<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>

'''

[1,2]=0.5 -> [2,3]=0.66 -> [3,4] = 0.75
[3,5]=0.6               -> [4,6] = 0.66
[2,2]=1 



[2,4] = 0.5  -> [3,5]=0.6                   -> [4,6]=0.66
[3,9] = 0.33                                -> [4,10]=0.4 
[4,5] = 0.8                                 -> [5,6]=0.85
[2,10] = 0.2                -> [3,11]=0.27  -> [4,12]=0.33


(a+1)/(b+1) > a/b  ->   1+1/a > 1 + 1/b

'''
class Solution:
    def maxAverageRatio(self, classes: List[List[int]], extraStudents: int) -> float:
        
        
        classes = [(-((classes[i][0]+1)/(classes[i][1]+1)-classes[i][0]/classes[i][1]), classes[i][0]/classes[i][1] ,classes[i]) for i in range(len(classes))]
        output = 0 
        heapq.heapify(classes)
        #print(classes)
        for i in range(extraStudents):
            temp, old_percent, old_list = heapq.heappop(classes)
            new_list = [num + 1 for num in old_list]
            new_percent = new_list[0]/new_list[1]
            new_impact = -((new_list[0]+1)/(new_list[1]+1) - new_list[0]/new_list[1])
            heapq.heappush(classes, (new_impact,new_percent, new_list))
        for item in classes:
            output = output + item[1]
        return(output/len(classes))
        
65900