Stacks & Monotonic Stacks
Stacks are last in, first out. Learn monotonic stacks for next greater element and histogram problems.
Lessons
1. Intro
The LIFO principle
2. Vocabulary - Stack
Last in, first out
3. Stack Visualization
See it work
4. Stack Implementation
Array-backed
5. Where Stacks Shine
Common applications
6. The Matching Problem
Nested structures
7. Problem - Valid Parentheses
Classic stack problem
8. Valid Parentheses - Algorithm
Push and match
9. Valid Parentheses - Implementation
Complete solution
10. Lessons from Valid Parentheses
core idea
11. Quiz: Stack Basics
LIFO behavior
12. A Harder Problem
Beyond matching
13. Vocabulary - Monotonic Stack
Ordered elements
14. Why Monotonic Works
The core idea
15. Monotonic Stack Visualization
Step by step
16. Problem - Next Greater Element I
Monotonic stack intro
17. Next Greater - Algorithm
Stack + hash map
18. Next Greater - Implementation
Complete solution
19. Lessons from Next Greater
Pattern recognition
20. Quiz: Monotonic Stack
Pop condition
21. Problem - Daily Temperatures
Next greater with indices
22. Daily Temperatures - The Idea
Store indices
23. Daily Temperatures - Implementation
Complete solution
24. Lessons from Daily Temperatures
Index tracking
25. A Famous Problem
Histogram rectangles
26. Histogram - Key Observation
Extension limits
27. Histogram - The Approach
When to calculate
28. Histogram - Visualization
Trace the algorithm
29. Histogram - Why It Works
Correctness argument
30. Histogram - Implementation
Complete solution
31. Lessons from Histogram
Advanced pattern
32. Quiz: Histogram
Boundary calculation
33. Monotonic Stack Variants
Increasing vs decreasing
34. Previous vs Next
Direction matters
35. Recognizing Stack Problems
Pattern hints
36. Problem - Trapping Rain Water
Advanced application
37. Trapping Water - Stack Approach
Layer by layer
38. Trapping Water - Implementation
Complete solution
39. Quiz: Stack Problem Types
Choosing approach
40. Section Recap
What we learned
Practice Problems
Classic bracket matching problem that teaches basic stack operations for finding the longest valid bracket subsequence.
Teaches bracket balance counting using stack-based thinking to determine minimum moves for a regular bracket sequence.
Reinforces greedy stack approach for extracting regular bracket subsequences of specified length.
Teaches using stacks to characterize bracket sequences and count valid concatenations via sequence signatures.
Excellent problem combining stack with greedy strategy to build lexicographically minimal strings.
Classic stack application for finding longest valid bracket sequences with counting. Teaches advanced stack indexing.
Fundamental monotonic stack problem for finding the range where each element is minimum. Essential optimization pattern.
Combines monotonic stack with LIS concepts. Teaches maintaining multiple stacks for optimal color assignment.
Teaches simulation with stacks for prefix removal operations, combining pattern recognition with bracket matching.
Constructive problem requiring generation of multiple distinct regular bracket sequences.
Advanced monotonic stack optimization for DP transitions. Efficiently find range maximums during state computation.
Advanced problem involving stack operation queries across time. Teaches persistent data structure concepts.
Perfect introduction to stack data structure; teaches the fundamental LIFO principle for matching paired elements.
Most popular monotonic stack problem; combines next greater element with distance calculation.
The gold standard for monotonic stack mastery; requires finding both previous and next smaller elements.
Can be solved with two pointers, DP, or monotonic stack. The stack solution processes elements layer by layer.
Teaches contribution technique with monotonic stacks. Each element contributes to multiple subarrays based on boundaries.
Teaches greedy monotonic stack for lexicographical ordering; combines frequency counting with stack manipulation.
Non-obvious monotonic stack application requiring reverse traversal; teaches maintaining candidates while searching.
Requires finding the second greater element using two stacks; advanced extension of classic next greater pattern.