题目：
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:
The range of n is [3, 10^18].The string representing n is always valid and will not have leading zeros.代码：
class Solution { public: string smallestGoodBase(string n) { long long num = stol(n); for (int i = log(num + 1) / log(2); i >= 2; --i) { long long left = 2, right = pow(num, 1.0 / (i - 1)) + 1; while (left < right) { long long mid = left + (right - left) / 2, sum = 0; for (int j = 0; j < i; ++j) { sum = sum * mid + 1; } if (sum == num) return to_string(mid); if (sum < num) left = mid + 1; else right = mid; } } return to_string(num - 1); } };想法：
结合数学知识，先固定指数m，再固定基数k，然后使用二分搜索法查找合适的数字。
