How do you solve Find the Maximum Factor Score of Array on LeetCode?

Find the Maximum Factor Score of Array (LeetCode #3334) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n) time complexity and O(n) space complexity. Key insight: Using prefix and suffix arrays can significantly reduce the number of calculations needed.

What is the brute force solution for Find the Maximum Factor Score of Array?

The brute force approach for Find the Maximum Factor Score of Array is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves calculating the GCD and LCM for every possible subarray formed by removing one element. This allows us to explore all combinations and find the maximum factor score. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Find the Maximum Factor Score of Array?

Find the Maximum Factor Score of Array uses the following concepts: Array, Math, Number Theory. The recommended patterns to study are: GCD/LCM calculations, Prefix/Suffix arrays.

What are the interview tips for Find the Maximum Factor Score of Array?

Always clarify the problem requirements and constraints before jumping into coding. Discuss your thought process and approach with the interviewer to showcase your understanding. Practice explaining your code and logic clearly, as communication is key during interviews.

What are common mistakes when solving Find the Maximum Factor Score of Array?

Not handling edge cases like arrays of length 1 properly. Confusing GCD and LCM calculations, leading to incorrect results.

#3334

Find the Maximum Factor Score of Array

Medium

ArrayMathNumber TheoryGCD/LCM calculationsPrefix/Suffix arrays

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n)Space O(n)

By using prefix and suffix arrays, we can compute the GCD and LCM of the entire array while excluding one element, avoiding the need for repeated calculations.

⚙️

Algorithm

3 steps

1Step 1: Create prefix and suffix arrays for GCD and LCM.
2Step 2: For each element, calculate the GCD and LCM of the remaining elements using the prefix and suffix arrays.
3Step 3: Compute the factor score and track the maximum score.

solution.py43 lines

1# Full working Python code
2import math
3from functools import reduce
4
5def gcd(a, b):
6    while b:
7        a, b = b, a % b
8    return a
9
10def lcm(a, b):
11    return abs(a * b) // gcd(a, b)
12
13def maxFactorScore(nums):
14    n = len(nums)
15    if n == 1:
16        return nums[0] * nums[0]
17    prefix_gcd = [0] * n
18    prefix_lcm = [0] * n
19    suffix_gcd = [0] * n
20    suffix_lcm = [0] * n
21
22    prefix_gcd[0] = nums[0]
23    prefix_lcm[0] = nums[0]
24    for i in range(1, n):
25        prefix_gcd[i] = gcd(prefix_gcd[i-1], nums[i])
26        prefix_lcm[i] = lcm(prefix_lcm[i-1], nums[i])
27
28    suffix_gcd[n-1] = nums[n-1]
29    suffix_lcm[n-1] = nums[n-1]
30    for i in range(n-2, -1, -1):
31        suffix_gcd[i] = gcd(suffix_gcd[i+1], nums[i])
32        suffix_lcm[i] = lcm(suffix_lcm[i+1], nums[i])
33
34    max_score = 0
35    for i in range(n):
36        current_gcd = prefix_gcd[i-1] if i > 0 else suffix_gcd[i+1]
37        current_lcm = prefix_lcm[i-1] if i > 0 else suffix_lcm[i+1]
38        if i > 0 and i < n - 1:
39            current_gcd = gcd(prefix_gcd[i-1], suffix_gcd[i+1])
40            current_lcm = lcm(prefix_lcm[i-1], suffix_lcm[i+1])
41        max_score = max(max_score, current_gcd * current_lcm)
42    return max_score
43

ℹ

Complexity note: The time complexity is O(n) because we compute GCD and LCM in linear time using prefix and suffix arrays. The space complexity is also O(n) due to the storage of these arrays.

1Using prefix and suffix arrays can significantly reduce the number of calculations needed.
2Understanding GCD and LCM properties is crucial for optimizing the solution.

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