Two-Number Sum Algorithm using a Set

Two-Number Sum Algorithm using a Set

• Function: twoNumberSum(data, targetSum) finds two numbers in a list that add up to a targetSum.
• Input: data (list of numbers), targetSum (integer).
• Output: A list containing the two numbers that sum to the target, or an empty list if no such pair exists.
• Algorithm:
  • Creates an empty seen set.
  • Iterates through each num in the input data.
  • Calculates secondNumber needed to reach targetSum.
  • Checks if secondNumber exists in seen. If it does, returns the pair [num, secondNumber].
  • Adds num to the seen set.
  • If the loop completes without finding a pair, returns an empty list.

Time and Space Complexity Analysis

• Time Complexity: O(n), where n is the length of the input list data. This is because each number is checked only once.
• Space Complexity: O(n) because the seen set can potentially store all the numbers in the input list.

Why Use a Set?

• Efficiency: Sets offer constant-time (O(1)) average-time complexity for checking if an element exists (using the in operator). Lists or arrays would take linear time (O(n)). This results in a faster overall algorithm compared to a nested loop approach (O(n^2)).
• Readability: The code using a set is more concise and easier to understand than a nested loop solution.
• Space-Time Tradeoff: Using a set does require extra space to store the seen numbers, but this is a worthwhile trade-off for the substantial improvement in efficiency when dealing with larger datasets.

This quiz covers the Two-Number Sum algorithm, which efficiently finds two numbers in a list that add up to a given target sum using a set for tracking seen numbers. It also explores the time and space complexity of the algorithm, emphasizing its optimal O(n) performance. Test your understanding of this important concept in algorithm design.