Solve complex optimization problems by identifying Overlapping Subproblems and Optimal Substructure using Top-Down Memoization and Bottom-Up Tabulation.
Dynamic Programming Paradigms
### Dynamic Programming Principles
Dynamic Programming (DP) optimizes recursive exponential algorithms ($O(2^N)$) down to polynomial time ($O(N)$ or $O(N cdot W)$) by storing intermediate subproblem solutions:
1. **Top-Down (Memoization)**: Recursive call tree storing cached results in a lookup table or hash map.
2. **Bottom-Up (Tabulation)**: Iterative DP table population building solutions from base cases upward.
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