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

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.

 

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'

 

Solutions

Solution: Bit Manipulation

• Time complexity: O(n - 1)
• Space complexity: O(1)
• carry = 0 and current = 0, number is even, have to divide it by 2, step + 1
• carry = 0 and current = 1, number is odd, have to add 1 and divide it by 2, step + 2
• carry = 1 and current = 1, number is even, divide it by 2, step + 1
• carry = 1 and current = 0, number is odd, have to add 1 and divide it by 2, step + 2

 

JavaScript

/**
 * @param {string} s
 * @return {number}
 */
const numSteps = function (s) {
  let step = 0;
  let carry = 0;

  for (let index = s.length - 1; index > 0; index--) {
    const value = s[index];

    if (value === '0') {
      step += carry ? 2 : 1;
      continue;
    }
    step += carry ? 1 : 2;
    carry = 1;
  }
  return step + carry;
};