1611. Minimum One Bit Operations to Make Integers Zero

Description

Given an integer n, you must transform it into 0 using the following operations any number of times:

• Change the rightmost (0th) bit in the binary representation of n.
• Change the ith bit in the binary representation of n if the (i-1)th bit is set to 1 and the (i-2)th through 0th bits are set to 0.

Return the minimum number of operations to transform n into 0.

 

Example 1:

Input: n = 3
Output: 2
Explanation: The binary representation of 3 is "11".
"11" -> "01" with the 2nd operation since the 0th bit is 1.
"01" -> "00" with the 1st operation.

Example 2:

Input: n = 6
Output: 4
Explanation: The binary representation of 6 is "110".
"110" -> "010" with the 2nd operation since the 1st bit is 1 and 0th through 0th bits are 0.
"010" -> "011" with the 1st operation.
"011" -> "001" with the 2nd operation since the 0th bit is 1.
"001" -> "000" with the 1st operation.

 

Constraints:

• 0 <= n <= 109

 

Solutions

Solution: Bit Manipulation

• Time complexity: O(logn)
• Space complexity: O(logn)

 

JavaScript

/**
 * @param {number} n
 * @return {number}
 */
const minimumOneBitOperations = function (n) {
  if (n <= 1) return n;
  let bit = 0;

  while (1 << bit <= n) {
    bit += 1;
  }

  // operations = (2 ** (n - 1)) - 1
  return (1 << bit) - 1 - minimumOneBitOperations(n - (1 << (bit - 1)));
};