To solve this problem, you need to figure out how to perform pair removals to make an array non-decreasing. The challenge lies in minimizing the number of operations needed. A combination of array scanning and hash lookups helps track which pairs can be removed efficiently.
Problem Statement
You are given an array nums. You can repeatedly remove one pair of elements from the array until it becomes non-decreasing. A pair of elements is removed if one of them is smaller than the other, but only the pair’s position is considered, not their values themselves. Your task is to return the minimum number of operations required to make the array non-decreasing.
An array is considered non-decreasing if for every i, nums[i] <= nums[i+1]. If the array is already non-decreasing, no operations are required. You can only remove one pair of elements in each operation. A solution that involves scanning the array and leveraging hash lookups will help minimize the operations.
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 <= 50
- -1000 <= nums[i] <= 1000
Solution Approach
Array Scanning
Iterate through the array from left to right, checking the order of elements. For each element, find the largest subset of consecutive elements that can be removed without breaking the non-decreasing property.
Hash Lookup Optimization
Use a hash set or table to keep track of which pairs can be removed efficiently. This avoids repetitive checks and reduces the computational cost of each step.
Greedy Pair Removal
Perform greedy pair removals by continuously removing the smallest removable pair in each operation. This ensures the minimum number of operations by focusing on the most impactful removals.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity is driven by the scanning of the array and the hash lookup process. In the worst case, it will be O(n) where n is the length of the array. Space complexity depends on the data structure used for tracking pairs, but it typically remains O(n) as well.
What Interviewers Usually Probe
- Can the candidate effectively track removable pairs using a hash table?
- Does the candidate approach the problem using greedy techniques?
- Is the candidate able to optimize the algorithm to reduce unnecessary steps?
Common Pitfalls or Variants
Common pitfalls
- Failing to consider the order of removals, which could lead to unnecessary operations.
- Not efficiently using hash lookups to reduce the number of pair checks.
- Misunderstanding the definition of 'non-decreasing' and attempting unnecessary operations.
Follow-up variants
- What if the array contains only one element?
- Can this problem be solved by applying dynamic programming?
- How would the approach change if you could remove more than one pair per operation?
How GhostInterview Helps
- GhostInterview can guide you through common pitfalls and ensure you don't overlook efficient tracking of pairs.
- It provides quick feedback on optimizing your algorithm and helps you focus on minimizing unnecessary operations.
- GhostInterview helps you refine your greedy and hash lookup approach, ensuring you maximize performance.
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 minimum number of operations for the array [5,2,3,1]?
The minimum number of operations is 2, as the array becomes non-decreasing after two pair removals.
How do hash lookups help in solving this problem?
Hash lookups allow you to efficiently track which pairs are removable, reducing the number of unnecessary checks.
What if the array is already non-decreasing?
If the array is already non-decreasing, no operations are needed, and the output is 0.
How can I optimize the solution for larger arrays?
Optimizing the solution involves using hash sets for fast lookups and minimizing redundant checks by scanning only the necessary elements.
What is the significance of greedy pair removal in this problem?
Greedy pair removal ensures that the largest possible subset is removed with each operation, minimizing the total number of operations required.
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The problem asks to find the minimum number of operations to make an array non-decreasing by removing pairs of elements.
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