Week 23 of 43
Core DSA
WEEK 23 LEARNING MODULE
Monotonic Stacks & Monotonic Queues
Explores the Monotonicity invariant, monotonic increasing/decreasing stacks/queues, amortized $O(n)$ analysis, and next greater/smaller element queries.
5 Practice Problems3 Core ConceptsVerified Curriculum: high Confidence
What You'll Learn
- ✓Understand the Monotonicity Invariant: keeping stack/queue elements strictly ordered.
- ✓Implement Monotonic Stack for Next Greater Element and Daily Temperatures in $O(n)$ amortized time.
- ✓Calculate maximum rectangular areas in histograms in $O(n)$ time using monotonic stacks.
- ✓Implement Monotonic Deque for Sliding Window Maximum in $O(n)$ total time.
- ✓Prove $O(1)$ amortized complexity: every element is pushed and popped at most once.
Core Concepts
Monotonic Stack Invariant
O(n) total amortizedStack where elements are sorted (increasing or decreasing); popping violating elements before pushing.
Monotonic Queue / Deque
O(n) total amortizedDouble-ended queue maintaining monotonic order by removing smaller elements from back and expired indices from front.
Histogram Area Calculation
O(n) time, O(n) spaceFinding left and right boundary limits for each bar using monotonic stack in linear time.
Algorithms Covered
Next Greater ElementDaily TemperaturesLargest Rectangle in HistogramSliding Window Maximum ($O(n)$)132 Pattern Detection
Data Structures Applied
Monotonic StackMonotonic Deque
“Be the one for the Queue not in the Queue”
— Kanika Sarna