How do you solve Apply Operations to Maximize Score on LeetCode?

Apply Operations to Maximize Score (LeetCode #2818) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n) time complexity and O(n) space complexity. Key insight: The prime score is crucial in determining which elements to select.

What is the time complexity of Apply Operations to Maximize Score?

The optimal solution for Apply Operations to Maximize Score runs in O(n log n) time and uses O(n) space. This complexity comes from sorting the scores, which is much more efficient than evaluating all subarrays.

What is the brute force solution for Apply Operations to Maximize Score?

The brute force approach for Apply Operations to Maximize Score is Brute Force, with O(n²) time complexity and O(1) space complexity. In the brute-force approach, we will evaluate all possible subarrays and calculate their prime scores. For each subarray, we will find the element with the highest prime score and multiply it into our score. This approach is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(n log n).

What are the interview tips for Apply Operations to Maximize Score?

Always clarify how many operations you can perform. Discuss your thought process and why you're choosing a particular approach. Consider edge cases, such as when k is larger than the number of unique prime scores.

What are common mistakes when solving Apply Operations to Maximize Score?

Failing to correctly calculate the prime score. Not considering the index when prime scores are equal.

#2818

Apply Operations to Maximize Score

Hard

ArrayMathStackGreedySortingMonotonic StackNumber TheoryGreedySorting

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(n log n)Space O(n)

In the optimal approach, we first calculate the prime scores for each number and then use a greedy strategy to select the top k elements based on their prime scores. This reduces the number of operations significantly by focusing only on the highest prime scores.

⚙️

Algorithm

3 steps

1Step 1: Calculate the prime score for each element in the array.
2Step 2: Create a list of pairs (prime score, index) and sort it in descending order based on prime scores.
3Step 3: Select the first k elements from the sorted list and multiply their corresponding nums values to get the maximum score.

solution.py26 lines

1# Full working Python code
2from math import isqrt
3
4MOD = 10**9 + 7
5
6def prime_score(x):
7    score = 0
8    for i in range(2, isqrt(x) + 1):
9        if x % i == 0:
10            score += 1
11            while x % i == 0:
12                x //= i
13    if x > 1:
14        score += 1
15    return score
16
17def max_score(nums, k):
18    scores = [(prime_score(num), i) for i, num in enumerate(nums)]
19    scores.sort(reverse=True, key=lambda x: (x[0], -x[1]))
20    max_product = 1
21    for i in range(k):
22        max_product = (max_product * nums[scores[i][1]]) % MOD
23    return max_product
24
25# Example usage
26print(max_score([8, 3, 9, 3, 8], 2))  # Output: 81

ℹ

Complexity note: This complexity comes from sorting the scores, which is much more efficient than evaluating all subarrays.

1The prime score is crucial in determining which elements to select.
2Sorting the elements based on their prime scores allows for efficient selection.

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