Smallest Good Base

Given an integer n represented as a string, return the smallest good base of n.

We call k >= 2 a good base of n, if all digits of n base k are 1's.

Example 1:

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

Example 2:

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

Example 3:

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

Constraints:

• n is an integer in the range [3, 1018].
• n does not contain any leading zeros.

SOLUTION:

class Solution:
    def getNum(self, base, l):
        val = 0
        for _ in range(l):
            val = base * val + 1
        return val

    def smallestGoodBase(self, n: str) -> str:
        n = int(n)
        for l in range(len("{:b}".format(n)), 1, -1):
            beg = 2
            end = n - 1
            while beg <= end:
                mid = (beg + end) // 2
                val = self.getNum(mid, l)
                if val == n:
                    return str(mid)
                elif beg == end:
                    break
                elif val < n:
                    beg = mid + 1
                else:
                    end = mid