Add Two Integers

Difficulty: Easy | Acceptance: 88.00% | Paid: No Topics: Math

Given two integers num1 and num2, return the sum of the two integers.

• Examples
• Constraints
• Direct Addition
• Bitwise Manipulation

Examples

Input: num1 = 12, num2 = 5
Output: 17
Explanation: num1 + num2 = 12 + 5 = 17

Input: num1 = -10, num2 = 4
Output: -6
Explanation: num1 + num2 = -10 + 4 = -6

Constraints

-100 <= num1, num2 <= 100

Direct Addition

Intuition The most straightforward way to add two integers is to use the built-in addition operator provided by the programming language.

Steps

• Return the result of num1 + num2.

class Solution:
    def sum(self, num1: int, num2: int) -> int:
        return num1 + num2

Complexity

• Time: O(1)
• Space: O(1)
• Notes: This is the optimal solution for readability and performance.

Bitwise Manipulation

Intuition We can simulate addition using bitwise operators. The XOR (^) operation handles the sum without carry, while the AND (&) operation followed by a left shift (<<) calculates the carry. We repeat this until there is no carry left.

Steps

• While num2 is not 0:
  • Calculate the carry where both bits are 1: carry = num1 & num2.
  • Calculate the sum without carry: num1 = num1 ^ num2.
  • Shift the carry to the left by 1 bit: num2 = carry << 1.
• Return num1.

class Solution:
    def sum(self, num1: int, num2: int) -> int:
        while num2 != 0:
            carry = num1 & num2
            num1 = num1 ^ num2
            num2 = carry << 1
        return num1

Complexity

• Time: O(1) - The loop runs at most 32 times (for 32-bit integers).
• Space: O(1)
• Notes: This approach is useful for understanding low-level arithmetic but is generally slower than direct addition.