Find the Sum: How to Determine if Any Two Numbers in a List Add Up to a Given Number K

In this guide, we will explore an algorithm to determine if any two numbers in a list add up to a given number K. This problem is a common interview question and can be solved using various approaches. We will discuss a step-by-step solution using a hash set, which allows for faster lookups and reduced time complexity.


Before diving into the solution, make sure you are familiar with the following concepts:

  1. Python syntax
  2. Lists in Python
  3. Sets in Python

Solution: Using a Hash Set

The hash set approach has a time complexity of O(n), making it an efficient solution to this problem.

Step 1: Create a function

First, let's create a function called find_sum that takes two arguments: a list of integers numbers and an integer K.

def find_sum(numbers, K):

Step 2: Create an empty hash set

Inside the function, create an empty hash set called seen_numbers. This will be used to store the numbers we have encountered in the list.

def find_sum(numbers, K):
    seen_numbers = set()

Step 3: Iterate through the list

Now, iterate through the list of numbers using a for loop. For each number, calculate the required complement that would add up to K (i.e., K minus the current number). Then, check if the complement is present in the seen_numbers set.

If the complement is found, it means we have a pair of numbers that add up to K. In this case, return True. If the complement is not found, add the current number to the seen_numbers set and continue to the next iteration.

def find_sum(numbers, K):
    seen_numbers = set()

    for num in numbers:
        complement = K - num
        if complement in seen_numbers:
            return True

    return False

That's it! Our function is now complete and can be used to determine if any two numbers in a list add up to a given number K.


Here are some examples of how to use the find_sum function:

print(find_sum([1, 2, 3, 4, 5], 9))  # Output: True (4+5=9)
print(find_sum([10, 15, 3, 7], 17))  # Output: True (10+7=17)
print(find_sum([1, 3, 5, 7, 9], 2))  # Output: False (No pair adds up to 2)


1. Why use a hash set instead of a list for storing seen numbers?

A hash set allows for faster lookups (O(1) on average), making it more efficient than a list (O(n) for lookups).

2. Can this problem be solved using a different data structure?

Yes, there are various approaches to solving this problem, such as using a sorted list and applying the two-pointer technique, or using a dictionary to store the frequency of each number.

3. What is the time complexity of this solution?

The time complexity of this solution is O(n), where n is the length of the input list.

4. Can this solution handle negative numbers?

Yes, this solution can handle negative numbers in the input list.

5. Can this solution handle duplicate numbers in the list?

Yes, this solution can handle duplicate numbers in the input list.

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