<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>

class Solution:
    def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:
        max_heap = []
        no_difference = []
        for ace, total in classes:
            current_ratio = ace / total
            potential_ratio = (ace + 1) / (total + 1)
            diff = potential_ratio - current_ratio
            if diff > 0:
                heapq.heappush(max_heap, (-diff, (ace, total)))
            else:
                no_difference.append((ace, total))
        for index in range(extraStudents):
            if max_heap:
                ace, total = heapq.heappop(max_heap)[1]
                ace += 1
                total += 1
                current_ratio = ace / total
                potential_ratio = (ace + 1) / (total + 1)
                diff = potential_ratio - current_ratio
                heapq.heappush(max_heap, (-diff, (ace, total)))
            else:
                ace, total = no_difference.pop()
                no_difference.append((ace, total))
        
        ratio_sum = 0
        for element in max_heap:
            ace, total = element[1]
            ratio_sum += (ace / total)
        for ace, total in no_difference:
            ratio_sum += (ace / total)
        return ratio_sum / len(classes)
1803