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

Description

Given a number s in their binary representation. 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's guaranteed that you can always reach to one for all testcases.

 

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(javascript)

/**
 * @param {string} s
 * @return {number}
 */
const numSteps = function (s) {
  const addOne = (str = '') => {
    const result = str.split('')
    let reminder = 1
    for (let i = result.length - 1; i >= 0; i--) {
      if (result[i] === '1' && reminder === 1) {
        result[i] = '0'
        reminder = 1
      } else {
        result[i] = parseInt(result[i], 10) + parseInt(reminder, 10)
        reminder = 0
      }
    }
    if (reminder) {
      return reminder + result.join('')
    }
    return result.join('')
  }
  let count = 0
  while (s !== '1') {
    if (s[s.length - 1] === '0') {
      s = s.slice(0, s.length - 1)
    } else {
      s = addOne(s)
    }
    count += 1
  }
  return count
}