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Advanced · Module 21 · Lesson 2 of 4

Order & Stack Patterns: Binary Search on Answer, Monotonic Stack/Queue, and Sweep-Line

Recognize 'minimize the maximum' clues for Binary Search on Answer, find Next Greater Elements and Sliding Window Maximums in O(N) with Monotonic Stacks/Deques, and count overlapping intervals with Sweep-Line events.

Pro — members onlyAbout 18 minutes

By the end you can

  • Recognize the 'minimize the maximum / maximize the minimum' clue and verify the monotonic feasibility predicate check(X) for Binary Search on the Answer
  • Maintain a strictly monotonic stack (Next Greater/Smaller Element) and monotonic deque (Sliding Window Max/Min) in amortized O(N) time
  • Solve interval merging, meeting rooms, and skyline overlap problems using sorting + Sweep-Line event points

Builds on Searching an answer space, Deques and monotonic stacks, Intervals and sweeping.

01 · A question first

When a problem asks 'What is the minimum ship capacity to deliver all packages in D days?' on an unsorted array, beginners try DP and time out at O(N^2). How do you spot in 5 seconds that the answer space itself is sorted `[False, False, ..., True, True]`?

Make a guess before you read on.

02 · The idea

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What's inside

  • Intuitive Explanation & Real-World Analogy
  • Core Concepts & Visual Walkthrough
  • Pseudocode
  • Multi-Language Implementations (C++, Java, Python)
  • Time & Auxiliary Space Complexity Derivation
  • Edge Cases & Common Beginner Mistakes
  • Alternative Approaches (Brute Force vs. Optimal)
  • Pattern Recognition Guide & Three-Stage Practice Plan
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03 · Practice

Practice · hard · LeetCodeSliding Window MaximumReturn the maximum value for every contiguous window of width k.Practice · hard · LeetCodeLargest rectangle in histogramFind the largest rectangle under a histogram in O(n), using an increasing stack to find each bar's previous and next smaller bars.Practice · medium · LeetCodeMerge intervalsMerge all overlapping intervals after sorting them by start, in one pass.Practice · medium · LeetCodeCar fleetCount how many groups of cars arrive at a destination, by sorting by position and stacking arrival times.

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