Assess students' ability to apply dynamic programming to solve 0/1 knapsack, longest common subsequence (LCS), and coin-change problems: design clear top-down and bottom-up algorithms (with pseudocode), reconstruct optimal solutions, derive and compare time and space complexity, and propose space-optimized variants (e.g., rolling arrays or memoization vs tabulation). Include discussion of trade-offs, correctness, and when each approach is preferable for given input sizes and constraints.