How do you solve Maximum Average Pass Ratio on LeetCode?

Maximum Average Pass Ratio (LeetCode #1792) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n log n + extraStudents log n) time complexity and O(n) space complexity. Key insight: The impact of adding an extra student diminishes as more students are added to a class.

What is the brute force solution for Maximum Average Pass Ratio?

The brute force approach for Maximum Average Pass Ratio is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves trying every possible distribution of extra students across the classes. This means calculating the average pass ratio for each possible assignment, which can be very slow. The optimal Optimal Solution approach improves this to O(n log n + extraStudents log n).

What algorithm or data structure is used to solve Maximum Average Pass Ratio?

Maximum Average Pass Ratio uses the following concepts: Array, Greedy, Heap (Priority Queue). The recommended patterns to study are: Greedy Algorithms, Priority Queue.

What are the interview tips for Maximum Average Pass Ratio?

Always think about how to optimize the problem after the brute force solution. Make sure to explain your thought process clearly, especially when discussing greedy algorithms. Practice implementing priority queues, as they are commonly used in optimization problems.

What are common mistakes when solving Maximum Average Pass Ratio?

Failing to account for the diminishing returns of adding extra students to a class. Not using a priority queue effectively to manage which class to assign students to.

#1792

Maximum Average Pass Ratio

Medium

ArrayGreedyHeap (Priority Queue)Greedy AlgorithmsPriority Queue

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

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Intuition

Time O(n log n + extraStudents log n)Space O(n)

The optimal solution uses a greedy approach with a priority queue to always assign extra students to the class where they will have the most significant impact on the average pass ratio. This is efficient and ensures we maximize the average pass ratio.

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Algorithm

4 steps

1Step 1: Create a max-heap (priority queue) to store the classes based on the potential increase in pass ratio when an extra student is added.
2Step 2: For each class, calculate the initial pass ratio and the potential increase if one extra student is added.
3Step 3: Assign extra students to the class with the highest potential increase until all extra students are assigned.
4Step 4: Calculate the final average pass ratio.

solution.py14 lines

1# Full working Python code
2import heapq
3
4def maxAverageRatio(classes, extraStudents):
5    heap = []
6    for pass_i, total_i in classes:
7        heapq.heappush(heap, (-((pass_i + 1) / (total_i + 1) - pass_i / total_i), pass_i, total_i))
8    for _ in range(extraStudents):
9        change, pass_i, total_i = heapq.heappop(heap)
10        pass_i += 1
11        total_i += 1
12        heapq.heappush(heap, (-((pass_i + 1) / (total_i + 1) - pass_i / total_i), pass_i, total_i))
13    total_ratio = sum(pass_i / total_i for _, pass_i, total_i in heap)
14    return total_ratio / len(classes)

ℹ

Complexity note: The complexity is dominated by the heap operations, where we perform log n operations for each of the extra students, leading to O(n log n) for the initial heap creation and O(extraStudents log n) for the student assignments.

1The impact of adding an extra student diminishes as more students are added to a class.
2Using a priority queue allows us to efficiently determine which class to assign the next extra student to maximize the increase in average pass ratio.

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