C++ 代码

#include <iostream>
#include <cstring>
#include <algorithm>

using namespace std;

typedef long long LL;

int n;

LL C(int a, int b) // 求排列组合C
{
    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) // 二分找到大于n的最小的数
{
    LL l = k * 2, r = max((LL)n, l);
    while (l < r)
    {
        LL mid = l + r >> 1;
        if (C(mid, k) >= n) r = mid;
        else l = mid + 1;
    }
    if (C(r, k) != n) return false;

    cout << r * (r + 1) / 2 + k + 1 << endl;

    return true;
}

int main()
{
    cin >> n;
    for (int k = 16; ; k -- ) // 从第16个斜行(最下面的斜行)开始遍历
        if (check(k))
            break;
    return 0;
}