algoadvance

  1. Are negative integers allowed in the input?
  2. What are the constraints on the integer values? Are they within the typical 32-bit signed integer range?
  3. Should the solution handle overflow situations explicitly, or can we assume the numbers will always be within a safe range?

Strategy

The problem statement asks us to find the sum of two integers without using the + or - operators. This can be done using bitwise operations.

Approach:

  1. Bitwise XOR (^): This operation will handle the addition without carrying. For example, 5 ^ 3 results in 6 (binary 101 ^ 011 = 110).
  2. Bitwise AND and Shift (& and <<): This will handle the carrying. For example, 5 & 3 results in 1 (binary 101 & 011 = 001), and 1 << 1 results in 2 (binary 001 << 1 = 010).

We will:

  1. Use XOR to add the numbers without carry.
  2. Use AND followed by left shift to calculate the carry.
  3. Repeat the process until there is no carry.

Handling Negative Numbers:

Python handles arbitrarily large integers with its built-in int type, but when simulating 32-bit integer behavior, we need to take special care of overflow:

Code

Let’s implement the solution with the above strategy.

def getSum(a: int, b: int) -> int:
    # 32 bits integer max
    MAX = 0x7FFFFFFF
    # Mask to get last 32 bits
    mask = 0xFFFFFFFF
    
    while b != 0:
        # calulate the carry
        carry = (a & b) << 1
        # add the bits without carry
        a = (a ^ b) & mask
        # apply the carry
        b = carry & mask
    
    # if a is negative, get its positive complement
    if a > MAX:
        a = ~(a ^ mask)
    
    return a

# Example usage:
# a = 1, b = 2, expected output = 3
print(getSum(1, 2)) # Output: 3

Time Complexity

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