字典序的第K小数字

今天zyb参加一场面试,面试官听说zyb是ACMer之后立马抛出了一道算法题给zyb:
有一个序列,是1到n的一种排列,排列的顺序是字典序小的在前,那么第k个数字是什么?
例如n=15,k=7, 排列顺序为1, 10, 11, 12, 13, 14, 15, 2, 3, 4, 5, 6, 7, 8, 9;那么第7个数字就是15.
那么,如果你处在zyb的场景下,你能解决这个问题吗

题解

https://blog.csdn.net/FJJ543/article/details/81908992

#include<bits/stdc++.h>
using namespace std ;
#define LL long long
#define INF 0x3f3f3f3f
#define mod 1000000007
int FF(int n , int k)
{
     int curr = ;
        k = k - ;
        while (k > ) {
            long steps = , first = curr, last = curr + ;
            while (first <= n) {
                steps += min((long)n + , last) - first;
                first *= ;
                last *= ;
            }
            if (steps <= k) {
                curr += ;
                k -= steps;
            } else {
                curr *= ;
                k -= ;
            }
        }
        return curr;
}
 
int main()
{
 
    int T;
    scanf("%d",&T);
    while(T--)
    {
        int n,k;
        scanf("%d%d",&n,&k);
        k--;
        int cnt=;
        while(k)
        {
            int st= , head=cnt , tail = cnt+;
            while(head<=n)
            {
                st+=min(n+,tail) - head;
                head*=;
                tail*=;
            }
            if(st<=k)
            {
                cnt++;
                k-=st;
            }
            else
            {
                cnt*=;
                k--;
            }
        }
        printf("%d\n",cnt);
    }
    return ;
}