advanced~6h
Dynamic Programming Problem Set
A themed set of classic dynamic programming problems — climbing stairs, 0/1 knapsack, longest common subsequence, coin change, and longest increasing subsequence — each one taught explicitly through the recursion-to-memoization-to-tabulation progression, so the transition from 'it works but it's slow' to 'it's fast' is never a magic trick.
Learning objectives
- Walk any DP problem through the three-stage progression: naive recursion, top-down memoization, and bottom-up tabulation
- Solve climbing stairs and recognize its recurrence as structurally identical to Fibonacci
- Solve 0/1 knapsack using a 2D DP table and explain why each item can only be taken once
- Compute longest common subsequence using a 2D DP table indexed by prefixes of both strings
- Solve coin change (minimum coins) and explain why a greedy approach fails on certain coin denominations
- Compute longest increasing subsequence using an O(n^2) DP approach and describe the O(n log n) improvement at a conceptual level
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Dynamic Programming Problem Set