To solve the problem, repeatedly remove adjacent pairs from the sorted array. By maximizing the number of operations, we can minimize the final array length. The key challenge lies in efficiently identifying removable pairs using array scanning and hash lookup.
Problem Statement
You are given an integer array nums sorted in non-decreasing order. Your task is to repeatedly remove adjacent pairs of equal elements, minimizing the array length.
You can perform the operation any number of times. Each operation removes a pair of adjacent equal elements, and the goal is to determine the minimum length of the array after performing zero or more operations.
Examples
Example 1
Input: nums = [1,2,3,4]
Output: 0
Example 2
Input: nums = [1,1,2,2,3,3]
Output: 0
Example 3
Input: nums = [1000000000,1000000000]
Output: 2
Since both numbers are equal, they cannot be removed.
Constraints
- 1 <= nums.length <= 105
- 1 <= nums[i] <= 109
- nums is sorted in non-decreasing order.
Solution Approach
Array Scanning with Hash Table
We scan through the array while using a hash table to keep track of the frequency of each element. By detecting pairs efficiently, we can remove them during each pass through the array. This approach ensures that we remove as many pairs as possible with each operation.
Two Pointers Technique
Using two pointers, one for the beginning of the array and another for the end, we can compare elements and remove pairs by shifting the pointers accordingly. This reduces unnecessary checks and minimizes the array length faster.
Greedy Approach with Frequency Count
A greedy strategy can be applied by focusing on removing pairs with the highest frequency first, reducing the array length optimally. The frequency count can be handled with a hash table, and the pair removal is based on this count.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity can vary depending on the approach. The array scanning with hash table approach can be done in O(n) time. Space complexity also depends on the method used, but typically it requires O(n) space due to the hash table or auxiliary storage used for element counts.
What Interviewers Usually Probe
- Look for efficiency in handling large input arrays (up to 10^5 elements).
- Evaluate the candidate's approach to minimizing operations and array length.
- Assess their understanding of array scanning and hash lookups in reducing problem complexity.
Common Pitfalls or Variants
Common pitfalls
- Not considering the sorted nature of the array could lead to unnecessary comparisons.
- Failing to efficiently track element frequencies, causing an excessive number of operations.
- Overcomplicating the solution by not using hash tables or efficient frequency counting methods.
Follow-up variants
- Consider unsorted arrays or arrays with more varied element frequencies.
- Explore variations with constraints on the number of allowed operations.
- What if the array contains only one element or no removable pairs?
How GhostInterview Helps
- GhostInterview's solver guides you in applying array scanning and hash lookup techniques to optimize pair removal operations.
- The solution approach focuses on maximizing the number of operations, which helps you reach the minimum array length effectively.
- The platform highlights common pitfalls and helps you avoid inefficient solutions during the problem-solving process.
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 main pattern used to solve the Minimum Array Length After Pair Removals problem?
The main pattern is array scanning combined with hash lookup. Efficient frequency counting allows us to identify and remove adjacent pairs.
How can two pointers help solve the problem?
Two pointers allow for efficient comparison of elements from both ends, removing adjacent pairs and minimizing the array length faster.
What is the time complexity of the solution for the Minimum Array Length After Pair Removals problem?
The time complexity can be O(n) depending on the solution approach, particularly when using array scanning with a hash table or two pointers.
Can the problem be solved without using a hash table?
While a hash table is efficient, alternative methods like two-pointer techniques can also be used to minimize operations and remove pairs.
How does GhostInterview help with this problem?
GhostInterview helps by guiding you through efficient approaches and avoiding common pitfalls, ensuring you maximize the number of operations for an optimal solution.
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