Number of Steps to Reduce a Number in Binary Representation to One

Given the binary representation of an integer as a string s, return the number of steps to reduce it to 1 under the following rules:

• If the current number is even, you have to divide it by 2.

• If the current number is odd, you have to add 1 to it.

It is guaranteed that you can always reach one for all test cases.

Example 1:

Input: s = "1101"
Output: 6
Explanation: "1101" corressponds to number 13 in their decimal representation.
Step 1) 13 is odd, add 1 and obtain 14. 
Step 2) 14 is even, divide by 2 and obtain 7.
Step 3) 7 is odd, add 1 and obtain 8.
Step 4) 8 is even, divide by 2 and obtain 4. 
Step 5) 4 is even, divide by 2 and obtain 2. 
Step 6) 2 is even, divide by 2 and obtain 1. 

Example 2:

Input: s = "10"
Output: 1
Explanation: "10" corressponds to number 2 in their decimal representation.
Step 1) 2 is even, divide by 2 and obtain 1. 

Example 3:

Input: s = "1"
Output: 0

Constraints:

• 1 <= s.length <= 500
• s consists of characters '0' or '1'
• s[0] == '1'

SOLUTION:

class Solution:
    def numSteps(self, s: str) -> int:
        steps = 0
        while s != "1":
            if s[-1] == "0":
                s = s[:-1]
            else:
                i = len(s) - 1
                carry = 1
                while carry > 0 and i >= 0:
                    curr = int(s[i]) + carry
                    s = s[:i] + str(curr % 2) + s[i+1:]
                    carry = curr // 2
                    i -= 1
                if carry > 0:
                    s = "1" + s
            steps += 1
        return steps