Find k most frequent in linear time
Problem Statement
Given an integer array nums and an integer k (where 1 ≤ k ≤ number of distinct values in nums), return any k values that appear most frequently.
Implementation Requirements
- O(n) Solution: Implement a solution that achieves average-case O(n) time complexity and O(n) space complexity. This solution must utilize a frequency map and bucket-based grouping. You must explain why this approach achieves linear time complexity.
- Comparison: Compare the O(n) solution with a heap-based O(n log k) approach. Discuss:
- When each approach is preferable.
- Memory trade-offs between the two.
- How you would break ties if multiple values have the same frequency and need to be selected.
Clarifications
- Address the handling of negative numbers within
nums. - Address the handling of very large value ranges for elements in
nums.
Deliverables
- Provide code for the O(n) solution.
- Analyze the time and space complexity for both discussed approaches.
AI interview prep
Core dilemma
The central dilemma is to achieve optimal linear time complexity (O(N)) for finding the k most frequent elements, understanding the specific constraints and assumptions that enable this, and critically comparing it against more general but less optimal solutions (O(N log K)) under various real-world scenarios.
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Interview prep
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Find k most frequent in linear time
Problem Statement
Given an integer array nums and an integer k (where 1 ≤ k ≤ number of distinct values in nums), return any k values that appear most frequently.
Implementation Requirements
- O(n) Solution: Implement a solution that achieves average-case O(n) time complexity and O(n) space complexity. This solution must utilize a frequency map and bucket-based grouping. You must explain why this approach achieves linear time complexity.
- Comparison: Compare the O(n) solution with a heap-based O(n log k) approach. Discuss:
- When each approach is preferable.
- Memory trade-offs between the two.
- How you would break ties if multiple values have the same frequency and need to be selected.
Clarifications
- Address the handling of negative numbers within
nums. - Address the handling of very large value ranges for elements in
nums.
Deliverables
- Provide code for the O(n) solution.
- Analyze the time and space complexity for both discussed approaches.