12. Monotonic Stack Pattern: Daily Temperatures & Next Greater Element • Data Structures & Algorithms: Blind 75 & Big Tech Interview Prep • Rishabh Ki Kaksha

Data Structures & Algorithms: Blind 75 & Big Tech Interview Prep › 12. Monotonic Stack Pattern: Daily Temperatures & Next Greater Element

45 mins

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Course Syllabus

Module 1: Big-O Asymptotics, Arrays & Sliding Window

01. Time & Space Complexity Masterclass: Big-O, Big-Theta, Big-Omega & Amortized Analysis 02. Arrays & Hashing: Two Sum, Contains Duplicate & Valid Anagram (Hash Table Lookups) 03. Prefix Sum & Kadane's Algorithm (Maximum Subarray Problem in O(N)) 04. Sliding Window Pattern: Fixed vs Dynamic Windows (Best Time to Buy/Sell Stock)

Module 2: Two Pointers & Binary Search Systems

05. Two Pointers Pattern: Valid Palindrome, 3Sum & Container With Most Water 06. Binary Search Foundations: Search in Rotated Sorted Array & Find Minimum 07. Binary Search on Answer Space: Koko Eating Bananas & Capacity to Ship Packages

Module 3: Linked Lists & Fast-Slow Pointer Patterns

08. Singly vs Doubly Linked Lists & In-Place Pointer Manipulation (Reverse Linked List) 09. Fast & Slow Pointer (Floyd's Cycle Detection): Linked List Cycle & Middle Node 10. Merging & Reordering: Merge Two Sorted Lists, Reorder List & Remove Nth Node

Module 4: Stacks, Queues & Monotonic Stack Architecture

11. Stack Fundamentals: Valid Parentheses & Min Stack in O(1) Time 12. Monotonic Stack Pattern: Daily Temperatures & Next Greater Element 13. Hard Stack Coding: Largest Rectangle in Histogram & Trapping Rain Water

Module 5: Trees, Binary Search Trees & DFS/BFS Traversals

14. Binary Tree Architecture: Max Depth, Same Tree & Invert Binary Tree 15. BFS Level-Order Traversal & Binary Tree Right Side View 16. Binary Search Tree (BST) Properties: Validate BST & Lowest Common Ancestor (LCA) 17. Tree Path Sums & Serialize / Deserialize Binary Tree (Hard)

Module 6: Heaps, Priority Queues & Top-K Problems

18. Min Heap & Max Heap Internals: Array Representation & Heapify in O(N) 19. Top-K Elements Pattern: Kth Largest Element in an Array & Top K Frequent Elements 20. Two-Heap Pattern: Find Median from Data Stream (Hard)

Module 7: Graphs, Topological Sort & Shortest Paths (Dijkstra)

21. Graph Representations (Adjacency Matrix vs List) & DFS/BFS Traversal 22. Matrix Graph Traversal: Number of Islands, Max Area of Island & Clone Graph 23. Topological Sort (Kahn's Algorithm): Course Schedule I & II (Cycle Detection) 24. Disjoint Set Union (DSU / Union-Find): Redundant Connection & Number of Connected Components

Module 8: Dynamic Programming, Backtracking & Bit Manipulation

25. Backtracking Pattern: Subsets, Permutations, Combination Sum & Word Search 26. 1D Dynamic Programming: Climbing Stairs, House Robber & Coin Change 27. Longest Increasing Subsequence (LIS): O(N^2) DP vs O(N log N) Patience Sort 28. 2D Dynamic Programming: Unique Paths, Longest Common Subsequence (LCS) & Edit Distance 29. 0/1 Knapsack Pattern & Partition Equal Subset Sum 30. Bit Manipulation Tricks: Number of 1 Bits (Hamming Weight), Counting Bits & Missing Number

Interactive Lesson Studio

# 12. Monotonic Stack Pattern: Daily Temperatures & Next Greater Element

> DSA Blind 75 Notes by Rishabh - Topic 12

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### 1. Monotonic Stack Kya Hai? (The Strict Order Guard 💂)

Monotonic Stack aisi stack hoti hai jiske elements **hamesha strictly strictly Increasing ya strictly Decreasing order** me maintain rehte hain!

> **Core Rule:** Jab bhi koi naya element purane order ko todta hai, toh stack ke elements tab tak **pop** hote hain jab tak order restore na ho jaye!

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### 2. LeetCode #739: Daily Temperatures ($O(N)$ Monotonic Decreasing Stack)

*Problem:* Har din ke liye pata lagao ki kitne din baad warmer temperature aayega.

```python
def dailyTemperatures(temperatures: list[int]) -> list[int]:
    n = len(temperatures)
    res = [0] * n
    stack = [] # stores indices [i]
    
    for current_day, current_temp in enumerate(temperatures):
        # Jab tak current temperature stack ke top se garam hai:
        while stack and current_temp > temperatures[stack[-1]]:
            prev_day = stack.pop()
            res[prev_day] = current_day - prev_day
            
        stack.append(current_day)
        
    return res
```
*Time Complexity:* $O(N)$ (Har element maximum 1 baar push aur 1 baar pop hota hai).

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### 3. Master Comparison Matrix

| Problem | Stack Monotonicity | Stack Stores | When to Pop? |
| :--- | :--- | :--- | :--- |
| **Next Greater Element** | Decreasing | Indices or Values | `current > stack[-1]` |
| **Next Smaller Element** | Increasing | Indices or Values | `current < stack[-1]` |
| **Daily Temperatures** | Decreasing | Day Indices | `temp[curr] > temp[stack[-1]]` |

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### 4. Interview Ke 3 Sawal Is Topic Se

1. **Monotonic stack ka nested `while` loop hone par bhi $O(N)$ time kyu hota hai?** -> Amortized analysis: $N$ elements me se har element array me exactly 1 baar stack me push hota hai aur maximum 1 baar pop hota hai (Total max $2N$ operations).
2. **Next Greater Element II (Circular Array) kaise solve hota hai?** -> Array ko virtual $2N$ length tak iterate karke (`i % n`).
3. **Monotonic Stack kab use karni chahiye?** -> Jab question me *"Next greater element"*, *"Previous smaller element"*, ya *"Span of subarray"* dhoondhna ho.

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**Next Topic:** 13. Hard Stack Coding: Largest Rectangle in Histogram & Trapping Rain Water

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