To solve the "Array of Doubled Pairs" problem, reorder the array and check if every element at index 2 * i + 1 equals double the element at index 2 * i. Use array scanning and hash lookup for an efficient solution. The main challenges are ensuring valid reordering and handling both positive and negative numbers.
Problem Statement
Given an integer array arr of even length, return true if it is possible to reorder arr such that for every index i where 0 <= i < len(arr) / 2, the condition arr[2 * i + 1] = 2 * arr[2 * i] holds true. Otherwise, return false.
For example, given arr = [3,1,3,6], it is impossible to reorder the array to satisfy the condition, and the output should be false. The task involves checking if such a reordering is possible using efficient techniques like hash lookup and array scanning.
Examples
Example 1
Input: arr = [3,1,3,6]
Output: false
Example details omitted.
Example 2
Input: arr = [2,1,2,6]
Output: false
Example details omitted.
Example 3
Input: arr = [4,-2,2,-4]
Output: true
We can take two groups, [-2,-4] and [2,4] to form [-2,-4,2,4] or [2,4,-2,-4].
Constraints
- 2 <= arr.length <= 3 * 104
- arr.length is even.
- -105 <= arr[i] <= 105
Solution Approach
Sort and Use Hash Map
First, sort the array in ascending order. Then, use a hash map to store the frequency of each element. This allows quick access to check if a valid pair exists for each element in the sorted array, ensuring that for each element, its double exists in the array.
Greedy Pairing with Sorting
After sorting, try to greedily pair each element with its double. For each element, check if its double exists in the hash map with a remaining frequency greater than zero. If such a pair cannot be found for any element, return false.
Efficient Frequency Management
Use a hash map to manage the frequency of elements. Every time a pair is found, decrease the frequency of both the current element and its double. This ensures that each element and its double are used exactly once.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(N \log N) |
| Space | O(N) |
The time complexity is dominated by the sorting step, which is O(N log N). The space complexity is O(N) due to the storage required for the hash map to track element frequencies.
What Interviewers Usually Probe
- Can the candidate efficiently solve the problem with an optimal time complexity?
- Does the candidate understand the importance of sorting and hash lookups for this problem?
- Is the candidate able to handle both positive and negative numbers correctly in the array?
Common Pitfalls or Variants
Common pitfalls
- Forgetting to handle negative numbers, which can cause incorrect results when pairing elements.
- Not efficiently updating the frequencies of elements after pairing, leading to incorrect answers.
- Trying to brute force the problem without using sorting or a hash map for efficient lookups.
Follow-up variants
- Allowing odd-length arrays as input and adjusting the logic to handle such cases.
- Extending the problem to handle arrays with more complex relationships between elements.
- Optimizing the solution to handle very large arrays with constraints closer to
arr.length <= 10^5.
How GhostInterview Helps
- GhostInterview helps by providing an optimal strategy involving sorting and hash maps, offering step-by-step guidance on solving this problem in a timely manner.
- It enables candidates to practice handling array scanning and hash lookups efficiently, which is critical for real-time interview scenarios.
- GhostInterview's detailed solution explanations and complexity breakdowns ensure a deeper understanding of the trade-offs involved in solving this problem.
Topic Pages
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FAQ
What is the main approach to solving the Array of Doubled Pairs problem?
The main approach is sorting the array and using a hash map to track element frequencies. Then, attempt to greedily pair each element with its double.
How does sorting help with the Array of Doubled Pairs problem?
Sorting the array ensures that you process smaller elements first, which makes it easier to find their corresponding doubles using hash lookups.
Can negative numbers be part of the array in the Array of Doubled Pairs problem?
Yes, negative numbers can be part of the array, and the solution must correctly pair them with their corresponding doubles, such as -2 with -4.
What is the time complexity of the Array of Doubled Pairs solution?
The time complexity is O(N log N) due to the sorting step, followed by a linear scan of the array using a hash map for lookups.
What is the space complexity of the Array of Doubled Pairs solution?
The space complexity is O(N) because of the hash map used to store the frequencies of array elements.
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