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Leetcode 371. Sum of Two Integers

Problem Statement

Leetcode 371: Sum of Two Integers

Given two integers a and b, return the sum of the two integers without using the operators + and -.

Clarifying Questions

1. Q: What are the constraints on the integers a and b (e.g., size, range)?
   • A: The integers a and b will be within the range of a typical 32-bit signed integer: ([-2^{31}, 2^{31} - 1]).
2. Q: Can I assume that a and b are always valid integers?
   • A: Yes, you can assume a and b are within the 32-bit signed integer range.
3. Q: Do we need to handle any special cases like overflow?
   • A: No explicit overflow handling is needed as the problem is about implementing the addition using bitwise operations.

Strategy

To calculate the sum of two integers without using + or -, we can use bitwise operations:

1. Sum Calculation:
   • The sum of two bits can be done with ^ (XOR) operator since 1 XOR 1 = 0, 1 XOR 0 = 1, 0 XOR 1 = 1, and 0 XOR 0 = 0.
2. Carry Calculation:
   • The carry can be calculated using the & (AND) operator followed by a left shift <<, since carry = (a & b) << 1. This handles the carry operation in binary addition.
3. Iterative Approach:
   • We use the iterative approach until there is no carry. In each iteration, we update a to be the sum (without carry) and b to be the carry. This process continues until b becomes zero.

Code

class Solution {
    public int getSum(int a, int b) {
        while (b != 0) {
            int carry = (a & b) << 1;  // Calculate carry
            a = a ^ b;                 // Calculate sum without carry
            b = carry;                 // Assign carry to b
        }
        return a;
    }
}

Time Complexity

• Time Complexity: The time complexity is O(1) on average. Although, in the worst case, the loop will execute for the number of bits in the integers (32 bits for a typical integer), making it O(32), which is still considered O(1).
• Space Complexity: The space complexity is O(1) since we are using a constant amount of space for variables irrespective of the input size.

This approach effectively computes the sum of two integers using bitwise operations while adhering to the constraints provided in the problem statement.

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