Monotonic Queue Optimization
You know CHT for lines. Monotonic queues handle sliding window min/max in O(1) per query.
Lessons
1. Intro
Deque optimization for sliding window DP
2. The Problem
When naive DP times out
3. Vocabulary - Monotonic Queue
Sorted deque
4. Quiz: Why Monotonic
Understanding the property
5. The Core Idea
Why old candidates become useless
6. Monotonic Queue - How It Works
Add and remove
7. Monotonic Queue - Walkthrough
Tracing the operations
8. Quiz: Monotonic Queue
Knowledge check
9. LeetCode 239 Sliding Window Maximum - Problem Statement
LeetCode 239
10. Sliding Maximum - The Approach
Why sorting fails
11. Sliding Maximum - The Pattern
Decreasing queue
12. Sliding Maximum - Implementation
The code
13. Sliding Maximum - Walkthrough
Detailed trace
14. LeetCode 1696 Jump Game VI - Problem Statement
LeetCode 1696
15. LeetCode 1696 Jump Game VI - DP Formulation
State and transition
16. LeetCode 1696 Jump Game VI - Optimization
Recognizing the pattern
17. LeetCode 1696 Jump Game VI - Implementation
The code
18. LeetCode 1696 Jump Game VI - Walkthrough
DP with window constraint
19. Quiz: Jump Game VI
Knowledge check
20. Challenge: Variable Window Size
Dynamic window bounds
21. LeetCode 1425 Constrained Subsequence Sum - Problem Statement
LeetCode 1425
22. Constrained Sum - DP Formulation
The twist
23. Constrained Sum - Implementation
The code
24. Constrained Sum - Walkthrough
Maximum sum with gap constraint
25. LeetCode 862 Shortest Subarray with Sum at Least K - Problem Statement
LeetCode 862
26. Shortest Subarray - Prefix Sums
Setting up the problem
27. Shortest Subarray - The Idea
Monotonic increasing queue
28. Shortest Subarray - Implementation
The code
29. Shortest Subarray - Walkthrough
Tracing the prefix sum approach
30. Quiz: Shortest Subarray
Knowledge check
31. Challenge: Negative Values
Why prefix sums help
32. When to Use Monotonic Queue
Pattern recognition
33. Max Sum of Rectangle - Problem Statement
2D extension
34. Max Consecutive Ones III - Problem Statement
Sliding window connection
35. Quiz: When Monotonic Queue
Pattern recognition
36. Increasing vs Decreasing
Choosing the right queue
37. Increasing vs Decreasing - Walkthrough
Choosing the right variant
38. Longest Continuous Subarray - Problem Statement
With absolute diff constraint
39. Longest Subarray - Implementation
Two deques pattern
40. Challenge: Online vs Offline
Query order matters
41. Monotonic Queue vs Other Techniques
When to use what
42. Pattern - Monotonic Queue Recognition
Identifying applicable problems
43. Implementation Template
Reusable code structure
44. What's Next
Preview of Aliens Trick
45. Section Recap
What we learned
Practice Problems
Covered with full walkthrough in this section.
Covered with full walkthrough in this section.
Covered with full walkthrough in this section.
Covered with full walkthrough in this section.
Classic monotonic deque + DP. Requires maintaining min/max in sliding window while computing optimal splits.
Sliding window DP optimization. Teaches converting absolute value costs into monotonic deque queries.
DP with segment removal. Monotonic queue maintains optimal previous states within window.
Counting with monotonic structure. Foundation for deque-based DP optimization.
Foundation problem for monotonic deque. Must master this before DP optimization variants.
Monotonic deque on prefix sums. Handles negative numbers unlike sliding window approaches.
Direct DP + monotonic deque. dp[i] = max(dp[j]) + nums[i] for j in window, classic pattern.
Clean monotonic deque DP. Optimal value within k-window directly maps to deque maximum.
Multi-segment DP with sliding window preprocessing. Good bridge to harder window DP.