How do you solve Find the Maximum Divisibility Score on LeetCode?

Find the Maximum Divisibility Score (LeetCode #2644) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * m) time complexity and O(m) space complexity. Key insight: Divisibility checks can be optimized using a counting approach.

What is the brute force solution for Find the Maximum Divisibility Score?

The brute force approach for Find the Maximum Divisibility Score is Brute Force, with O(n²) time complexity and O(1) space complexity. We will check each divisor against all numbers in the nums array to count how many numbers are divisible by that divisor. This is straightforward but can be slow for large inputs. The optimal Optimal Solution approach improves this to O(n * m).

What algorithm or data structure is used to solve Find the Maximum Divisibility Score?

Find the Maximum Divisibility Score uses the following concepts: Array. The recommended patterns to study are: Hash Map, Array.

What are the interview tips for Find the Maximum Divisibility Score?

Clarify the problem requirements before coding. Think about edge cases, such as empty arrays. Explain your thought process while coding.

What are common mistakes when solving Find the Maximum Divisibility Score?

Not considering ties correctly. Forgetting to initialize score counters.

#2644

Find the Maximum Divisibility Score

Easy

ArrayHash MapArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n * m)Space O(m)

We can optimize the brute force approach by counting the divisibility scores in a single pass through the nums array for each divisor, which reduces the number of checks needed.

⚙️

Algorithm

4 steps

1Step 1: Create a dictionary to store the divisibility scores for each divisor.
2Step 2: Iterate through each number in nums and for each number, check its divisibility against all divisors.
3Step 3: For each divisor that divides the number, increment its score in the dictionary.
4Step 4: After processing all numbers, find the divisor with the maximum score. In case of a tie, return the smallest divisor.

solution.py18 lines

1def max_divisibility_score(nums, divisors):
2    scores = {}
3    for n in nums:
4        for d in divisors:
5            if n % d == 0:
6                if d in scores:
7                    scores[d] += 1
8                else:
9                    scores[d] = 1
10    max_score = -1
11    result_divisor = float('inf')
12    for d in divisors:
13        if d in scores:
14            score = scores[d]
15            if score > max_score or (score == max_score and d < result_divisor):
16                max_score = score
17                result_divisor = d
18    return result_divisor

ℹ

Complexity note: This approach is more efficient than the brute force as we only check divisibility once per number for each divisor, leading to a linear relationship with respect to the number of divisors.

1Divisibility checks can be optimized using a counting approach.
2When dealing with ties, always consider the smallest divisor.

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