Minimum Pair Removal to Sort Array I - Video Solutions

Problem Overview: You are given an array and repeatedly remove pairs of adjacent elements following a specific rule until the array becomes non‑decreasing. The task is to compute the minimum number of pair removals required to make the remaining sequence sorted.

Approach 1: Brute Force Simulation (O(n^2) time, O(1) space)

The straightforward approach repeatedly scans the array to locate candidate adjacent pairs, removes the required pair, and rebuilds the array. After each removal you check whether the array is already non‑decreasing. Because each removal requires shifting elements and rescanning the array, the total cost grows quickly. This approach is useful to understand the mechanics of the operation but becomes inefficient when the array is large.

Approach 2: Heap + Doubly Linked List Simulation (O(n log n) time, O(n) space)

A more efficient solution treats the array as a dynamic structure where adjacent pairs are updated after each removal. Store all adjacent pairs in a min‑heap keyed by their pair value (for example the pair sum). Each heap entry also tracks the indices of the two elements. To support efficient deletions and neighbor updates, represent the array using a doubly‑linked list. When a pair is removed, update the neighboring nodes and push the newly formed adjacent pair into the heap.

Since removed elements invalidate some heap entries, lazy deletion is used: when a pair is popped from the heap, verify that both nodes are still active in the linked structure. If valid, remove the pair and connect its neighbors. This keeps pair updates local and avoids rescanning the entire array.

The heap ensures the next candidate pair is selected in O(log n) time, while the linked list handles removals and neighbor connections in constant time. The algorithm simulates the process efficiently and maintains the correct ordering constraints as the structure evolves. Concepts from heap (priority queue), array, and simulation are combined to maintain dynamic adjacency relationships.

Recommended for interviews: The heap + doubly linked list simulation is the expected approach. It demonstrates control over dynamic array updates, priority queues, and efficient neighbor maintenance. Starting with a brute force explanation shows you understand the process, while the optimized simulation shows practical problem‑solving skills.