LeetCode 3510 | Minimum Pair Removal to Sort Array II | Java | Hard | CodeByTushu
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In today’s video, we solve LeetCode 3510 - Minimum Pair Removal to Sort Array II using Doubly Linked List and Min-Heap in Java.
We are given an array of integers where we repeatedly find the adjacent pair with the minimum sum, breaking ties by picking the leftmost pair, and replace them with their sum until the array becomes sorted in non-decreasing order. Because the array size can be up to 100,000 elements, an O(n^2) brute-force simulation will exceed time limits. Instead, we model the sequence as an index-based Doubly Linked List so element deletions and neighbor re-linking execute in O(1) time.
To efficiently identify the minimum sum adjacent pair, we utilize a Min-PriorityQueue with lazy version validation. We also track the number of adjacent inversions, meaning adjacent descents where a left element is strictly greater than its right neighbor, dynamically in O(1) time per operation. The simulation halts immediately when the inversion count drops to zero. With 64-bit integer arithmetic to safely prevent numeric overflow on sums up to 2 * 10^14, our algorithm achieves optimal O(n log n) time and O(n) space complexity.
🔥 Problem Highlights
✅ Doubly Linked List representation via prev and next pointer arrays for O(1) element deletion and neighbor relinking
✅ Min-PriorityQueue tracking adjacent pair sums with leftmost index tie-breaking
✅ Versioning mechanism enabling lazy deletion of stale heap pairs in O(log n)
✅ O(1) dynamic adjacent inversion tracking to detect non-decreasing order without full array scans
✅ 64-bit integer arithmetic using long in Java and C++, and BigInt in JavaScript, preventing integer overflow
✅ Optimal O(n log n) overall time complexity and O(n) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro
01:01 Problem Understanding and Constraints
02:24 Core Observations and Mathematical Insight
03:16 Algorithmic Approach and Simulation Strategy
04:22 Line-by-Line Java Code Walkthrough
05:41 Step-by-Step Test Run and Dry Run
07:34 Time Complexity Analysis
08:30 Space Complexity Analysis
09:14 Outro and Key Takeaways
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.js
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🔥 Perfect For
LeetCode Hard Problems
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Doubly Linked List Pattern
Min-Heap with Lazy Deletion
Adjacent Inversion Counting
Time Complexity Optimization
Coding Interview Preparation
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💬 Question of the Day
Why does an O(N^2) simulation fail on LeetCode 3510, and how does lazy invalidation in a Min-Heap solve this?
1️⃣ An input size of up to 10^5 can cause up to 10^10 operations; the heap with lazy versioning processes merges in O(N log N)
2️⃣ An O(N^2) approach uses too much auxiliary recursion stack space
3️⃣ The sum of adjacent elements cannot be computed in O(1) without a heap
4️⃣ JavaScript cannot handle arrays with more than 10^4 elements
#LeetCode3510 #LeetCode #MinimumPairRemovalToSortArrayII #Java #JavaDSA #DoublyLinkedList #MinHeap #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description
In today’s video, we solve LeetCode 3510 - Minimum Pair Removal to Sort Array II using Doubly Linked List and Min-Heap in Java.
We are given an array of integers where we repeatedly find the adjacent pair with the minimum sum, breaking ties by picking the leftmost pair, and replace them with their sum until the array becomes sorted in non-decreasing order. Because the array size can be up to 100,000 elements, an O(n^2) brute-force simulation will exceed time limits. Instead, we model the sequence as an index-based Doubly Linked List so element deletions and neighbor re-linking execute in O(1) time.
To efficiently identify the minimum sum adjacent pair, we utilize a Min-PriorityQueue with lazy version validation. We also track the number of adjacent inversions, meaning adjacent descents where a left element is strictly greater than its right neighbor, dynamically in O(1) time per operation. The simulation halts immediately when the inversion count drops to zero. With 64-bit integer arithmetic to safely prevent numeric overflow on sums up to 2 * 10^14, our algorithm achieves optimal O(n log n) time and O(n) space complexity.
🔥 Problem Highlights
✅ Doubly Linked List representation via prev and next pointer arrays for O(1) element deletion and neighbor relinking
✅ Min-PriorityQueue tracking adjacent pair sums with leftmost index tie-breaking
✅ Versioning mechanism enabling lazy deletion of stale heap pairs in O(log n)
✅ O(1) dynamic adjacent inversion tracking to detect non-decreasing order without full array scans
✅ 64-bit integer arithmetic using long in Java and C++, and BigInt in JavaScript, preventing integer overflow
✅ Optimal O(n log n) overall time complexity and O(n) auxiliary space complexity
⏱️ TIMESTAMPS
00:00 Intro
01:01 Problem Understanding and Constraints
02:24 Core Observations and Mathematical Insight
03:16 Algorithmic Approach and Simulation Strategy
04:22 Line-by-Line Java Code Walkthrough
05:41 Step-by-Step Test Run and Dry Run
07:34 Time Complexity Analysis
08:30 Space Complexity Analysis
09:14 Outro and Key Takeaways
📂 Problem Folder and Detailed Documentation:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/tree/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II
☕ Java Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/Solution.java
🐍 Python Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.py
⚡ C++ Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.cpp
🌐 JavaScript Solution:
https://github.com/CodeByTushu/CodeByTushu-LeetCode-Solutions/blob/main/solutions/January/23-January/3510-Minimum-Pair-Removal-to-Sort-Array-II/solution.js
🔗 LeetCode Source Code
📌 Admin type the link
🌐 All LeetCode Solutions
📌 https://codebytushu.com/Leetcode/
📱 Join CodeByTushu on WhatsApp
Get coding updates, LeetCode solutions, daily questions and more.
https://whatsapp.com/channel/0029Vb8k5mCDeON2Xwlkxe40
❤️ Donate
📌 https://codebytushu.com/Leetcode/donate.php
🔥 Perfect For
LeetCode Hard Problems
Java DSA Preparation
Doubly Linked List Pattern
Min-Heap with Lazy Deletion
Adjacent Inversion Counting
Time Complexity Optimization
Coding Interview Preparation
Problem Solving
🌐 Follow CodeByTushu
▶️ YouTube: https://www.youtube.com/@codebytushu
📸 Instagram: https://instagram.com/codebytushu/
💼 LinkedIn: https://www.linkedin.com/company/codebytushu/
🌍 Website: https://codebytushu.com
🐙 GitHub: https://github.com/CodeByTushu
❤️ Don’t Forget To
👍 Like | 💬 Comment | 🔔 Subscribe
💬 Question of the Day
Why does an O(N^2) simulation fail on LeetCode 3510, and how does lazy invalidation in a Min-Heap solve this?
1️⃣ An input size of up to 10^5 can cause up to 10^10 operations; the heap with lazy versioning processes merges in O(N log N)
2️⃣ An O(N^2) approach uses too much auxiliary recursion stack space
3️⃣ The sum of adjacent elements cannot be computed in O(1) without a heap
4️⃣ JavaScript cannot handle arrays with more than 10^4 elements
#LeetCode3510 #LeetCode #MinimumPairRemovalToSortArrayII #Java #JavaDSA #DoublyLinkedList #MinHeap #DSA #CodingInterview #ProblemSolving #LeetCodeHard #DailyLeetCode #JavaProgramming #CodeByTushu
👇 Comment the answer below! 🔥 Close description