Monotonic Structures
Go beyond basic stacks and queues with Monotonic structures to solve range queries and boundary problems.
Go beyond basic stacks and queues with Monotonic structures to solve range queries and boundary problems. This hands-on tutorial focuses on practical implementation of monotonic structures concepts.
Monotonic Structures
A Monotonic Structure maintains its elements in a specific order (always increasing or always decreasing). This is powerful for problems involving "nearest" elements or finding minimums/maximums in a sliding window.
1. Monotonic Stack Recap
We use a monotonic decreasing stack to find the Next Greater Element.
2. Largest Rectangle in Histogram
This is a classic "hard" problem solved beautifully with a monotonic stack.
The area 5x2 = 10 is the maximum.
3. Monotonic Queue
Used primarily for the Sliding Window Maximum (which we covered in Module 6). It allows us to get the max element in $O(1)$ while sliding the window in $O(1)$ amortized.
AI Mentor
Confused about "monotonic structures monotonic stack queue next greater element largest rectangle histogram sliding window max"? Ask our AI mentor for a simplified explanation.
Quiz
Quiz
Question 1 of 1What property does a 'Monotonic Increasing' stack maintain?