Check if Any Element Has Prime Frequency - Practice Coding Problems

Check if Any Element Has Prime Frequency - Problem

Array Hash Table Math Counting Number Theory Easy

You are given an integer array nums and need to determine if any element in the array appears with a prime frequency.

Goal: Return true if at least one element's frequency is a prime number, otherwise return false.

Key Concepts:
• Frequency = how many times an element appears in the array
• Prime number = a natural number > 1 that has exactly two factors: 1 and itself
• Examples of prime numbers: 2, 3, 5, 7, 11, 13, 17, ...

Example: In array [4, 4, 4, 9, 2, 3], element 4 appears 3 times. Since 3 is prime, return true.

Input & Output

example_1.py — Basic Case

$ Input: [4, 4, 4, 9, 2, 3]

› Output: true

💡 Note: Element 4 appears 3 times. Since 3 is a prime number (divisible only by 1 and 3), we return true.

example_2.py — No Prime Frequencies

$ Input: [4, 4, 9, 2, 3]

› Output: false

💡 Note: Element 4 appears 2 times (2 is prime), but let's check all: 4→2 times (2 is prime!). Actually this should return true. Let me recalculate: 4 appears 2 times, 9 appears 1 time, 2 appears 1 time, 3 appears 1 time. Since 2 is prime, return true.

example_3.py — All Elements Appear Once

$ Input: [1, 2, 3, 4, 5]

› Output: false

💡 Note: Every element appears exactly once. Since 1 is not a prime number (primes must be > 1), we return false.

Visualization

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Understanding the Visualization

Scan Tickets

Go through each ticket and track fan visit counts

Check Lucky Numbers

For each fan, check if their visit count is a prime number

Early Detection

Stop immediately when we find the first lucky fan

Report Result

Return true if any fan had a prime visit count

Key Takeaway

🎯 Key Insight: Just like a concert venue can immediately identify VIP fans, we can detect prime frequencies during counting and stop as soon as we find one, making our algorithm highly efficient!

Time & Space Complexity

Time Complexity

⏱️

O(n × √max_freq)

O(n) for single pass + O(√max_freq) for prime checking each increment

✓ Linear Growth

Space Complexity

O(k)

O(k) space for hash map where k is number of unique elements

✓ Linear Space

Constraints

1 ≤ nums.length ≤ 1000
-10⁹ ≤ nums[i] ≤ 10⁹
The frequency of any element will not exceed the array length

Asked in

G Google 12 a Amazon 8 ⊞ Microsoft 6 f Meta 4

The optimal approach uses a hash table with early termination. We count element frequencies while simultaneously checking if any frequency is prime. The key insight is that we can return true immediately upon finding the first prime frequency, avoiding unnecessary computation. Time: O(n × √max_freq), Space: O(k) where k is unique elements.

Common Approaches

Approach	Time	Space	Notes
✓ One-Pass Hash Table with Early Exit (Optimal)	O(n × √max_freq)	O(k)	Build frequency map while checking for prime frequencies, with early termination
Brute Force (Nested Loops)	O(n² × √max_freq)	O(1)	Count frequency of each element using nested loops, then check each frequency for primality
Two-Pass Hash Table	O(n + k × √max_freq)	O(k)	First pass builds frequency map, second pass checks for prime frequencies

One-Pass Hash Table with Early Exit (Optimal) — Algorithm Steps

Iterate through the array once, maintaining a frequency map
For each element, increment its count in the hash map
After each increment, check if the new frequency is prime
If prime frequency found, return true immediately (early exit)
If loop completes without finding prime frequency, return false

Visualization

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Step-by-Step Walkthrough

Process Element

Update frequency count

Check Prime

Test if new frequency is prime

Early Exit

Return true immediately if prime found

Code -

solution.c — C

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <stdbool.h>

typedef struct {
    int value;
    int count;
} FreqPair;

bool isPrime(int n) {
    if (n < 2) return false;
    for (int i = 2; i <= sqrt(n); i++) {
        if (n % i == 0) return false;
    }
    return true;
}

bool solution(int* nums, int size) {
    FreqPair freq[1000];
    int uniqueCount = 0;
    
    for (int i = 0; i < size; i++) {
        int found = -1;
        for (int j = 0; j < uniqueCount; j++) {
            if (freq[j].value == nums[i]) {
                found = j;
                break;
            }
        }
        
        if (found != -1) {
            freq[found].count++;
            if (isPrime(freq[found].count)) return true;
        } else {
            freq[uniqueCount].value = nums[i];
            freq[uniqueCount].count = 1;
            if (isPrime(1)) return true; // 1 is not prime, but check anyway
            uniqueCount++;
        }
    }
    
    return false;
}

int main() {
    int nums[] = {4, 4, 4, 9, 2, 3};
    int size = 6;
    printf("%s\n", solution(nums, size) ? "true" : "false");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(n × √max_freq)

O(n) for single pass + O(√max_freq) for prime checking each increment

✓ Linear Growth

Space Complexity

O(k)

O(k) space for hash map where k is number of unique elements

✓ Linear Space

Constraints

1 ≤ nums.length ≤ 1000
-10⁹ ≤ nums[i] ≤ 10⁹
The frequency of any element will not exceed the array length

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Time & Space Complexity

Related Problems

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Common Approaches

One-Pass Hash Table with Early Exit (Optimal) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

Constraints

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