Minimum One Bit Operations to Make Integers Zero

class Solution {
public:
    int minBitOperations(int number) {
        int result = number;
        result ^= result >> 16;
        result ^= result >> 8;
        result ^= result >> 4;
        result ^= result >> 2;
        result ^= result >> 1;
        return result;
    }
};

This C++ solution details an approach to determine the minimum number of bit operations required to convert a given integer to zero. The strategy employed involves repeatedly using bit-wise XOR operations on progressively right-shifted versions of the integer. Here’s how you understand the process:

• Start with the input number.
• Perform a XOR operation between number and number right-shifted by 16. Store the result back in number.
• Repeat the XOR operation with the result right-shifted by progressively smaller exponents: 8, 4, 2, and finally 1.

Each XOR operation essentially reduces the number of one-bits through combining pairs of bits, hence moving closer to zero with each step. The final result from the sequence of operations gives the minimal number of operations needed. The function returns this result. The code itself is compact and executes efficiently by reducing the problem size logarithmically, adjusting the scope of XOR operations through the use of right shifts.

class Solution {
    public int minOneBitConversion(int n) {
        int result = n;
        result ^= result >> 16;
        result ^= result >> 8;
        result ^= result >> 4;
        result ^= result >> 2;
        result ^= result >> 1;
        return result;
    }
}

The solution provided in Java addresses the problem of determining the minimum one-bit operations required to transform an integer into zero using bitwise operations. The function minOneBitConversion(int n) calculates this by repeatedly applying bitwise XOR operations. Each XOR operation is performed between the current result and the result right-shifted by increasing powers of two (1, 2, 4, 8, 16). This technique cleverly utilizes the properties of XOR to gradually reduce the number by isolating and eliminating bits from evaluation, leading to the final result which is a derivative of the input number transformed in such a way to minimize operations. Finally, the method returns the result after processing all shifts, providing the minimum number of operations needed.

class Solution:
    def minBitFlips(self, number: int) -> int:
        result = number
        result ^= result >> 16
        result ^= result >> 8
        result ^= result >> 4
        result ^= result >> 2
        result ^= result >> 1
        return result

The Python code presented solves the problem of determining the minimum one-bit operations required to convert an integer to zero. The function minBitFlips takes an integer number as an argument and utilizes bit manipulation to calculate the minimum operations.

• The process starts by assigning the input number to a variable result.
• It then enters a series of XOR operations, each time shifting result right by an increasingly smaller power of two (from 16 down to 1).
• These operations sequentially reduce result by flipping differing sets of bits.

Each of the bit shift operations aims to isolate and manipulate individual bits of the integer, exploiting the properties of XOR to effectively count the bits that need to be flipped. The final return gives the count of these operations, representing the answer to the problem. This function is efficient, harnessing bitwise operations for a quick computation that runs in constant time relative to the size of the integer.