The KSum problem generalizes 2Sum, 3Sum, and 4Sum into a flexible recursive solution that can find all unique combinations of k numbers in an array that sum to a target. It’s a fantastic problem for practicing recursion, backtracking, and thinking about how to build modular solutions that scale with complexity. Once you’ve nailed KSum, you can solve any of the others as special cases.

This is a great follow-up to 2Sum and 3Sum. It challenges you to apply the same two-pointer strategy but adds complexity by requiring a quadruplet instead of a pair or triplet. This kind of problem comes up when you're working on systems that require combinatorial sum checks, like budgeting scenarios, fraud detection with transaction records, or even algorithmic trading strategies. The key here is optimization over brute-force enumeration.

This is a great warm-up for array and two-pointer problems. It’s similar to the classic 3Sum, but instead of finding a triplet that adds to a specific number, we need the closest possible sum. This introduces an optimization twist that requires careful comparison and pointer movement, making it an excellent real-world scenario—think of situations where you need to get as close as possible to a threshold value without hitting it exactly, such as budget planning or resource all

Finding triplets that sum to zero is a foundational exercise in two-pointer techniques, sorting, and careful duplicate handling. The “3Sum” problem tests your ability to combine sorting with pointer sweeps to achieve O(n²) performance.

Determining the maximum water a container can hold between vertical lines is foundational in graphics rendering, fluid simulations, and two-pointer optimizations. The “Container With Most Water” problem challenges you to squeeze the best area in O(n) time.

The Two Sum Problem is one of the first stops on our journey. It’s simple enough to focus on thought process, yet rich enough to demonstrate key problem‑solving techniques. Here’s how to walk through it using our nine‑step framework.