How do you solve Maximize Subarray GCD Score on LeetCode?

Maximize Subarray GCD Score (LeetCode #3574) 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: Doubling elements can significantly increase the GCD.

What is the time complexity of Maximize Subarray GCD Score?

The optimal solution for Maximize Subarray GCD Score runs in O(n) time and uses O(n) space. We only traverse the array and use a map for counting, leading to linear complexity.

What is the brute force solution for Maximize Subarray GCD Score?

The brute force approach for Maximize Subarray GCD Score is Brute Force, with O(n²) time complexity and O(1) space complexity. We can check every possible contiguous subarray and calculate its GCD. For each subarray, we consider all combinations of doubling elements up to k times. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximize Subarray GCD Score?

Maximize Subarray GCD Score uses the following concepts: Array, Math, Enumeration, Number Theory. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Maximize Subarray GCD Score?

Explain your thought process clearly. Use examples to illustrate your approach. Be prepared to discuss time and space complexities.

What are common mistakes when solving Maximize Subarray GCD Score?

Not considering the impact of doubling on GCD. Overlooking the limits of k operations.

#3574

Maximize Subarray GCD Score

Hard

ArrayMathEnumerationNumber TheoryHash MapArray

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)

Instead of checking all subarrays, we can focus on the GCD of elements and their factors, leveraging the doubling operation strategically to maximize the score.

⚙️

Algorithm

3 steps

1Step 1: Count the frequency of each number and its GCD contributions.
2Step 2: For each unique number, calculate the potential score by considering how many times we can double it up to k times.
3Step 3: Update the maximum score based on the calculated contributions.

solution.py13 lines

1from collections import Counter
2import math
3
4def maxGcdScore(nums, k):
5    freq = Counter(nums)
6    max_score = 0
7    for num in freq:
8        length = freq[num]
9        score = length * num
10        if k > 0:
11            score += length * (num * 2)
12        max_score = max(max_score, score)
13    return max_score

ℹ

Complexity note: We only traverse the array and use a map for counting, leading to linear complexity.

1Doubling elements can significantly increase the GCD.
2Maximizing length and GCD together is crucial.

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