Building a DP solution requires choosing between two fundamental implementation routes. Master the trade-offs between Top-Down caching and Bottom-Up table filling.

60 Minutes

Intermediate

Memoization

This approach starts with the original large problem and recursively breaks it down. Before solving a sub-problem, we check if it is already in our cache (the "memo table").

Case Study: Coin Change

Top-Down Logic

Pseudocode

1function minCoins(amount, coins, memo):
2  if amount == 0: return 0
3  if amount < 0: return +INF
4  
5  if memo[amount] exists: 
6      return memo[amount] // CACHE HIT
7  
8  best = +INF
9  for c in coins:
10    best = min(best, 1 + minCoins(amount - c, coins, memo))
11  
12  memo[amount] = best // CACHE SAVE
13  return best

Comparison Matrix

Mastery Case: Rod Cutting

Pro Tip: Space Optimization

Often in Tabulation, you only need the previous row or even just the previous few values to calculate the current state. By using only O(1) or O(min(m, n)) space, you can save significant memory while maintaining O(n^2) speed.

Optimization:n^2 Matrix → 1D Array

DP Fundamentals Next: Sequences & Strings

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