#3591

Easy

auto_awesomeArray scanning plus hash lookup

LeetCode Problem Workspace

Check if Any Element Has Prime Frequency

Check if any element in the array has a prime frequency count, leveraging array scanning and hash table lookup.

array hash table math counting number theory

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?

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.

terminal

Solution

Solution 1: Counting + Prime Check

We use a hash table $\text{cnt}$ to count the frequency of each element. Then, we iterate through the values in $\text{cnt}$ and check if any of them is a prime number. If there is a prime, return `true`; otherwise, return `false`.

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class Solution:
    def checkPrimeFrequency(self, nums: List[int]) -> bool:
        def is_prime(x: int) -> bool:
            if x < 2:
                return False
            return all(x % i for i in range(2, int(sqrt(x)) + 1))

        cnt = Counter(nums)
        return any(is_prime(x) for x in cnt.values())

Continue Practicing

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