[leetcode]483. Smallest Good Base

题目链接：https://leetcode.com/problems/smallest-good-base/description/

For an integer n, we call k>=2 a good base of n, if all digits of n base k are 1.

Now given a string representing n, you should return the smallest good base of n in string format. 

Example 1:

Input: "13"Output: "3"Explanation: 13 base 3 is 111.

Example 2:

Input: "4681"Output: "8"Explanation: 4681 base 8 is 11111.

Example 3:

Input: "1000000000000000000"Output: "999999999999999999"Explanation: 1000000000000000000 base 999999999999999999 is 11.

Note:

1. The range of n is [3, 10^18].
2. The string representing n is always valid and will not have leading zeros.

class Solution {public:    string smallestGoodBase(string n) {        unsigned long long tn=(unsigned long long)stoll(n);        unsigned long long x=1;        for(int i=62;i>=1;i--)        {            if((x<<i)<tn)            {                unsigned long long cur=mysolve(tn,i);                if(cur!=0) return to_string(cur);            }        }        return to_string(tn-1);    }private:    unsigned long long mysolve(unsigned long long n,int d)    {                unsigned long long right=(unsigned long long)(pow(n,1.0/d)+1);        unsigned long long left=1;        while(left<=right)        {            unsigned long long mid=left+(right-left)/2;            unsigned long long sum=1,cur=1;            for(int i=1;i<=d;i++)            {                cur*=mid;                sum+=cur;            }            if(sum==n) return mid;            if(sum>n) right=mid-1;            else left=mid+1;        }        return 0;    }};