How do you solve Distinct Prime Factors of Product of Array on LeetCode?

Distinct Prime Factors of Product of Array (LeetCode #2521) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * sqrt(m)) time complexity and O(n) space complexity. Key insight: Calculating the product directly can lead to overflow; focus on prime factors instead.

What is the brute force solution for Distinct Prime Factors of Product of Array?

The brute force approach for Distinct Prime Factors of Product of Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves calculating the product of all numbers and then finding the prime factors of that product. However, this method can lead to very large numbers that are impractical to handle. The optimal Optimal Solution approach improves this to O(n * sqrt(m)).

What algorithm or data structure is used to solve Distinct Prime Factors of Product of Array?

Distinct Prime Factors of Product of Array uses the following concepts: Array, Hash Table, Math, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Distinct Prime Factors of Product of Array?

Always consider the constraints and avoid unnecessary calculations. Think about how to break down the problem into smaller parts. Discuss your thought process with the interviewer to clarify your approach.

What are common mistakes when solving Distinct Prime Factors of Product of Array?

Forgetting to check for prime factors greater than the square root. Not using a set to store distinct primes, leading to incorrect counts.

#2521

Distinct Prime Factors of Product of Array

Medium

ArrayHash TableMathNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * sqrt(m))
Space	O(1)	O(n)

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Intuition

Time O(n * sqrt(m))Space O(n)

Instead of calculating the product, we can directly find the prime factors of each number in the array. This way, we avoid overflow and only focus on the distinct prime factors.

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Algorithm

4 steps

1Step 1: Create a set to store distinct prime factors.
2Step 2: For each number in the array, find its prime factors.
3Step 3: Add each prime factor to the set.
4Step 4: Return the size of the set as the count of distinct prime factors.

solution.py18 lines

1# Full working Python code
2from math import isqrt
3
4def prime_factors(n):
5    factors = set()
6    for i in range(2, isqrt(n) + 1):
7        while n % i == 0:
8            factors.add(i)
9            n //= i
10    if n > 1:
11        factors.add(n)
12    return factors
13
14def distinct_prime_factors(nums):
15    primes = set()
16    for num in nums:
17        primes.update(prime_factors(num))
18    return len(primes)

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Complexity note: The time complexity is O(n * sqrt(m)) where n is the number of elements in nums and m is the maximum value in nums. This is because we find prime factors for each number, and the space complexity is O(n) due to the storage of distinct primes.

1Calculating the product directly can lead to overflow; focus on prime factors instead.
2Using a set helps in automatically handling duplicates.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.