解释

code

#include<iostream>
#include<algorithm>
#include<cstdio>

using namespace std;

typedef long long LL;

int n;

LL c(int a,int b)
{   
    // c(a,b) = a! / b! / (a-b)!
    // a > b
    // a ... a-b   1 ... b
    LL res = 1;
    for(int i = a, j = 1;j <= b;i--,j ++)
    {
     res = res * i / j;
     if (res > n)
     return res;
     }
     return res;
}

bool check(int k)
{
    int l = 2 * k; int r = max(n,2 * k);

    while(l < r)
    {   
        int mid = (l + r) >> 1; 
        if(c(mid,k) >= (LL)n)  r = mid;
        else l = mid + 1;
    }
    if(c(r,k) != n) return false;
    else cout << 1ll * r * (r + 1) / 2 + k + 1 << endl;

    return true;
}


int main()
{   
   cin >> n;

   for(int k = 16; ; k--)
   if(check(k)) break;

   return 0;
}

参考: https://www.acwing.com/solution/content/47358/