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1611. Minimum One Bit Operations to Make Integers Zero

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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

Python3

class Solution:
    def minimumOneBitOperations(self, n: int) -> int:
        if n <= 1:
            return n
        for i in range(64):
            if (n >> i) == 1:
                base = 1 << i
                break
        return 2 * base - 1 - self.minimumOneBitOperations(n - base)

Go

func minimumOneBitOperations(n int) int {
	if n <= 1 {
		return n
	}
	base := 0
	for i := 0; i < 64; i++ {
		if (n >> i) == 1 {
			base = 1 << i
			break
		}
	}
	return (base << 1) - 1 - minimumOneBitOperations(n-base)
}

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