What are some variations of the two-sum problem?

What are some variations of the two-sum problem?

The two-sum problem typically involves finding two numbers in an array that add up to a specific target. Variations include:

1. Three Sum: Finding three numbers that add up to a target.
2. Four Sum: Extending to four numbers.
3. Two Sum II: Where the input array is sorted.
4. Two Sum with Multiplicity: Counting pairs with duplicates.
5. Two Sum Less Than Target: Finding pairs that sum to less than a target.

Can you explain the Three Sum variation?

Sure! The Three Sum problem involves finding three distinct numbers in an array that add up to a given target. A common approach is to sort the array first, then use a two-pointer technique to find pairs that complement the third number. This reduces the time complexity compared to a brute-force solution.

What is the time complexity of the Three Sum problem?

The time complexity of the Three Sum problem is O(n^2) after sorting the array, which takes O(n log n). The two-pointer technique then runs in O(n) for each element, leading to the overall complexity.

Are there any common pitfalls when solving these problems?

Yes, common pitfalls include:

1. Not handling duplicates properly, which can lead to incorrect counts.
2. Failing to consider edge cases, like arrays with fewer than two or three elements.
3. Inefficient algorithms that exceed time limits for larger inputs.