// Source : https://leetcode.com/problems/maximum-average-pass-ratio/
// Author : Hao Chen
// Date   : 2021-03-19

/***************************************************************************************************** 
 *
 * 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]. You know beforehand that in 
 * the ith class, there are totali total students, but only passi number of students will pass the 
 * exam.
 * 
 * You are also given an integer extraStudents. There are another extraStudents brilliant students 
 * that are guaranteed to pass the exam of any class they are assigned to. You want to assign each of 
 * the extraStudents students to a class in a way that maximizes the average pass ratio across all the 
 * classes.
 * 
 * The pass ratio 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 average pass ratio is the sum of pass 
 * ratios of all the classes divided by the number of the classes.
 * 
 * Return the maximum possible average pass ratio after assigning the extraStudents students. Answers 
 * within 10-5 of the actual answer will be accepted.
 * 
 * Example 1:
 * 
 * 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.
 * 
 * Example 2:
 * 
 * Input: classes = [[2,4],[3,9],[4,5],[2,10]], extraStudents = 4
 * Output: 0.53485
 * 
 * Constraints:
 * 
 * 	1 <= classes.length <= 105
 * 	classes[i].length == 2
 * 	1 <= passi <= totali <= 105
 * 	1 <= extraStudents <= 105
 ******************************************************************************************************/

class Solution {
private:
    template<typename T>
    void print_queue(T q) { // NB: pass by value so the print uses a copy
        while(!q.empty()) {
            auto [profit, c] = q.top();
            auto [pass, total] = c;
            cout <<  "[" << profit << " - " << pass << ", " << total <<"], ";
            q.pop();
        }
        cout << '\n';
    }

    //calculating ratio
    double ratio(double pass, double total) {
        return pass / total;
    }
    //calculating the profit
    double profit(double pass, double total) {
        return ratio(pass + 1, total + 1)  - ratio(pass, total);
    }

public:
    double maxAverageRatio(vector<vector<int>>& classes, int extraStudents) {
        
        priority_queue<pair<double, pair<int,int>> > q;
        
        double total_ratio = 0;
        int cnt = 0;
        for (auto& c : classes) {
            total_ratio += ratio(c[0], c[1]);
            q.push({profit(c[0], c[1]), {c[0],c[1]}});
        }
        //print_queue(q);
        
        while(extraStudents--){
            auto [added_profit, c] = q.top();
            auto [pass, total] = c;
            q.pop();
            
            total_ratio += added_profit;
            pass++; total++;
            q.push({profit(pass, total), {pass, total}});
        }
        //print_queue(q);
        
        return total_ratio / classes.size();
    }
};