Problem Description

This problem asks you to find the sum of two given integers.

You are provided with two integer inputs: num1 and num2. Your task is to calculate and return their sum.

For example:

• If num1 = 5 and num2 = 3, the function should return 8
• If num1 = -2 and num2 = 7, the function should return 5
• If num1 = 0 and num2 = 0, the function should return 0

The solution is straightforward - simply add the two numbers together using the addition operator + and return the result. The implementation return num1 + num2 directly computes the sum of the two input integers.

Intuition

The problem is asking for the most fundamental arithmetic operation - addition of two numbers. When we need to find the sum of two integers, the direct approach is to use the built-in addition operator +.

Since we're dealing with basic integer addition, there's no need for complex algorithms or data structures. The mathematical operation of addition is already optimized at the language and hardware level.

The key insight is recognizing that this is a straightforward problem that doesn't require any transformation or manipulation of the input data. We simply need to perform the operation that the problem statement directly asks for: num1 + num2.

This direct approach works for all integer values, including positive numbers, negative numbers, and zero. The addition operator handles all these cases correctly by default, making it the most efficient and clean solution.

Learn more about Math patterns.

Solution Approach

The implementation uses the most direct approach possible - a single arithmetic operation.

The function sum takes two parameters:

• num1: the first integer
• num2: the second integer

The entire solution consists of one line: return num1 + num2

This approach:

1. Takes the two input integers num1 and num2
2. Applies the addition operator + to compute their sum
3. Returns the calculated result directly

No additional variables, loops, or conditional statements are needed. The Python addition operator handles all integer cases automatically:

• Positive + Positive (e.g., 3 + 5 = 8)
• Negative + Negative (e.g., -3 + (-5) = -8)
• Positive + Negative (e.g., 3 + (-5) = -2)
• Any number + Zero (e.g., 3 + 0 = 3)

The time complexity is O(1) since addition is a constant-time operation for integers within the standard range. The space complexity is also O(1) as we don't use any additional data structures - we simply return the computed sum.

This solution represents the optimal approach for adding two integers, as it directly leverages the fundamental arithmetic operation provided by the programming language.

Example Walkthrough

Let's walk through the solution with a concrete example: num1 = 7 and num2 = -3.

Step 1: Identify the inputs

• We have two integers: num1 = 7 (positive) and num2 = -3 (negative)
• Our goal is to find their sum

Step 2: Apply the addition operation

• The solution directly computes num1 + num2
• This translates to: 7 + (-3)

Step 3: Evaluate the expression

• When adding a positive and negative number, we essentially perform subtraction
• 7 + (-3) = 4

Step 4: Return the result

• The function returns 4 as the final answer

Let's trace through another quick example with num1 = -5 and num2 = -2:

• Input: num1 = -5, num2 = -2
• Operation: (-5) + (-2)
• Result: -7
• Return: -7

The beauty of this solution is its simplicity. Regardless of whether the inputs are positive, negative, or zero, the single expression return num1 + num2 handles all cases correctly. The addition operator automatically performs the correct arithmetic based on the signs of the numbers, making this a clean, efficient, and universally applicable solution.

Solution Implementation

Time and Space Complexity

Time Complexity: O(1)

• The addition operation between two integers is a constant-time operation, regardless of the size of the input values
• The function performs a single arithmetic operation and returns the result directly

Space Complexity: O(1)

• The function only uses a fixed amount of memory to store the two input parameters num1 and num2
• No additional data structures or variables are created
• The space used does not scale with the input size

Learn more about how to find time and space complexity quickly.

Common Pitfalls

1. Integer Overflow in Other Languages

While Python handles arbitrarily large integers automatically, in languages like C++, Java, or C, integer overflow can occur when the sum exceeds the maximum value for the integer type.

Example scenario:

• In Java, if num1 = Integer.MAX_VALUE and num2 = 1, the result would overflow and wrap around to a negative number.

Solution:

• In Python: No action needed as Python handles big integers automatically
• In other languages: Use larger data types (like long long in C++) or check for overflow before performing the addition:

  // Java overflow check
  if (num1 > 0 && num2 > Integer.MAX_VALUE - num1) {
      // Handle overflow case
  }

2. Type Confusion with String Concatenation

A common mistake occurs when inputs are accidentally strings instead of integers, leading to concatenation rather than addition.

Example scenario:

• If num1 = "5" and num2 = "3", using + would result in "53" instead of 8.

Solution:

• Ensure type conversion when necessary:

  def sum(self, num1, num2):
      return int(num1) + int(num2)

• Or validate input types:

  def sum(self, num1: int, num2: int) -> int:
      if not isinstance(num1, int) or not isinstance(num2, int):
          raise TypeError("Both inputs must be integers")
      return num1 + num2

3. Floating-Point Precision Issues

If the function is modified to handle floats, precision errors can occur.

Example scenario:

• 0.1 + 0.2 might not equal exactly 0.3 due to floating-point representation.

Solution:

• For monetary calculations or when precision matters, use the Decimal module:

  from decimal import Decimal
  
  def sum(self, num1, num2):
      return Decimal(str(num1)) + Decimal(str(num2))

4. None or Null Values

If either input is None (or null in other languages), the addition operation will fail.

Example scenario:

• num1 = None and num2 = 5 would raise a TypeError.

Solution:

• Add null checks or provide default values:

  def sum(self, num1: int, num2: int) -> int:
      if num1 is None or num2 is None:
          return 0  # or raise an exception
      return num1 + num2