[i]-b[j];
ans+=upper_bound(f+1,f+n*n+1,F)-lower_bound(f+1,f+n*n+1,F);
}
printf("%d\n",ans);
return 0;
}