What is Dynamic Programming? Compare Memoization (Top-Down) with Tabulation (Bottom-Up) using the 0/1 Knapsack Problem.
Quick Revision Summary
Dynamic programming caches overlapping subproblems. Top-Down uses recursion with memoization, while Bottom-Up uses iterative tabulation, often enabling 1D array space optimization.
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Model Answer & Deep-Dive Explanation
Dynamic Programming (DP) solves complex optimization problems by breaking them down into simpler subproblems, applicable when problems exhibit: (1) Overlapping Subproblems, and (2) Optimal Substructure.
Two Core Approaches:
- Top-Down (Memoization): Recursively solves problems from target down to base cases, caching computed intermediate results in a hash map or table to prevent redundant recomputations. More intuitive, but incurs recursion call-stack overhead.
- Bottom-Up (Tabulation): Solves all smallest subproblems iteratively first, filling an n-dimensional table sequentially until reaching the final answer. Eliminates stack overflow risk and often permits space optimization (e.g. keeping only the last 2 rows).
Interviewer Evaluation Points & Scoring Rubric
- 1 1. States conditions for DP (overlapping subproblems, optimal substructure). 2. Compares recursion+memoization vs iterative tabulation. 3. Demonstrates space optimization.
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