93 lines
3.2 KiB
C++
93 lines
3.2 KiB
C++
// Source : https://leetcode.com/problems/maximum-average-pass-ratio/
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// Author : Hao Chen
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// Date : 2021-03-19
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/*****************************************************************************************************
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*
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* There is a school that has classes of students and each class will be having a final exam. You are
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* given a 2D integer array classes, where classes[i] = [passi, totali]. You know beforehand that in
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* the ith class, there are totali total students, but only passi number of students will pass the
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* exam.
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*
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* You are also given an integer extraStudents. There are another extraStudents brilliant students
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* that are guaranteed to pass the exam of any class they are assigned to. You want to assign each of
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* the extraStudents students to a class in a way that maximizes the average pass ratio across all the
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* classes.
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*
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* The pass ratio of a class is equal to the number of students of the class that will pass the exam
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* divided by the total number of students of the class. The average pass ratio is the sum of pass
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* ratios of all the classes divided by the number of the classes.
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*
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* Return the maximum possible average pass ratio after assigning the extraStudents students. Answers
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* within 10-5 of the actual answer will be accepted.
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*
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* Example 1:
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*
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* Input: classes = [[1,2],[3,5],[2,2]], extraStudents = 2
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* Output: 0.78333
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* Explanation: You can assign the two extra students to the first class. The average pass ratio will
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* be equal to (3/4 + 3/5 + 2/2) / 3 = 0.78333.
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*
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* Example 2:
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*
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* Input: classes = [[2,4],[3,9],[4,5],[2,10]], extraStudents = 4
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* Output: 0.53485
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*
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* Constraints:
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*
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* 1 <= classes.length <= 105
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* classes[i].length == 2
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* 1 <= passi <= totali <= 105
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* 1 <= extraStudents <= 105
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******************************************************************************************************/
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class Solution {
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private:
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template<typename T>
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void print_queue(T q) { // NB: pass by value so the print uses a copy
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while(!q.empty()) {
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auto [profit, c] = q.top();
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auto [pass, total] = c;
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cout << "[" << profit << " - " << pass << ", " << total <<"], ";
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q.pop();
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}
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cout << '\n';
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}
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//calculating ratio
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double ratio(double pass, double total) {
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return pass / total;
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}
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//calculating the profit
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double profit(double pass, double total) {
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return ratio(pass + 1, total + 1) - ratio(pass, total);
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}
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public:
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double maxAverageRatio(vector<vector<int>>& classes, int extraStudents) {
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priority_queue<pair<double, pair<int,int>> > q;
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double total_ratio = 0;
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int cnt = 0;
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for (auto& c : classes) {
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total_ratio += ratio(c[0], c[1]);
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q.push({profit(c[0], c[1]), {c[0],c[1]}});
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}
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//print_queue(q);
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while(extraStudents--){
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auto [added_profit, c] = q.top();
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auto [pass, total] = c;
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q.pop();
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total_ratio += added_profit;
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pass++; total++;
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q.push({profit(pass, total), {pass, total}});
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}
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//print_queue(q);
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return total_ratio / classes.size();
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}
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};
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