Ezvor

2521. Distinct Prime Factors of Product of Array

MediumArray Preparing judge… LeetCode

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.
  • An integer val1 is a factor of another integer val2 if val2 / val1 is an integer.

 

Example 1:

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.

Example 2:

Input: nums = [2,4,8,16]
Output: 1
Explanation:
The product of all the elements in nums is: 2 * 4 * 8 * 16 = 1024 = 210.
There is 1 distinct prime factor so we return 1.

 

Constraints:

  • 1 <= nums.length <= 104
  • 2 <= nums[i] <= 1000
ArrayHash TableMathNumber TheoryPrime FactorizationEuclidean AlgorithmPrimality TestGreatest Common DivisorSieve TheoryPrime Number Sieve

Hints

Hint 1
Do not multiply all the numbers together, as the product is too big to store.
Hint 2
Think about how each individual number's prime factors contribute to the prime factors of the product of the entire array.
Hint 3
Find the prime factors of each element in nums, and store all of them in a set to avoid duplicates.