<p>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 <code>classes</code>, where <code>classes[i] = [pass<sub>i</sub>, total<sub>i</sub>]</code>. You know beforehand that in the <code>i<sup>th</sup></code> class, there are <code>total<sub>i</sub></code> total students, but only <code>pass<sub>i</sub></code> number of students will pass the exam.</p>

<p>You are also given an integer <code>extraStudents</code>. There are another <code>extraStudents</code> brilliant students that are <strong>guaranteed</strong> to pass the exam of any class they are assigned to. You want to assign each of the <code>extraStudents</code> students to a class in a way that <strong>maximizes</strong> the <strong>average</strong> pass ratio across <strong>all</strong> the classes.</p>

<p>The <strong>pass ratio</strong> of a class is equal to the number of students of the class that will pass the exam divided by the total number of students of the class. The <strong>average pass ratio</strong> is the sum of pass ratios of all the classes divided by the number of the classes.</p>

<p>Return <em>the <strong>maximum</strong> possible average pass ratio after assigning the </em><code>extraStudents</code><em> students. </em>Answers within <code>10<sup>-5</sup></code> of the actual answer will be accepted.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> classes = [[1,2],[3,5],[2,2]], <code>extraStudents</code> = 2
<strong>Output:</strong> 0.78333
<strong>Explanation:</strong> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> classes = [[2,4],[3,9],[4,5],[2,10]], <code>extraStudents</code> = 4
<strong>Output:</strong> 0.53485
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= classes.length &lt;= 10<sup>5</sup></code></li>
	<li><code>classes[i].length == 2</code></li>
	<li><code>1 &lt;= pass<sub>i</sub> &lt;= total<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= extraStudents &lt;= 10<sup>5</sup></code></li>
</ul>

from heapq import heappush, heappop
from typing import List

class Solution:
    def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:
        # Function to calculate the impact of adding an extra student
        def impact(passed, total):
            return (passed + 1) / (total + 1) - passed / total
        
        # Max-heap to store classes based on their impact
        heap = []
        
        # Initialize the heap with the negative impact (since heapq is a min-heap by default)
        for passed, total in classes:
            heappush(heap, (-impact(passed, total), passed, total))
        
        # Assign each extra student to the class with the highest impact
        for _ in range(extraStudents):
            imp, passed, total = heappop(heap)
            passed += 1
            total += 1
            heappush(heap, (-impact(passed, total), passed, total))
        
        # Calculate the final average pass ratio
        total_ratio = 0
        for _, passed, total in heap:
            total_ratio += passed / total
        
        return total_ratio / len(classes)

# Example usage:
# solution = Solution()
# print(solution.maxAverageRatio([[1,2],[3,5],[2,2]], 2))  # Output: 0.78333
# print(solution.maxAverageRatio([[2,4],[3,9],[4,5],[2,10]], 4))  # Output: 0.53485
1882