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Abhishek Chaudhary

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# 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
``````