LeetCopilot

Monotonic Stack & Queue

Master monotonic stack and queue patterns for next greater/smaller element, histogram, and sliding window maximum problems. Learn O(n) optimization techniques.

The Monotonic Stack & Queue patterns transform $O (N^{2})$ nested-loop solutions into elegant $O (N)$ single-pass algorithms. Master monotonic decreasing stacks for next greater element, increasing stacks for histogram problems, and monotonic queues for sliding window maximum. Learn the contribution technique, handle duplicates correctly, and recognize when to use each variant.

Featured Guide

Complete Guide

The Complete Monotonic Stack & Queue Guide: Master All Patterns, Templates, and Techniques

The ultimate comprehensive guide to monotonic stacks and queues. Learn all variants, when to use each pattern, complete templates in multiple languages, and a systematic approach to solve any monotonic stack/queue problem.

25 min read

Interactive Tool

Roadmap

Monotonic Stack Visualizer

Master monotonic stack and queue patterns through interactive visualization. Step through Next Greater Element, Daily Temperatures, and Sliding Window Maximum algorithms. Watch how the stack maintains monotonicity and processes elements in O(N).

Monotonic Stack & Queue Learning Roadmap: From Beginner to Interview-Ready in 6 Weeks

A structured 6-week learning path to master all monotonic stack and queue patterns. Progress from basic concepts to advanced techniques with curated problems, templates, and milestones.

Tutorials

Why Your Monotonic Stack Fails on Duplicates (And How to Fix It)

Discover why duplicates break monotonic stack solutions and learn the asymmetric comparison technique to handle them correctly. Avoid double-counting in contribution problems.

Monotonic StackDuplicatesCommon Mistakes

10 min

5 Common Mistakes in Next Greater Element Problems (And How to Avoid Them)

Identify and fix the most common bugs in next greater element solutions: wrong loop direction, incorrect popping condition, uninitialized results, circular array handling, and stack processing.

Monotonic StackNext Greater ElementCommon Mistakes

9 min

3 Critical Mistakes in Largest Rectangle in Histogram (And How to Fix Them)

Avoid the most common bugs in histogram problems: wrong width calculation, missing sentinels, and incorrect stack order. Learn the correct approach with detailed examples.

Monotonic StackHistogramLargest Rectangle

8 min

4 Common Mistakes in Sliding Window Maximum (Monotonic Queue)

Fix the most common bugs in sliding window maximum: using stack instead of deque, wrong window boundaries, not removing out-of-window elements, and incorrect result timing.

Monotonic QueueSliding Window MaximumDeque

6 min

Why Monotonic Stack Beats Brute Force: The O(n²) to O(n) Transformation

Understand the amortized analysis proof of why monotonic stacks are O(n), not O(n²). Learn the mathematical intuition, see visual proofs, and build deep understanding of when this optimization applies.

Monotonic StackTime ComplexityAmortized Analysis

14 min

How to Recognize Monotonic Stack Problems in 30 Seconds

Learn the exact keywords, problem structures, and mental models to instantly identify monotonic stack problems in interviews. Includes a 10-problem recognition quiz with detailed explanations.

Monotonic StackPattern RecognitionInterview Strategy

12 min

When to Store Indices vs Values in Monotonic Stack

Learn the decision framework for choosing between storing indices or values in your monotonic stack. Understand when each approach is optimal with practical examples.

Monotonic StackImplementationBest Practices

5 min

Trapping Rain Water: Edge Cases and Two Solution Approaches

Master trapping rain water edge cases with both monotonic stack and two pointers approaches. Learn when to use each method and handle all corner cases correctly.

Monotonic StackTwo PointersTrapping Rain Water

4 min

Handling Circular Arrays in Monotonic Stack Problems

Master the double-pass technique for circular array problems. Learn why single pass fails and how to correctly handle wraparound with modulo indexing.

Monotonic StackCircular ArraysNext Greater Element II

3 min

Monotonic Queue vs Priority Queue: When to Use Each

Understand the performance difference between monotonic queue (O(n)) and priority queue (O(n log k)) for sliding window problems. Learn when each approach is optimal.

Monotonic QueuePriority QueuePerformance

3 min

Stock Span Problem: Complete Solution with Monotonic Stack

Master the stock span problem with a complete walkthrough, visual examples, and edge case handling. Understand why monotonic decreasing stack is the optimal solution.

Monotonic StackStock SpanLeetCode 901

12 min

Debugging Monotonic Stack Solutions: A Systematic Approach

Learn a systematic debugging process for monotonic stack problems. Trace stack state, identify common bugs, verify invariants, and fix solutions quickly with this step-by-step guide.

Monotonic StackDebuggingTroubleshooting

11 min

Monotonic Decreasing Stack: Template, Next Greater Element, and When to Use It

Master the monotonic decreasing stack pattern with production-ready templates in Python, JavaScript, and Java. Learn when to use decreasing order, solve next greater element problems, and avoid common mistakes.

Monotonic StackDecreasing StackNext Greater Element

18 min

Monotonic Increasing Stack: Template, Next Smaller Element, and Histogram Problems

Master the monotonic increasing stack pattern for next smaller element and histogram problems. Learn production-ready templates, understand why increasing order works, and solve the canonical largest rectangle problem.

Monotonic StackIncreasing StackNext Smaller Element

20 min

Monotonic Queue: Template, Sliding Window Maximum, and When to Use Deque

Master the monotonic queue pattern for sliding window maximum problems. Learn why deque beats priority queue, understand the O(n) solution, and get production-ready templates in Python, JavaScript, and Java.

Monotonic QueueDequeSliding Window Maximum

22 min

Monotonic Stack vs Sliding Window vs DP: When to Use Each Pattern

Build a decision framework to instantly recognize monotonic stack problems and distinguish them from sliding window, dynamic programming, and two pointers. Learn the keywords, problem structures, and 30-second recognition checklist.

Monotonic StackPattern RecognitionSliding Window

20 min

Contribution Technique: Sum of Subarray Minimums and Advanced Monotonic Stack

Master the contribution technique to solve counting and summing problems with monotonic stacks. Learn how to calculate each element's contribution across all subarrays in O(n) time.

Monotonic StackContribution TechniqueSum of Subarray Minimums

18 min

Monotonic Stack for Range Queries: Stock Span, Trapping Rain Water, and Optimization

Learn how monotonic stacks solve range query problems and optimize nested loops. Master stock span, trapping rain water, and understand when to store indices vs values.

Monotonic StackRange QueriesStock Span

16 min