The goal is to find the length of the longest subsequence of perfect squares in a given array. Start by sorting the array and then use hash lookups to determine square relationships. If no valid subsequence exists, return -1.
Problem Statement
You are given an integer array nums. A subsequence is called a square streak if each element is the square of the previous one. The task is to find the length of the longest such subsequence in nums.
Return the length of the longest square streak in nums, or -1 if no such subsequence exists. The subsequence must maintain the order of elements and can be derived by deleting some or no elements from the array.
Examples
Example 1
Input: nums = [4,3,6,16,8,2]
Output: 3
Choose the subsequence [4,16,2]. After sorting it, it becomes [2,4,16].
- 4 = 2 * 2.
- 16 = 4 * 4. Therefore, [4,16,2] is a square streak. It can be shown that every subsequence of length 4 is not a square streak.
Example 2
Input: nums = [2,3,5,6,7]
Output: -1
There is no square streak in nums so return -1.
Constraints
- 2 <= nums.length <= 105
- 2 <= nums[i] <= 105
Solution Approach
Sort and Hash Lookup
Start by sorting the array. This helps to scan through the elements and check if any element is a square of its predecessor using hash lookup, ensuring efficiency. Use a hash set to quickly check for the presence of the square of an element.
Dynamic Programming or Hash Table Tracking
Track subsequences using a hash table where each number points to the length of the longest streak it can form. Iterate through the sorted array and update the streak lengths based on whether an element is a square of the previous element.
Binary Search Optimization
Use binary search to find squares of elements in the sorted array to reduce time complexity. This helps when you are scanning through large datasets, optimizing the search for potential square pairs.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | O(n \cdot \log n) |
| Space | O(n) |
The time complexity of the solution is O(n \cdot \log n) due to the sorting step, and the space complexity is O(n) as we are storing intermediate results in a hash table.
What Interviewers Usually Probe
- The candidate should show a clear understanding of the array scanning technique and how hash lookups can optimize the search for subsequences.
- An efficient implementation using hash tables or dynamic programming will demonstrate good problem-solving and optimization skills.
- Candidates may struggle with the correct approach to binary search optimization, which can lead to an O(n^2) solution if not handled properly.
Common Pitfalls or Variants
Common pitfalls
- Forgetting to sort the array first, which can make it impossible to find valid subsequences.
- Not using hash lookups effectively, which can lead to excessive computation time when searching for square relationships.
- Confusing the problem with simple subsequence length problems, leading to incorrect solutions.
Follow-up variants
- Consider variations where the subsequence length could be constrained differently.
- What if the subsequence has to be contiguous? That would require additional modifications.
- Handle arrays with duplicate elements and ensure they don’t interfere with subsequence counting.
How GhostInterview Helps
- GhostInterview provides direct, problem-specific solver assistance, walking through each approach while suggesting optimizations.
- With step-by-step guidance, GhostInterview helps tackle common pitfalls such as missing sorting or incorrect hash set usage.
- GhostInterview assists with optimizing complex cases by suggesting dynamic programming solutions and binary search enhancements.
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 strategy to solve the Longest Square Streak in an Array problem?
The primary strategy is to scan through the array, sort it, and use hash lookups to find elements that are squares of previous ones.
What happens if there is no valid square streak in the array?
If no square streak exists, return -1 as specified in the problem.
How does the sorting of the array help in this problem?
Sorting the array helps to efficiently find subsequences where each element is a perfect square of the previous one using hash lookups.
What is the time complexity of the solution?
The time complexity is O(n \cdot \log n) due to the sorting step, and the space complexity is O(n) due to the hash table used for tracking subsequences.
Can the solution be optimized further for large arrays?
Yes, using binary search techniques to find the squares of numbers in the sorted array can help optimize the search process.
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