Sum of Two Integers
Problem Statement
Given two integers a and b, return the sum of the two integers without using the operators + and -.
Constraints:
- -1000 <= a, b <= 1000
Input Format:
- Two integers a and b
Output Format:
- Return the sum of a and b
Examples:
Example 1:
Input:
a = 1, b = 2
Output:
3
Explanation:
1 + 2 = 3
Example 2:
Input:
a = 2, b = 3
Output:
5
Explanation:
2 + 3 = 5
Example 3:
Input:
a = -1, b = 1
Output:
0
Explanation:
-1 + 1 = 0
Solutions
Bitwise Operations Approach
Use bitwise operations to simulate binary addition without using + or -. XOR to find the sum without carry, AND with left shift to find the carry, and repeat until carry is 0.
Recursive Approach
Same bitwise operations approach but implemented recursively. The base case is when there's no carry (b = 0).
Algorithm Walkthrough
Example input: nums = []
Step-by-step execution:
- a = 2 (binary 10), b = 3 (binary: 11)
- XOR of a and b: 2 ^ 3 = 1 (binary: 01) (sum without carry)
- AND with shift: (2 & 3) << 1 = (10 & 11) << 1 = (10) << 1 = 100 = 4 (carry)
- Next iteration: a = 1, b = 4
- XOR of a and b: 1 ^ 4 = 5 (binary: 101) (sum without carry)
- AND with shift: (1 & 4) << 1 = (01 & 100) << 1 = (0) << 1 = 0 (no carry)
- Since there's no carry left, return a = 5
Hints
Hint 1
Hint 2
Hint 3
Hint 4
Video Tutorial
Video tutorials can be a great way to understand algorithms visually
Visualization
Visualize the bitwise operations step by step, showing how the binary representation changes in each iteration.
Key visualization elements:
- current bits
- XOR operation
- AND with shift
- carry calculation
Similar Questions
Counting Bits
EasyGiven an integer n, return an array ans of length n + 1 such that for each i (0 <= i <= n), ans[i] is the number of 1's in the binary representation of i.
Number of 1 Bits
EasyWrite a function that takes an unsigned integer and returns the number of '1' bits it has (also known as the Hamming weight). Note that in some languages, such as Java, there is no unsigned integer type. In this case, the input will be given as a signed integer type. It should not affect your implementation, as the integer's internal binary representation is the same, whether it is signed or unsigned.
Implementation Notes
This problem tests understanding of bitwise operations and binary addition. The key insight is to separate the addition process into two parts: the sum without carry (XOR) and the carry (AND with shift).