K - 4 Values whose Sum is 0(中途相遇法)

K - 4 Values whose Sum is 0

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Submit Status Practice UVA 1152

Appoint description:
System Crawler (2015-03-12)

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 ) AxBxCxD are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n .

Input

The input begins with a single positive integer on a line by itself indicating the number of the cases following, each of them as described below. This line is followed by a blank line, and there is also a blank line between two consecutive inputs.

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 test case, the output must follow the description below. The outputs of two consecutive cases will be separated by a blank line.

For each input file, your program has to write the number quadruplets whose sum is zero.

Sample Input

1

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

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).

 #include <iostream>
 #include <cstdio>
 #include <cstring>
 #include <cmath>
 #include <algorithm>
 #include <string>
 #include <vector>
 #include <stack>
 #include <queue>
 #include <set>
 #include <map>
 #include <list>
 #include <iomanip>
 #include <cstdlib>
 #include <sstream>
 using namespace std;
 typedef long long LL;
 const int INF=0x5fffffff;
 const double EXP=1e-;
 const int MS=;
 int A[MS],B[MS],C[MS],D[MS],n,sum[MS*MS];

 int main()
 {
     int T;
     scanf("%d",&T);
     while(T--)
     {
         scanf("%d",&n);
         for(int i=;i<n;i++)
             scanf("%d%d%d%d",&A[i],&B[i],&C[i],&D[i]);
         int cnt=;
         for(int i=;i<n;i++)
             for(int j=;j<n;j++)
                 sum[cnt++]=A[i]+B[j];
         sort(sum,sum+cnt);
         LL ans=;
         for(int i=;i<n;i++)
             for(int j=;j<n;j++)
         {
             ans+=upper_bound(sum,sum+cnt,-C[i]-D[j])-lower_bound(sum,sum+cnt,-C[i]-D[j]);
         }
         printf("%lld\n",ans);
         if(T)
             printf("\n");
     }
     return ;
 }