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

Problem Description

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.

Key Insights

• The binary representation can be treated as a sequence of bits to determine the number's parity.
• Operations depend on whether the number is odd or even:
  • Odd numbers require an addition operation to make them even.
  • Even numbers can be halved, significantly reducing their value.
• The process continues until the number is reduced to 1.

Space and Time Complexity

Time Complexity: O(n), where n is the number of bits in the binary string. Space Complexity: O(1), as we only use a fixed amount of space for variables.

Solution

To solve this problem, we can track the number of operations needed to reduce the binary number to 1 by simulating the process:

1. Convert the binary string to an integer.
2. Use a loop to repeatedly check if the number is odd or even.
3. If odd, increment the count and add 1 to the number; if even, increment the count and divide the number by 2.
4. Continue until the number reaches 1.

This approach effectively utilizes basic arithmetic operations and a loop to count the steps.

Code Solutions