Interval DP
You've compared sequences with LCS. Now solve problems where the answer depends on breaking ranges apart.
Lessons
1. Intro
Why ranges need special thinking
2. Core Concept
Range-based states
3. Vocabulary - Interval
Range definition
4. The Split Point Approach
Dividing ranges
5. Loop Order
Why length matters
6. Quiz: Interval DP Basics
Testing core concepts
7. LeetCode 516 Longest Palindromic Subsequence - Problem Statement
Entry problem
8. LeetCode 516 Longest Palindromic Subsequence - Key Observation
Endpoints determine structure
9. LeetCode 516 Longest Palindromic Subsequence - State Design
The 2D table
10. LeetCode 516 Longest Palindromic Subsequence - Transition
Match or skip
11. LeetCode 516 Longest Palindromic Subsequence - Implementation
The code
12. LeetCode 516 Longest Palindromic Subsequence - Walkthrough
Tracing the algorithm
13. Quiz: LPS Transition
Understanding the recurrence
14. Lessons from LPS
summary
15. Matrix Chain Multiplication - Problem Statement
Classic interval DP
16. Matrix Chain Multiplication - The Setup
Understanding dimensions
17. Matrix Chain Multiplication - State Definition
What dp[i][j] means
18. Matrix Chain Multiplication - Transition
Try all split points
19. Matrix Chain Multiplication - Implementation
The code
20. Matrix Chain Multiplication - Walkthrough
Tracing optimal splits
21. Challenge: Matrix Chain Reconstruction
Finding optimal parenthesization
22. Quiz: Matrix Chain Complexity
Understanding the cost
23. Lessons from Matrix Chain
summary
24. LeetCode 312 Burst Balloons - Problem Statement
LeetCode 312
25. LeetCode 312 Burst Balloons - The Trick
Think about last
26. LeetCode 312 Burst Balloons - State Definition
Open intervals
27. LeetCode 312 Burst Balloons - Transition
Last balloon
28. LeetCode 312 Burst Balloons - Implementation
The code
29. LeetCode 312 Burst Balloons - Walkthrough
Tracing the trick
30. Quiz: Burst Balloons Insight
Why think backwards
31. Lessons from Burst Balloons
summary
32. LeetCode 132 Palindrome Partitioning II - Problem Statement
LeetCode 132
33. LeetCode 132 Palindrome Partitioning II - Two DPs
Precompute + solve
34. LeetCode 132 Palindrome Partitioning II - Implementation
The code
35. LeetCode 132 Palindrome Partitioning II - Walkthrough
Minimum cuts trace
36. Challenge: Palindrome Partitioning All
Finding all partitions
37. Pattern - Interval DP
When to use it
38. LeetCode 877 Stone Game - Problem Statement
Interval DP game
39. LeetCode 877 Stone Game - Implementation
Game theory meets intervals
40. Quiz: Stone Game Insight
Difference formulation
41. LeetCode 1039 Minimum Score Triangulation of Polygon - Problem Statement
Polygon DP
42. LeetCode 1039 Minimum Score Triangulation of Polygon - Implementation
MCM variant
43. Pattern - When Interval DP
Recognizing the pattern
44. What's Next
Preview of Tree DP
45. Section Recap
What we learned
Practice Problems
Perfect intro to interval DP - merge adjacent elements pattern.
Adds game theory - think from opponent's perspective.
Palindrome removal with interval merging when endpoints match.
Classic - think backwards, consider each balloon as LAST to burst.
3D DP with K-pile constraint - teaches when problems are impossible.
Covered with full walkthrough in this section.
Covered with full walkthrough in this section.
Color balanced brackets with constraints. Interval DP on bracket structures.
Count palindromic substrings in ranges. Precompute with interval DP, answer queries O(1).
Build BST where adjacent nodes share common factor. Interval DP with number theory twist.
Classic interval DP - order cuts to minimize total cost. Direct MCM variant.
Maximize points removing consecutive boxes. 3D interval DP with extra state.
Count ways to paint strip with interval constraints. Classic interval DP counting.
Sum of equal pair weights in subarrays. Contribution technique with DP.
Minimize sum of max-min in prefixes. Interval DP on sorted array.
Minimize array by merging equal adjacent pairs. Interval DP with value tracking.
Make array zero with XOR operations. Interval-style parity analysis.
Select non-overlapping intervals to maximize score - segment tree optimized interval DP.