二分尋找的應用

標籤：

 1 #include <iostream> 2 #include <algorithm> 3 #include <cstdio> 4 using namespace std; 5  6 int a1[4001],a2[4001]; 7 int b1[4001],b2[4001]; 8 int sum1[4001*4000],sum2[4001*4000]; 9 10 int  binarySearch(int left,int right,int key)11 {12     __int64 ans=0; //64位整數13     while(left<=right)14     {15         int mid = (left + right) / 2;16         if(sum2[mid] == key)17         {18             ans++;19             for(int i=mid-1; i>=left; i--)   //搜到後可能相鄰的左邊有相等的也滿足條件的數！20             {21                 if(sum2[i]!=key)22                 {23                     break;24                 }25                 ans++;26             }27             for(int j=mid+1; j<=right; j++)28             {29                 if(sum2[j]!=key)30                 {31                     break;32                 }33                 ans++;34             }35             return ans;36         }37         else if(sum2[mid] < key) left = mid+1;38         else right = mid -1;39     }40     return 0;41 }42 43 int main()44 {45     int n;46     cin>>n;47     __int64 ans=0;48     for(int i = 0; i < n; i++)49     {50         cin>>a1[i]>>a2[i]>>b1[i]>>b2[i];51 52     }53     int times = 0;54     for(int i = 0; i < n; i++) //四數相加轉化為兩數，通過兩兩隨機相加，以便二分55         for(int j = 0; j < n; j++)56         {57             sum1[times] = a1[i] + a2[j];58             sum2[times] = b1[i] + b2[j];59             times++; //加時的下表60         }61     sort(sum2,sum2 + times);62 63     for(int i = 0; i < times; i++)64     {65         int key = -sum1[i];66         ans += binarySearch(0,times-1,key);67     }68     cout<<ans<<endl;69     return 0;70 }

View Code二分 基礎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 -4626 -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).

二分尋找的應用