DP Related

Start by clarifying the exact contract for DP Related: input representation, mutation rules, duplicate behavior, and what should happen on invalid or empty input. The core idea is classifying sequence grid interval tree subset or digit dependencies. 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 gather constraints; identify dependency structure; define state; establish acyclic evaluation order; compute state-transition complexity. Exponential masks are only valid when n is small enough. 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 time is states times transitions. 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.

Complexity: The complexity must follow the state graph: n states with a transitions each take O(na) time and O(n) stored state.