C# Solution for Maximum Average Pass Ratio Problem
IntuitionThe goal is to maximize the average pass ratio across all classes after assigning a number of extra students. To achieve this:
•	The pass ratio improve
# Intuition\n<!-- Describe your first thoughts on how to solve this problem. -->\nThe goal is to maximize the average pass ratio across all classes after assigning a number of extra students. To achieve this:\n\u2022\tThe pass ratio improvement for each class is calculated when adding an extra passing student.\n\u2022\tAssign the extra students to the classes where they will have the greatest impact on improving the average.\n\u2022\tThis requires identifying the class with the maximum improvement efficiently after each assignment, which can be managed using a priority queue (or SortedSet in C#).\n\n# Approach\n<!-- Describe your approach to solving the problem. -->\n1.\tPass Ratio Improvement Calculation:\n\t\u2022\tThe improvement is calculated as the difference between the current pass ratio and the new pass ratio after adding one extra passing student:\n\n{Improvement} = frac{{passi} + 1}{{totali} + 1} - frac{{passi}}{{totali}}\n\n\u2022\tThis ensures we always add an extra student to the class that yields the greatest improvement.\n2.\tData Structure:\n\t\u2022\tUse a priority queue (via SortedSet in C#) to efficiently retrieve and update the class with the maximum improvement.\n3.\tSteps:\n\t\u2022\tInitialization: Calculate the improvement for all classes and store them in the priority queue.\n\t\u2022\tExtra Student Allocation:\n\t\u2022\tExtract the class with the maximum improvement.\n\t\u2022\tAssign one extra passing student to this class and update its improvement.\n\t\u2022\tReinsert the updated class back into the priority queue.\n\t\u2022\tFinal Average Calculation:\n\t\u2022\tAfter all extra students are assigned, calculate the total average pass ratio by summing the pass ratios of all classes.\n4.\tTie-Breaking:\n\t\u2022\tIn case two classes have the same improvement, sort them by their index to ensure deterministic behavior.\n\n# Complexity\n- Time complexity:\n<!-- Add your time complexity here, e.g. $$O(n)$$ -->\n1.\tInitialization:\n\t\u2022\tCalculating the initial improvement for all classes and inserting them into the priority queue: O(n . log n)\n\n2.\tExtra Student Assignment:\n\t\u2022\tFor each of the extraStudents, extracting and reinserting the class with the maximum improvement takes: O(log n)\n\n\t\u2022\tFor k = {extraStudents}, this results in: O(k . log n)\n\n3.\tFinal Calculation:\n\t\u2022\tCalculating the total average pass ratio involves a single pass over all classes: O(n)\n\nTotal Time Complexity: O((n + k) . log n)\n\nWhere n is the number of classes and k is the number of extra students.\n\n- Space complexity:\n<!-- Add your space complexity here, e.g. $$O(n)$$ -->\n1.\tPriority Queue:\n\t\u2022\tStores up to n entries, one for each class: O(n)\n\n2.\tAuxiliary Space:\n\t\u2022\tA constant amount of space is used for intermediate calculations.\n\nTotal Space Complexity: O(n)\n\n# Code\n```csharp []\npublic class Solution {\n    public double MaxAverageRatio(int[][] classes, int extraStudents) {\n        var pq = new SortedSet<(double improvement, int index)>(\n            Comparer<(double improvement, int index)>.Create((a, b) =>\n                a.improvement == b.improvement ? a.index.CompareTo(b.index) : b.improvement.CompareTo(a.improvement))\n        );\n        for (int i = 0; i < classes.Length; i++) {\n            double improvement = GetImprovement(classes[i][0], classes[i][1]);\n            pq.Add((improvement, i));\n        }\n        while (extraStudents > 0) {\n            var (maxImprovement, index) = pq.Min;\n            pq.Remove(pq.Min);\n            classes[index][0]++;\n            classes[index][1]++;\n            double newImprovement = GetImprovement(classes[index][0], classes[index][1]);\n            pq.Add((newImprovement, index));\n\n            extraStudents--;\n        }\n\n        double totalRatio = 0;\n        foreach (var c in classes) {\n            totalRatio += (double)c[0] / c[1];\n        }\n\n        return totalRatio / classes.Length;\n    }\n    private double GetImprovement(int passi, int totali) {\n        double currentRatio = (double)passi / totali;\n        double newRatio = (double)(passi + 1) / (totali + 1);\n        return newRatio - currentRatio;\n    }\n}\n```
['C#']