How do you solve Split the Array to Make Coprime Products on LeetCode?

Split the Array to Make Coprime Products (LeetCode #2584) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * log(max(nums))) time complexity and O(n) space complexity. Key insight: Understanding coprimality through prime factors can simplify the problem.

What is the brute force solution for Split the Array to Make Coprime Products?

The brute force approach for Split the Array to Make Coprime Products is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach checks every possible split index and calculates the products of the two segments to see if they are coprime. This is straightforward but inefficient as it requires recalculating products for each split. The optimal Optimal Solution approach improves this to O(n * log(max(nums))).

What algorithm or data structure is used to solve Split the Array to Make Coprime Products?

Split the Array to Make Coprime Products 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 Split the Array to Make Coprime Products?

Always clarify the problem requirements and constraints before diving into coding. Discuss your thought process and potential approaches with the interviewer. Be mindful of edge cases and test your solution against them.

What are common mistakes when solving Split the Array to Make Coprime Products?

Not considering edge cases where the array has only two elements. Failing to optimize product calculations, leading to unnecessary computations.

#2584

Split the Array to Make Coprime Products

Hard

ArrayHash TableMathNumber TheoryHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * log(max(nums)))
Space	O(1)	O(n)

💡

Intuition

Time O(n * log(max(nums)))Space O(n)

Instead of calculating products directly, we can use prime factorization to check for common prime factors. This reduces the need for repeated calculations and allows us to efficiently determine coprimality.

⚙️

Algorithm

4 steps

1Step 1: Create a function to get the prime factors of a number.
2Step 2: Use two sets to track prime factors for the left and right segments as we iterate through the array.
3Step 3: For each split index, check if the sets of prime factors intersect. If they do not, return the index.
4Step 4: If no valid split is found, return -1.

solution.py26 lines

1from collections import defaultdict
2
3def prime_factors(n):
4    factors = set()
5    for i in range(2, int(n**0.5) + 1):
6        while n % i == 0:
7            factors.add(i)
8            n //= i
9    if n > 1:
10        factors.add(n)
11    return factors
12
13def find_valid_split(nums):
14    n = len(nums)
15    left_factors = set()
16    total_factors = defaultdict(int)
17    for num in nums:
18        for factor in prime_factors(num):
19            total_factors[factor] += 1
20    for i in range(n - 1):
21        for factor in prime_factors(nums[i]):
22            left_factors.add(factor)
23            total_factors[factor] -= 1
24        if all(total_factors[factor] == 0 for factor in left_factors):
25            return i
26    return -1

ℹ

Complexity note: The complexity arises from factorizing each number, which takes logarithmic time relative to the number's value, and we do this for each element in the array.

1Understanding coprimality through prime factors can simplify the problem.
2Using sets to track prime factors allows for efficient checking of overlaps.

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