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 1

Python Code
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class Solution:
    def minimumOneBitOperations(self, n: int) -> int:
        ans = 0
        while n:
            ans ^= n
            n >>= 1
        return ans

Java Code
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class Solution {
    public int minimumOneBitOperations(int n) {
        int ans = 0;
        for (; n > 0; n >>= 1) {
            ans ^= n;
        }
        return ans;
    }
}

C++ Code
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class Solution {
public:
    int minimumOneBitOperations(int n) {
        int ans = 0;
        for (; n > 0; n >>= 1) {
            ans ^= n;
        }
        return ans;
    }
};

Go Code
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func minimumOneBitOperations(n int) (ans int) {
	for ; n > 0; n >>= 1 {
		ans ^= n
	}
	return
}

TypeScript Code
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function minimumOneBitOperations(n: number): number {
    let ans = 0;
    for (; n > 0; n >>= 1) {
        ans ^= n;
    }
    return ans;
}

Solution 2

Python Code
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class Solution:
    def minimumOneBitOperations(self, n: int) -> int:
        if n == 0:
            return 0
        return n ^ self.minimumOneBitOperations(n >> 1)

Java Code
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class Solution {
    public int minimumOneBitOperations(int n) {
        if (n == 0) {
            return 0;
        }
        return n ^ minimumOneBitOperations(n >> 1);
    }
}

C++ Code
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class Solution {
public:
    int minimumOneBitOperations(int n) {
        if (n == 0) {
            return 0;
        }
        return n ^ minimumOneBitOperations(n >> 1);
    }
};

Go Code
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func minimumOneBitOperations(n int) int {
	if n == 0 {
		return 0
	}
	return n ^ minimumOneBitOperations(n>>1)
}

TypeScript Code
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function minimumOneBitOperations(n: number): number {
    if (n === 0) {
        return 0;
    }
    return n ^ minimumOneBitOperations(n >> 1);
}