To solve this problem, you need to repeatedly remove pairs of elements from the array to make it non-decreasing. A good approach is to use array scanning combined with hash lookups to identify and remove pairs efficiently. This method works well within the problem's constraints, requiring careful handling of array scanning and lookup operations.
Problem Statement
Given an array nums, you can perform the following operation any number of times: remove one pair of elements that are out of order. Return the minimum number of operations needed to make the array non-decreasing.
An array is said to be non-decreasing if each element is greater than or equal to its previous element (if it exists). This means you need to remove pairs where nums[i] > nums[i+1] until the array satisfies the non-decreasing condition.
Examples
Example 1
Input: nums = [5,2,3,1]
Output: 2
The array nums became non-decreasing in two operations.
Example 2
Input: nums = [1,2,2]
Output: 0
The array nums is already sorted.
Constraints
- 1 <= nums.length <= 105
- -109 <= nums[i] <= 109
Solution Approach
Array Scanning and Hash Lookups
The key to solving this problem is efficiently scanning the array and using hash lookups to track the operations. By checking pairs of elements and using a hash table to record pairs for removal, you can determine the minimum operations needed.
Simulation of Pair Removal
Simulate the removal process using data structures such as heaps or ordered sets to identify the elements that should be removed. By simulating the removal of elements, you can efficiently calculate the minimum number of operations.
Optimized Handling of Edge Cases
Consider edge cases such as arrays that are already non-decreasing or arrays with only one element. These special cases can simplify the logic by avoiding unnecessary operations.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time and space complexity depend on the final approach, which includes factors such as the number of elements in the array and the specific data structures used. Typically, the time complexity is O(n) or O(n log n) depending on the optimization chosen, and space complexity is proportional to the number of elements being stored for processing (O(n)).
What Interviewers Usually Probe
- The candidate should be able to describe the correct approach of using array scanning and hash lookups.
- The candidate should demonstrate an understanding of when to simulate pair removal and which data structures are efficient for this.
- The candidate must identify edge cases and explain how they handle them during the simulation.
Common Pitfalls or Variants
Common pitfalls
- Not optimizing the scanning process and hash lookup steps, resulting in higher time complexity.
- Failing to handle edge cases, such as already sorted arrays or arrays of length one.
- Using inefficient data structures that increase space complexity unnecessarily.
Follow-up variants
- Consider a variation where the array is sorted in descending order initially.
- What if the array contains negative numbers as well? This would add complexity to the solution.
- Explore a variant where only specific pairs are allowed for removal, adding constraints to the operations.
How GhostInterview Helps
- GhostInterview assists by providing a framework to solve this problem efficiently using array scanning and hash lookup techniques.
- It helps you practice the pattern of minimizing operations with specific removal actions by using appropriate data structures like heaps and ordered sets.
- GhostInterview also provides a variety of problem variants and edge cases to sharpen your problem-solving skills.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the primary approach to solving the Minimum Pair Removal to Sort Array II problem?
The primary approach is to use array scanning combined with hash lookups to identify pairs for removal, minimizing the number of operations.
How do data structures like heaps and ordered sets help in solving this problem?
Heaps and ordered sets help efficiently simulate the pair removal process by allowing you to quickly identify and remove out-of-order pairs.
What are the edge cases I need to handle when solving this problem?
Edge cases include already sorted arrays, arrays with one element, and arrays with negative numbers.
Can the solution to this problem be optimized further?
Yes, by choosing the appropriate data structures and optimizing the scanning and lookup processes, you can reduce the time complexity.
How does GhostInterview assist in preparing for the Minimum Pair Removal to Sort Array II problem?
GhostInterview provides step-by-step assistance in practicing the solution approach, offering examples and a variety of problem variants to help master the technique.
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This problem asks for the minimum number of operations to make an array non-decreasing by removing pairs of elements.
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