#371

Medium

LeetCode Problem Workspace

Sum of Two Integers

Solve the Sum of Two Integers problem using bit manipulation and math to avoid using the operators + and -.

Problem Statement

Given two integers, a and b, return their sum without using the + or - operators. You must leverage an alternative method to achieve this task.

The typical approach to addition is to use the + operator, but this problem requires you to find a solution without it. You'll need to utilize bit manipulation and mathematical principles to arrive at the correct sum.

Examples

Example 1

Input: a = 1, b = 2

Output: 3

Example details omitted.

Example 2

Input: a = 2, b = 3

Output: 5

Example details omitted.

Constraints

-1000 <= a, b <= 1000

Solution Approach

Bitwise XOR

Use the XOR operator to perform bit addition without carrying over. XOR will handle the bits that don't need a carry, effectively adding the numbers together.

Bitwise AND

Use the AND operator to find the carry bits, then shift them left to prepare for the next iteration. This helps propagate the carry over to the next higher bit.

Iterative Calculation

Repeat the process of XOR and AND until there is no carry left. This will give you the final sum of the two integers without using the + or - operators.

Complexity Analysis

Metric	Value
Time	Depends on the final approach
Space	Depends on the final approach

The time complexity of this solution is O(log(max(a, b))) because in each iteration, the number of bits in the carry and the result decreases by one. The space complexity is O(1) as no additional space is used beyond the input variables.

What Interviewers Usually Probe

Look for a clear understanding of bitwise operations and how they apply to addition.
Evaluate if the candidate can explain the iterative nature of the algorithm and its relation to the binary representation of integers.
Check if the candidate can identify the edge cases, such as when no carry is present or when both integers are zero.

Common Pitfalls or Variants

Common pitfalls

Not correctly handling the case when there is no carry, leading to infinite loops or incorrect results.
Failing to explain the shift operation and why it is necessary to propagate the carry bit.
Overcomplicating the solution or using additional data structures when bitwise operations alone suffice.

Follow-up variants

The problem can be extended to work with multiple integers, where you need to find the sum of an arbitrary number of integers.
An alternative version could ask you to perform subtraction using bitwise operations, leading to a similar but inverted process.
You could be asked to find the difference between two integers without using the subtraction operator, relying on bitwise operations.

FAQ

What is the main strategy for solving the Sum of Two Integers problem?

The main strategy is to use bitwise XOR and AND to simulate the process of addition without using the + or - operators.

Can I use any other operations besides XOR and AND?

No, the problem specifically asks for a solution that avoids using the + or - operators, and bitwise operations like XOR and AND are the most suitable.

How does XOR contribute to the addition of two integers?

XOR adds bits where there is no carry. It is used to compute the sum of two numbers at each bit position without carrying over.

What should I do if I encounter edge cases like negative numbers?

Ensure that the bitwise operations handle the sign bits correctly, especially when working with negative integers in a two's complement representation.

What is the time complexity of the solution?

The time complexity is O(log(max(a, b))) because each iteration reduces the number of bits in the result and carry.

terminal

Solution

Solution 1

#### Python3

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class Solution:
    def getSum(self, a: int, b: int) -> int:
        a, b = a & 0xFFFFFFFF, b & 0xFFFFFFFF
        while b:
            carry = ((a & b) << 1) & 0xFFFFFFFF
            a, b = a ^ b, carry
        return a if a < 0x80000000 else ~(a ^ 0xFFFFFFFF)

Continue Practicing

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