Lilly Tech Systems
Dynamic Programming Patterns
Master dynamic programming from first principles. Every problem follows the same progression: brute force recursion, add memoization, convert to tabulation, then optimize space. This course covers 30+ real coding exam problems with complete Python solutions and clear explanations.
Your Learning Path
Follow these lessons in order to build DP mastery from the ground up, or jump to any pattern you need to practice.
1. DP Fundamentals
What is dynamic programming, overlapping subproblems, optimal substructure, memoization vs tabulation, and when to use DP. The foundation for everything that follows.
2. 1D DP Problems
Six classic problems: climbing stairs, house robber, coin change, longest increasing subsequence, maximum subarray, and decode ways. Each solved three ways.
3. 2D DP Problems
Five grid and sequence problems: unique paths, minimum path sum, edit distance, longest common subsequence, and matrix chain multiplication.
4. Knapsack Patterns
Five knapsack variants: 0/1 knapsack, unbounded knapsack, subset sum, partition equal subset sum, and target sum. The most tested DP family in interviews.
5. String DP
Five string problems: longest palindromic substring, word break, regular expression matching, interleaving string, and distinct subsequences.
6. Interval & Game DP
Five interval problems: burst balloons, stone game, minimum cost tree from leaf values, palindrome partitioning, and optimal BST construction.
7. DP Optimization Techniques
Space optimization, bitmask DP for subset problems, digit DP for counting, and DP on trees. Techniques that separate good from great DP solutions.
8. DP Pattern Recognition
Decision framework for identifying DP problems, pattern matching guide, common pitfalls, and a comprehensive FAQ for coding exams.
What You Will Learn
By the end of this course, you will be able to:
Recognize DP Problems
Instantly identify when a problem requires dynamic programming by spotting overlapping subproblems and optimal substructure in the problem statement.
Write Three Solutions
For any DP problem, write brute force recursion, add memoization for top-down, then convert to bottom-up tabulation — the progression interviewers expect.
Optimize Time & Space
Apply space optimization to reduce memory from O(n^2) to O(n), use bitmask DP for subset problems, and recognize when DP on trees applies.
Ace DP Interviews
Solve 30+ classic problems covering all major DP patterns: 1D, 2D, knapsack, string, interval, and optimization — the patterns that appear in 90% of DP interview questions.