Classic DP Problems
Master the most common dynamic programming patterns: Knapsack, LCS, and more.
Master the most common dynamic programming patterns: Knapsack, LCS, and more. This hands-on tutorial focuses on practical implementation of classic dp problems concepts.
Classic DP Problems
Now that you understand the core concepts of memoization and tabulation, let's apply them to problems that are frequently asked in top-tier interviews.
1. 0/1 Knapsack Problem
Given weights and values of $n$ items, put these items in a knapsack of capacity $W$ to get the maximum total value. You cannot break items (0/1).
2. Longest Common Subsequence (LCS)
Find the length of the longest subsequence present in both strings.
- Example: "abcde" and "ace" -> "ace" (Length 3)
Pattern Comparison: Knapsack vs LCS
| Problem | Dimension | Space Complexity | Core Logic |
|---|---|---|---|
| Knapsack | 2D (Items x Weight) | O(W) optimized | Taking vs Leaving |
| LCS | 2D (String1 x String2) | O(min(m,n)) optimized | Match vs Mismatch |
AI Mentor
Confused about "classic dynamic programming knapsack LCS overlapping subproblems optimal substructure memoization tabulation"? Ask our AI mentor for a simplified explanation.
Quiz
Quiz
Question 1 of 2In the 0/1 Knapsack problem, why can't we use a greedy approach based on value/weight ratio?