DP LIS | DSA Interview Patterns - Study Chapter | QuizMaker

Increasing subsequences, chains, divisibility, and ordered transitions.

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DSA Interview Patterns Roadmap

Dynamic Programming

Increasing subsequences, chains, divisibility, and ordered transitions.

Item	Detail
Core signal	A known interview family appears and the constraints reward the standard pattern.
Use when	LIS variants become easier when sorted order and predecessor relation are separated.
Avoid when	The required invariant is not monotonic or the input constraints point to a simpler direct scan.

LIS variants become easier when sorted order and predecessor relation are separated.

identify pattern
initialize state/container
for each input unit:
  update state safely
  update answer when invariant is valid
return answer

Take the smallest DP LIS example, track the state after every operation, and verify the final answer before coding.

Item	Detail
Expected time	Usually O(n log n), O(V + E), or states times transitions depending on the family.
Expected space	Usually O(n), O(V + E), or number of DP states.

Java: prefer explicit classes and clear helper methods over clever one-liners.
C++: use vector, unordered_map, set, priority_queue, and long long when sums can grow.
Python: keep state readable with dict, set, deque, heapq, and lru_cache where appropriate.