Explain dynamic programming with examples. What are the key characteristics?

🔢 Data Structures And Algorithm• 9/21/2025
Understanding dynamic programming principles, memoization vs tabulation, with classic examples like Fibonacci and coin change.

Dynamic Programming (DP)

Key Characteristics

  1. Overlapping Subproblems - Same subproblems are solved multiple times
  2. Optimal Substructure - Optimal solution contains optimal solutions to subproblems

Two Main Approaches

1. Memoization (Top-down)

  • Start with original problem
  • Break down into subproblems
  • Store results to avoid recomputation

2. Tabulation (Bottom-up)

  • Start with smallest subproblems
  • Build up to original problem
  • Fill table iteratively

Classic Examples

  • Fibonacci sequence
  • Coin change problem
  • Longest common subsequence
  • 0/1 Knapsack problem
By: System Admin