Divide and Conquer based

Start by clarifying the exact contract for Divide and Conquer: input representation, mutation rules, duplicate behavior, and what should happen on invalid or empty input. The core idea is deriving a recurrence from explicit split and combine work. Work a tiny example aloud and name the invariant after each step, because that is the proof that the approach stays correct as the input grows.

A dependable implementation plan is to state base case; split into smaller independent problems; define subcall results; combine them; derive recurrence and stack use. Overlapping subproblems may require DP rather than plain divide and conquer. Keep the code aligned with that invariant instead of adding special cases that silently change the contract. Test the smallest input, a normal case, duplicates or ties where relevant, an adversarial boundary, and a case that exercises the failure path. The expected complexity is depends on recurrence, such as O(n log n) for balanced merge work. Explain both time and auxiliary memory, including recursion or helper structures; do not hide sorting, copying, or repeated scans. If the title omits critical constraints, say what you need to know before committing to a more specialized solution.