Leetcode #1792: Maximum Average Pass Ratio
In this guide, we solve Leetcode #1792 Maximum Average Pass Ratio in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
There is a school that has classes of students and each class will be having a final exam. You are given a 2D integer array classes, where classes[i] = [passi, totali].
Quick Facts
- Difficulty: Medium
- Premium: No
- Tags: Greedy, Array, Heap (Priority Queue)
Intuition
A locally optimal choice leads to a globally optimal result for this structure.
That means we can commit to decisions as we scan without backtracking.
Approach
Sort or preprocess if needed, then repeatedly take the best available local choice.
Maintain the minimal state necessary to validate the greedy decision.
Steps:
- Sort or preprocess as needed.
- Iterate and pick the best local option.
- Track the current solution.
Example
Input: classes = [[1,2],[3,5],[2,2]], extraStudents = 2
Output: 0.78333
Explanation: You can assign the two extra students to the first class. The average pass ratio will be equal to (3/4 + 3/5 + 2/2) / 3 = 0.78333.
Python Solution
class Solution:
def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:
h = [(a / b - (a + 1) / (b + 1), a, b) for a, b in classes]
heapify(h)
for _ in range(extraStudents):
_, a, b = heappop(h)
a, b = a + 1, b + 1
heappush(h, (a / b - (a + 1) / (b + 1), a, b))
return sum(v[1] / v[2] for v in h) / len(classes)
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.