LeetCode 2235 - Add Two Integers

LeetCode Problem 2235

Difficulty: 🟢 Easy
Topics: Math

Solution

Problem Understanding

The problem is asking for the sum of two integers num1 and num2. In simpler terms, you are given two numbers, and you need to calculate their total. The input integers can be negative, zero, or positive, and the output should be a single integer representing the sum.

The constraints specify that both num1 and num2 are within the range -100 to 100. This tells us that the numbers are small, so concerns like integer overflow are not relevant in Python or Go. Since the numbers are bounded, the solution does not require optimization for very large inputs, and even the simplest arithmetic approach will run efficiently.

Important edge cases include when one or both numbers are negative, when both numbers are zero, and when the sum is zero. These edge cases ensure that the implementation correctly handles negative numbers and zero values.

Approaches

The brute-force approach in this scenario would be to simulate addition manually, for instance using repeated incrementing or decrementing. This would technically give the correct answer because addition is essentially repeated incrementing, but it would be unnecessarily complex for such small numbers and not idiomatic in a programming language.

The key insight is that the problem is simply asking for integer addition, which is a built-in operation in all programming languages. Using the built-in + operator provides a direct, optimal solution because it is already implemented efficiently at the hardware level.

Approach	Time Complexity	Space Complexity	Notes
Brute Force	O(abs(num1))	O(1)	Simulate addition using loops, unnecessary here
Optimal	O(1)	O(1)	Use the built-in + operator for constant-time addition

Algorithm Walkthrough

1. Receive the two input integers, num1 and num2.
2. Apply the built-in addition operator + to compute the sum of the two integers.
3. Return the result as the output.

Why it works: Addition is a fundamental arithmetic operation, and the + operator in Python and Go guarantees correct integer addition for numbers within the specified constraints. Because there are no complicated conditions or data structures involved, the algorithm always produces the correct sum.

Python Solution

class Solution:
    def sum(self, num1: int, num2: int) -> int:
        # Compute the sum of num1 and num2 using the built-in addition operator
        result = num1 + num2
        return result

In this implementation, we directly use the + operator to calculate the sum of num1 and num2. The result is stored in the variable result and returned. This corresponds directly to the algorithm steps described above. There are no loops or additional data structures needed because the problem is simple arithmetic.

Go Solution

func sum(num1 int, num2 int) int {
    // Compute the sum of num1 and num2 using the built-in addition operator
    result := num1 + num2
    return result
}

The Go implementation is similar to Python. We use the + operator to compute the sum. In Go, variable declaration requires a type or := shorthand, which we use here for clarity. Edge cases such as negative numbers or zero are naturally handled by Go's integer addition.

Worked Examples

Example 1:

Step	num1	num2	result
Initial	12	5	-
Add	12	5	17
Return	-	-	17

Example 2:

Step	num1	num2	result
Initial	-10	4	-
Add	-10	4	-6
Return	-	-	-6

Complexity Analysis

Measure	Complexity	Explanation
Time	O(1)	Addition of two integers is constant time
Space	O(1)	Only a single integer variable is used to store the result

The reasoning behind the complexity is straightforward: the operation does not depend on the size of the numbers beyond the input, and no additional data structures are used. Therefore, both time and space complexities are constant.

Test Cases

# test cases
sol = Solution()
assert sol.sum(12, 5) == 17  # normal positive numbers
assert sol.sum(-10, 4) == -6  # negative and positive
assert sol.sum(0, 0) == 0  # both zero
assert sol.sum(-50, -50) == -100  # both negative
assert sol.sum(100, -100) == 0  # sum to zero
assert sol.sum(100, 0) == 100  # positive and zero
assert sol.sum(-100, 0) == -100  # negative and zero

Test	Why
12, 5	Normal positive numbers addition
-10, 4	Handling negative and positive
0, 0	Both numbers zero
-50, -50	Both numbers negative
100, -100	Sum resulting in zero
100, 0	Positive number with zero
-100, 0	Negative number with zero

Edge Cases

The first important edge case is when both numbers are zero. Zero is the identity for addition, so the sum should be zero. Our implementation handles this naturally because 0 + 0 = 0.

The second edge case is when both numbers are negative. Adding two negative numbers produces a more negative number, which can sometimes trip up implementations that assume only positive inputs. Since we use the + operator, the result is correctly calculated.

The third edge case is when the sum is zero because the numbers are equal in magnitude but opposite in sign. For instance, num1 = 100 and num2 = -100. Our solution handles this correctly because the + operator correctly calculates 100 + (-100) = 0.

This approach covers all potential pitfalls in the given input range.