原题链接https://www.luogu.com.cn/problem/P8749

有组合数的性质

#include <iostream>
#include <map>
#include <cmath>

#define ll long long
ll n;
const ll inf = 1e9;

ll C(ll a,ll b){
    ll res = 1;
    for(ll i = a,j = 1; j <= b; i --,j ++){
        res =  res * i / j;
        if(res > n) return res;
    }
    return res;
}

void solve(){
    std::cin >> n;
    if(n == 1){
        std::cout << 1;
        return ;
    }
    for(ll i = 16; i >= 0; i --){
        ll l = 2 * i;
        ll r = inf;
        while(l <= r){
            ll mid = (l + r) >> 1;
            ll ans = C(mid,i);
            if(ans == n){
                std::cout << (mid * (mid + 1)) / 2 + i + 1 << "\n";
                return;
            }
            else if(ans < n){
                l = mid + 1;
            }
            else r = mid - 1;
        }
    }
    return ;
}

int main(){
    ll t = 1;
    while(t --)
    solve();
    return 0;
}