文章标题 SPOJ PHT ： Pigeonhole Tower（二分）

Pigeonhole Tower

Pigeon SSNA want to build a tower with some wood walls. Let’s describe the tower they want to make:

A Tower can consist of different number of level.
If a tower contain L levels then 1st level must contain L holes , 2nd level L-1 , 3rd level L-2 ….. L level contain 1 hole .
Each room contain 3 wood walls.
See the picture below:

3 level 4level
3 Level Tower 4 Level tower
Now pigeon SSNA has n wood walls. What is maximum number of level he can made.

Input

Input starts with an integer T (≤ 100000), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1012)

Output

For each case of input you have to print the case number and expected answer.

Sample Input

Output for Sample Input

2
15
24
Case 1: 3
Case 2: 4
题意： 给你n个木棒，然后看能堆成几层。
分析：通过看规律可知每层的数目是一个等差数列，所以对于所给数目n可以通过二分查找n所在的区间，通过所给数据可知，层数在1~1*10^6之间。
代码：

#include
#include
#include
#include
#include
#include
#include
#include 
#include
using namespace std;
const int inf = 0x3f3f3f3f;
long long n;
int bs(){
    long long lo=1,hi=10e6;
    long long mid;
    while (lo2;
        //如果找到区间就直接返回
        if (n2)&&n>=(mid-1)*(mid+1)) return mid-1;
        if (n>=mid*(mid+2))lo=mid;
        else hi=mid;
    }
}
int main ()
{
    int t;
    scanf ("%d",&t);
    int cnt=1;
    while (t--){
        scanf ("%lld",&n);
        if (n<3){
            printf ("Case %d: 0\n",cnt++);
            continue;
        }
        int ans=bs();
        printf ("Case %d: %d\n",cnt++,ans);
    }   
    return 0;
}