Sum Of Two Integers Leetcode Problem 371 [Python Solution]

Sum Of Two Integers LeetCode problem is under the category umbrella of Bit Manipulation and is considered a medium difficulty challenge.

The task at hand is to find the sum of two integers, ‘a’ and ‘b’, without using the standard addition or subtraction operators.

Instead, we’ll employ a clever approach involving bit manipulation.

Example 1:

Input: a = 1, b = 2
Output: 3

Example 2:

Input: a = 2, b = 3
Output: 5

Problem Solution

To solve this problem, we’ll use bit manipulation operations, mainly XOR and AND.

Let’s delve into the solution step by step.

Efficient Python Code Solution:

def getSum(self, a: int, b: int) -> int:
    def add(a, b):
        if not a or not b:
            return a or b
        return add(a ^ b, (a & b) << 1)

    if a * b < 0:
        if a > 0:
            return self.getSum(b, a)
        if add(~a, 1) == b:  # -a == b
            return 0
        if add(~a, 1) < b:  # -a < b
            return add(~add(add(~a, 1), add(~b, 1)), 1)  # -add(-a, -b)

    return add(a, b)  # a*b >= 0 or (-a) > b > 0

This Python code solution efficiently calculates the sum of two integers without using the standard operators.

Time and Space Complexity

The time complexity of this solution is constant (O(1)), as it performs the operation in a fixed number of steps, irrespective of the input size.

The space complexity is also O(1), as we use only a constant amount of additional memory.

Reasoning Behind Our Approach

We’ve employed a clever combination of bit manipulation operations, namely XOR and AND, to simulate addition without using the typical plus and minus operators.

This solution is efficient and takes care of negative numbers as well.

Constraints

• -1000 <= a, b <= 1000

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Edge Cases a Valid Solution Must Consider

• Negative numbers
• Overflow issues with large integers

We hope this detailed explanation helps you understand how to tackle the Sum Of Two Integers problem efficiently.

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Link to the original problem on LeetCode

Happy coding!