二分求解 三角形 stl的应用 涉及范围的二分查找可以先求上界再算下界，结果即上界减下界

 二分

Time Limit:2000MS     Memory Limit:32768KB     64bit IO Format:%lld & %llu

 

Description

You are given N sticks having distinct lengths; you have to form some triangles using the sticks. A triangle is valid if its area is positive. Your task is to find the number of ways you can form a valid triangle using the sticks.

Input

Input starts with an integer T (≤ 10), denoting the number of test cases.

Each case starts with a line containing an integer N (3 ≤ N ≤ 2000). The next line contains N integers denoting the lengths of the sticks. You can assume that the lengths are distinct and each length lies in the range [1, 10⁹].

Output

For each case, print the case number and the total number of ways a valid triangle can be formed.

Sample Input

3

5

3 12 5 4 9

6

1 2 3 4 5 6

4

100 211 212 121

Sample Output

Case 1: 3

Case 2: 7

Case 3: 4

 #include <iostream>
 #include <stdio.h>
 #include <algorithm>
 #include <math.h>

 using namespace std;
 typedef long long LL;
 LL a[+];
 int n;

 int Binary_search(int x)
 {
     int l = ,r = n-;
     while(l<=r)
     {
         int mid = (l+r)/;
         if(a[mid] == x)
             return mid;
         else if(a[mid] > x)
             r= mid-;
         else
             l = mid +;
     }
     return l;

 }

 int main()
 {
     int T;
     cin>>T;
     int flag = ;
     while(T--)
     {

         cin>>n;
         for(int i = ; i < n; i++)
             scanf("%lld",&a[i]);
         sort(a,a+n);
         int ans = ;
         for(int i = ; i < n-; i++)
             for(int j = i+; j < n; j++)
             {
                 LL sum = a[i] + a[j];
                 LL cha = abs(a[j] - a[i]);

                 int up = Binary_search(sum)-;
                 if(up <= j)
                     continue;
                 int low = Binary_search(cha);
                 if(low < j)
                     low = j;
                 ans +=  (up-low);

             }

         cout<<"Case "<<++flag<<": "<<ans<<endl;

     }
     return ;
 }

 #include <iostream>
 #include <stdio.h>
 #include <algorithm>
 #include <math.h>

 using namespace std;
 typedef long long LL;
 LL a[+];
 int n;

 int Binary_search(int x)
 {
     int l = ,r = n;
     while(l<r)
     {
         int mid = (l+r)/;
         if(a[mid] == x)
             return mid;
         else if(a[mid] > x)
             r= mid;
         else
             l = mid +;
     }
     return l;

 }

 int main()
 {
     int T;
     cin>>T;
     int flag = ;
     while(T--)
     {

         cin>>n;
         for(int i = ; i < n; i++)
             scanf("%lld",&a[i]);
         sort(a,a+n);
         int ans = ;
         for(int i = ; i < n-; i++)
             for(int j = i+; j < n; j++)
             {
                 LL sum = a[i] + a[j];
                 LL cha = abs(a[j] - a[i]);

                 int up = Binary_search(sum)-;
                 if(up <= j)
                     continue;
                 int low = Binary_search(cha);
                 if(low < j)
                     low = j;
                 ans +=  (up-low);

             }

         cout<<"Case "<<++flag<<": "<<ans<<endl;

     }
     return ;
 }

 #include <iostream>
 #include <stdio.h>
 #include <algorithm>
 #include <math.h>

 using namespace std;
 typedef long long LL;
 LL a[+];
 int n;

 int main()
 {
     int T;
     cin>>T;
     int flag = ;
     while(T--)
     {

         cin>>n;
         for(int i = ; i < n; i++)
             scanf("%lld",&a[i]);
         sort(a,a+n);
         int ans = ;
         for(int i = ; i < n-; i++)
             for(int j = i+; j < n; j++)
             {
                 LL sum = a[i] + a[j];
                 LL cha = abs(a[j] - a[i]);

                 int up = upper_bound(a+j+,a+n,sum)-a;

                 int low = lower_bound(a+j+,a+n,cha)-a;

                 ans +=  (up-low);

             }

         cout<<"Case "<<++flag<<": "<<ans<<endl;

     }
     return ;
 }