1404. Number of Steps to Reduce a Number in Binary Representation to One

[mah-shamim]

Discussed in #271

^{Originally posted by mah-shamim August 9, 2024}
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: "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'