Minimum Pair Removal to Sort Array I

Minimum Pair Removal to Sort Array I

What is this problem about?

The Minimum Pair Removal to Sort Array I problem gives you an array of integers and asks for the minimum number of "pair removal" operations to make it non-decreasing. In each operation, you pick any adjacent pair and replace them with their sum. The challenge is figuring out the minimum number of such merge operations needed. This Minimum Pair Removal to Sort Array I coding problem combines simulation with smart data structure choices.

Why is this asked in interviews?

Amazon and Google ask this because it tests simulation intuition and knowledge of efficient ordered data structures. Naive brute force is too slow; the real test is whether you can maintain a dynamic list and efficiently find the next violating pair. The linked list, heap, and ordered set interview pattern is central, making this a strong signal for candidates who understand amortized complexity and data structure selection.

Algorithmic pattern used

The optimal approach uses a doubly-linked list combined with a min-heap (priority queue). Store adjacent pairs in a heap by their sum. When you merge a pair, update the linked list and push new adjacent pairs into the heap. Continue until no pair a[i] > a[i+1] remains. This avoids re-scanning the whole array after each merge and keeps operations efficient.

Example explanation

Take array [5, 2, 3, 1]. The pair (5, 2) violates the non-decreasing order. Merge to get [7, 3, 1]. Now (7, 3) violates. Merge: [10, 1]. Now (10, 1) violates. Merge: [11]. That's 3 operations. A smarter selection order might do better — always merging the pair with the smallest sum tends to minimize total operations needed.

Common mistakes candidates make

• Re-scanning the full array after each operation, leading to O(n²) complexity.
• Not handling the updated neighbors correctly after a merge in the linked list.
• Treating this as purely greedy without verifying the heap-based simulation strategy.
• Forgetting to remove stale entries from the heap (lazy deletion needed).

Interview preparation tip

This problem is an excellent exercise in combining data structures. The key insight is that merging changes local neighbors, so you need a structure that supports O(log n) deletion and insertion while maintaining order. Practice doubly-linked list manipulation alongside heap operations. Simulate small examples by hand first to verify your merge logic before coding the full solution.