Sum of Two Integers
Problem Description
Question
Given two integers a and b, return the sum of the two integers without using the operators + and -.
Example 1:
Input: a = 1, b = 2
Output: 3
Example 2:
Input: a = 2, b = 3
Output: 5
Constraints:
-1000 <= a, b <= 1000
Solve it on LeetCode
Approaches
1. Iterative Bit Manipulation
The problem states that we need to sum two integers without using the operators + or -. This can be achieved through bit manipulation using the concepts of XOR and carry. Here's the step-by-step breakdown:
- XOR operation (
a ^ b): This operation is like addition but ignores the carry. If only one of the bits is set (either inaor inb, but not both), it will be set in the result. - AND operation (
a & b): This helps to determine where there would be a carry. When both bits are set (inaandb), a carry is generated. - Left shift operation (
<<): After identifying the carry bits usingAND, they need to be shifted left to add them at the next higher bit position. - Repeat this process until there are no carries left to process.
Code:
Complexity Analysis
- Time Complexity: O(1), because the number of bits is fixed, the loop will iterate a finite number of times.
- Space Complexity: O(1), as no additional space is used.
Example Walkthrough:
Stop when b == 0. Final a = 14 → 5 + 9 = 14.
2. Recursive Bit Manipulation
This approach uses the same logic as the iterative approach but utilizes recursion instead.
Code:
Complexity Analysis
- Time Complexity: O(1) since the recursion depth is limited by the number of bits in an integer.
- Space Complexity: O(1) if we consider just the computation. However, there is a recursive call stack used which would typically be O(n) where n is the number of bits, but due to limits in integer size, it is effectively constant.