This problem asks to check if any element in an array has a prime frequency of occurrences. To solve, scan the array to count element frequencies, then verify if any of these frequencies are prime. Implementing a helper function to check primality will simplify the solution.
Problem Statement
You are given an integer array nums. Return true if any element in the array has a prime frequency of occurrences, otherwise return false. The frequency of an element is how many times it appears in the array.
The array length can range from 1 to 100, and the values in the array are integers from 0 to 100.
Examples
Example 1
Input: nums = [1,2,3,4,5,4]
Output: true
4 has a frequency of two, which is a prime number.
Example 2
Input: nums = [1,2,3,4,5]
Output: false
All elements have a frequency of one.
Example 3
Input: nums = [2,2,2,4,4]
Output: true
Both 2 and 4 have a prime frequency.
Constraints
- 1 <= nums.length <= 100
- 0 <= nums[i] <= 100
Solution Approach
Count Element Frequencies
Iterate through the array to count how many times each element occurs using a hash map or dictionary. This allows easy access to each element's frequency for checking.
Prime Checking Function
To determine if an element's frequency is prime, implement a helper function that checks whether a number is prime. This will be used to validate the frequencies obtained in the previous step.
Scan and Validate
After counting the frequencies, scan through them to check if any of the values are prime. Return true if any frequency is prime, otherwise return false.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
The time complexity depends on the method used to count frequencies and check primes. The frequency count is O(n), where n is the number of elements in the array. Checking if a number is prime can take O(sqrt(m)), where m is the frequency value, leading to a total time complexity of O(n * sqrt(m)). The space complexity is O(n) due to storing frequencies in a hash table.
What Interviewers Usually Probe
- Candidate identifies the prime checking pattern and efficiently counts frequencies.
- Candidate demonstrates knowledge of basic number theory to optimize the primality check.
- Candidate implements a clear and correct array scanning strategy with hash table lookups.
Common Pitfalls or Variants
Common pitfalls
- Not implementing an efficient prime checking function leading to slower performance.
- Incorrectly counting frequencies or misunderstanding the concept of frequency.
- Failing to handle edge cases such as small arrays or the case where no element has a prime frequency.
Follow-up variants
- What if the array contains repeated zeros?
- What if the array has a length of 1?
- How does the solution change if the array contains a larger range of numbers?
How GhostInterview Helps
- GhostInterview helps by providing instant feedback on your implementation, highlighting key areas such as prime checking and frequency counting.
- It guides you through the steps needed to optimize your solution, from counting frequencies to ensuring your prime check is efficient.
- With guided tips, GhostInterview improves your approach to array scanning and hash lookup techniques, helping you avoid common mistakes.
Topic Pages
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- 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
How do I check if a number is prime?
You can check if a number is prime by verifying that it is greater than 1 and not divisible by any number other than 1 and itself. An efficient way to check is by testing divisibility up to the square root of the number.
How can I optimize the prime checking part of this problem?
You can optimize by checking divisibility only up to the square root of the number, and skipping even numbers greater than 2, as they are not prime.
What if there is no element with a prime frequency?
If no element has a prime frequency, the solution should return false, as there are no frequencies that are prime.
How does the array size impact the solution?
The array size affects the time complexity, especially in counting frequencies, but the maximum size of 100 ensures the approach will run efficiently within the problem's constraints.
Why is the prime checking function necessary?
The prime checking function is essential for determining if any of the element frequencies are prime, which is the core requirement of the problem.
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