二分查找的应用

#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;

int a1[4001],a2[4001];
int b1[4001],b2[4001];
int sum1[4001*4000],sum2[4001*4000];

int  binarySearch(int left,int right,int key)
{
    __int64 ans=0; //64位整数
    while(left<=right)
    {
        int mid = (left + right) / 2;
        if(sum2[mid] == key)
        {
            ans++;
            for(int i=mid-1; i>=left; i--)   //搜到后可能相邻的左边有相等的也满足条件的数！
            {
                if(sum2[i]!=key)
                {
                    break;
                }
                ans++;
            }
            for(int j=mid+1; j<=right; j++)
            {
                if(sum2[j]!=key)
                {
                    break;
                }
                ans++;
            }
            return ans;
        }
        else if(sum2[mid] < key) left = mid+1;
        else right = mid -1;
    }
    return 0;
}

int main()
{
    int n;
    cin>>n;
    __int64 ans=0;
    for(int i = 0; i < n; i++)
    {
        cin>>a1[i]>>a2[i]>>b1[i]>>b2[i];

    }
    int times = 0;
    for(int i = 0; i < n; i++) //四数相加转化为两数，通过两两随机相加，以便二分
        for(int j = 0; j < n; j++)
        {
            sum1[times] = a1[i] + a2[j];
            sum2[times] = b1[i] + b2[j];
            times++; //加时的下表
        }
    sort(sum2,sum2 + times);

    for(int i = 0; i < times; i++)
    {
        int key = -sum1[i];
        ans += binarySearch(0,times-1,key);
    }
    cout<<ans<<endl;
    return 0;
}

二分 基础

Time Limit:15000MS     Memory Limit:228000KB     64bit IO Format:%I64d & %I64u

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 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).