**π‘ Problem Formulation:** In Python, checking if one number is the one’s complement of another involves comparing two integers to determine if they are exact opposites in binary form. This operation is quite common in low-level programming or algorithms concerning bitwise operations. For instance, if the two values are ‘5’ and ‘-6,’ the function should determine that ‘-6’ is indeed the one’s complement of ‘5’.

## Method 1: Using Bitwise NOT and Comparison

This method involves applying the bitwise NOT operator to one of the numbers and then comparing it to the second number. If the two numbers are one’s complement of each other, this operation will equate them. The bitwise NOT operator in Python is expressed as `~`

, which flips every bit of a number.

Here’s an example:

def is_ones_complement(num1, num2): return num1 == ~num2 print(is_ones_complement(5, -6))

Output: `True`

This code snippet defines a function `is_ones_complement(num1, num2)`

which returns `True`

if `num2`

is the one’s complement of `num1`

. It employs the bitwise NOT operator `~`

on the second number and compares the result to the first number. If equal, they are one’s complements.

## Method 2: Using Bit Length and Masking

This technique takes advantage of Python’s ability to calculate the bit length of an integer and uses a mask to create the one’s complement manually. The mask is created with the `bit_length()`

method, ensuring dynamic handling of different integer sizes.

Here’s an example:

def is_ones_complement(num1, num2): mask = (1 << num1.bit_length()) - 1 return num1 == (~num2 & mask) print(is_ones_complement(5, -6))

Output: `True`

The function `is_ones_complement(num1, num2)`

first calculates a mask based on the bit length of `num1`

. It then applies the bitwise NOT operator to `num2`

, masks it, and checks if the result is equal to `num1`

.

## Method 3: Using String Representation and Comparison

By converting the numbers to their binary string representations, it’s possible to check for one’s complement by ensuring one string is the negation of the other, where ‘1’s correspond to ‘0’s and vice versa.

Here’s an example:

def is_ones_complement(num1, num2): bin_num1 = bin(num1)[2:] bin_num2 = bin(-num2 - 1)[2:].rjust(len(bin_num1), '0') return all(b1 != b2 for b1, b2 in zip(bin_num1, bin_num2)) print(is_ones_complement(5, -6))

Output: `True`

This snippet defines the function `is_ones_complement(num1, num2)`

, which converts both numbers to binary and strips the leading ‘0b’. It then checks each corresponding bit to ensure they are different, using the `zip`

function for pairwise comparison.

## Method 4: Using Bitwise XOR and Bit Check

This strategy employs the bitwise XOR operator to verify if the bits of both numbers differ at all positions, as required for one’s complement pairs. A subsequent bit check confirms that all bits indeed take opposing values.

Here’s an example:

def is_ones_complement(num1, num2): xor_result = num1 ^ num2 return xor_result == (1 << (xor_result.bit_length())) - 1 print(is_ones_complement(5, -6))

Output: `True`

Within the `is_ones_complement`

function, the bitwise XOR operation creates a result that, if num1 and num2 are one’s complements, should consist entirely of ‘1’s. A check is then made to ensure the XOR result matches the sequence of ‘1’s it would equate to if they were indeed one’s complements.

## Bonus One-Liner Method 5: Using Bitwise NOT in a Lambda Function

For those who prefer concise code, a one-liner using a lambda function might be appealing. This method applies the same principle as Method 1 but written in a more compact form.

Here’s an example:

is_ones_complement = lambda num1, num2: num1 == ~num2 print(is_ones_complement(5, -6))

Output: `True`

The one-liner defines `is_ones_complement`

as a lambda function that immediately returns the result of the comparison between `num1`

and the bitwise NOT of `num2`

.

## Summary/Discussion

**Method 1: Bitwise NOT and Comparison.**Simple and efficient for most cases. However, can behave unexpectedly with negative numbers due to Python’s infinite precision integers.**Method 2: Bit Length and Masking.**More verbose but handles varying integer sizes gracefully. It can be slower due to additional computation of the mask.**Method 3: String Representation and Comparison.**Intuitive approach, but inefficient due to the overhead of string operations and manual comparison of bits.**Method 4: Bitwise XOR and Bit Check.**Clever use of XOR operation, but requires an understanding of bitwise operations. It may be less readable for those unfamiliar with such techniques.**Method 5: One-Liner Lambda Function.**Very concise, best for those who favor one-liner solutions. Has similar drawbacks to Method 1.