POJ 2785 4 Values whose Sum is 0 （折半搜索 ）

【题目链接】：click here~~

【题目大意】：

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 .

【思路】：当数据很大，无法进行全部搜索判断，可以采用折半搜索，将数据规模缩小一半，从而进行判断，此题，我们考虑先预处理a,b数组的和，那么只要找到满足

c[i]+d[i]=-(a[i]+b[i])条件即可。对于如何寻找，这里巧妙利用了STL的upper_bound and lower_bound我们知道upper_bound 返回的在前闭后开区间查找的关键字的上界,lower_bound返回的在前闭后开区间查找的关键字的下界，用上界减去下界即可得到区间内满足条件的个数，累加即可。

代码：

/*  * Problem: POJ No.2785* Running time: 6844MS  * Complier: G++  * Author: herongwei * Create Time: 8:24 2015/9/30 星期三*/  #include <stdio.h>#include <string.h>#include <iostream>#include <algorithm>using namespace std;typedef long long LL;const int MAXN =4005;int a[MAXN],b[MAXN],c[MAXN],d[MAXN];int ab[MAXN*MAXN]; /// !!! maxn*maxnint n,m;LL res;int main(){    while(~scanf("%d",&n))    {        memset(a,0,sizeof(a));memset(b,0,sizeof(b));        memset(c,0,sizeof(c));memset(d,0,sizeof(d));        memset(cd,0,sizeof(cd));        for(int i=0; i<n; ++i)            scanf("%d%d%d%d",&a[i],&b[i],&c[i],&d[i]);        res=0;        int ll=0;        for(int i=0; i<n; ++i)        {            for(int j=0; j<n; ++j)            {                ab[ll++]=a[i]+b[j];            }        }        sort(ab,ab+ll);        for(int i=0; i<n; ++i)        {            for(int j=0; j<n; ++j)            {                int cd=-(c[i]+d[j]);                res+=upper_bound(ab,ab+ll,cd)-lower_bound(ab,ab+ll,cd);            }        }        printf("%lld\n",res);    }}