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Subtract Without Subtract - Solutions

Approach 1: Two's Complement and Bitwise Operations​

Description​

This approach leverages the concept of two's complement to perform subtraction using bitwise operations. In two's complement representation, the negative of a number x can be obtained by inverting all bits of x (~x) and adding 1. Thus, number1 - number2 can be computed as number2 + (~number1 + 1).

Implementation​

func subtractWithoutSubtract(subtract number1: Int, from number2: Int) -> Int {
    let subtracted = number2 + (~number1 + 1)
    return subtracted
}

Pros​

  • Efficient in terms of both time and space complexity.
  • Utilizes fundamental properties of binary arithmetic.

Cons​

  • Might be less intuitive for those unfamiliar with bitwise operations and two's complement representation.
  • Requires understanding of low-level binary arithmetic concepts.

Approach 2: Using Addition and Iterative Borrowing​

Description​

This approach iteratively borrows from higher bits to perform subtraction without using the - operator. The idea is to simulate the borrowing process that happens in manual subtraction.

Implementation​

func subtractWithoutSubtract(subtract number1: Int, from number2: Int) -> Int {
    var a = number2
    var b = number1

    while b != 0 {
        let borrow = (~a) & b
        a = a ^ b
        b = borrow << 1
    }

    return a
}

Pros​

  • Mimics the manual subtraction process, which can be more intuitive.
  • Avoids direct bitwise manipulation of negative numbers.

Cons​

  • More complex than the two's complement approach.
  • Requires multiple iterations to complete the subtraction, potentially making it slower for large numbers.

Approach 3: Using Swift's Built-in Methods (Discussion)​

Description​

While the problem specifically restricts the use of the - operator, it is worth noting that Swift provides built-in methods and operators for arithmetic operations. Using these built-in methods ensures code simplicity and readability.

Pros​

  • Simplifies code and enhances readability.
  • Utilizes Swift's optimized arithmetic operations.

Cons​

  • Does not adhere to the problem constraint of avoiding the - operator.
  • Not applicable to this specific challenge but useful in real-world applications for simplicity and maintainability.

Conclusion​

The two's complement approach using bitwise operations is the most efficient and concise method for this problem. It leverages fundamental properties of binary arithmetic to perform subtraction without using the - operator. The iterative borrowing approach, while more intuitive for those familiar with manual subtraction, is more complex and less efficient. Understanding both methods provides valuable insights into different ways to approach arithmetic operations at a low level.