Leetcode #2521: Distinct Prime Factors of Product of Array

In this guide, we solve Leetcode #2521 Distinct Prime Factors of Product of Array in Python and focus on the core idea that makes the solution efficient.

You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.

Leetcode

Problem Statement

Given an array of positive integers nums, return the number of distinct prime factors in the product of the elements of nums. Note that: A number greater than 1 is called prime if it is divisible by only 1 and itself.

Quick Facts

Difficulty: Medium
Premium: No
Tags: Array, Hash Table, Math, Number Theory

Intuition

Fast membership checks and value lookups are the heart of this problem, which makes a hash map the natural choice.

By storing what we have already seen (or counts/indexes), we can answer the question in one pass without backtracking.

Approach

Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.

This keeps the solution linear while remaining easy to explain in an interview setting.

Steps:

Initialize a hash map for seen items or counts.
Iterate through the input, querying/updating the map.
Return the first valid result or the final computed value.

Example

Input: nums = [2,4,3,7,10,6]
Output: 4
Explanation:
The product of all the elements in nums is: 2 * 4 * 3 * 7 * 10 * 6 = 10080 = 25 * 32 * 5 * 7.
There are 4 distinct prime factors so we return 4.

Python Solution

class Solution:
    def distinctPrimeFactors(self, nums: List[int]) -> int:
        s = set()
        for n in nums:
            i = 2
            while i <= n // i:
                if n % i == 0:
                    s.add(i)
                    while n % i == 0:
                        n //= i
                i += 1
            if n > 1:
                s.add(n)
        return len(s)

Complexity

The time complexity is $O(n \times \sqrt{m})$ , and the space complexity is $O(\frac{m}{\log m})$ . The space complexity is $O(\frac{m}{\log m})$ .

Edge Cases and Pitfalls

Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.

Summary

This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.

Approach

Scan the input once, using the map to detect when the condition is satisfied and to update state as you go.

This keeps the solution linear while remaining easy to explain in an interview setting.

Steps:

Initialize a hash map for seen items or counts.

Iterate through the input, querying/updating the map.

Return the first valid result or the final computed value.

Python Solution

class Solution:
    def distinctPrimeFactors(self, nums: List[int]) -> int:
        s = set()
        for n in nums:
            i = 2
            while i <= n // i:
                if n % i == 0:
                    s.add(i)
                    while n % i == 0:
                        n //= i
                i += 1
            if n > 1:
                s.add(n)
        return len(s)

Leetcode #2521: Distinct Prime Factors of Product of Array

Problem Statement

Quick Facts

Intuition

Approach

Example

Python Solution

Complexity

Edge Cases and Pitfalls

Summary

Ace your next coding interview

Leetcode #2521: Distinct Prime Factors of Product of Array

Problem Statement

Quick Facts

Intuition

Approach

Example

Python Solution

Complexity

Edge Cases and Pitfalls

Summary

Ace your next coding interview