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g1701_1800.s1792_maximum_average_pass_ratio.Solution Maven / Gradle / Ivy

package g1701_1800.s1792_maximum_average_pass_ratio;

// #Medium #Array #Greedy #Heap_Priority_Queue
// #2022_05_03_Time_456_ms_(89.78%)_Space_83.8_MB_(96.44%)

import java.util.PriorityQueue;

/**
 * 1792 - Maximum Average Pass Ratio\.
 *
 * Medium
 *
 * 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
**/
public class Solution {
    // O(m*logn+n*logn)
    // PriorityQueue
    public double maxAverageRatio(int[][] classes, int extraStudents) {
        PriorityQueue heap =
                new PriorityQueue<>((o1, o2) -> Double.compare(o2[0], o1[0]));
        for (int[] clas : classes) {
            double delta = profit(clas[0], clas[1]);
            heap.offer(new double[] {delta, clas[0], clas[1]});
        }
        while (extraStudents >= 1) {
            double[] temp = heap.poll();
            double pass = temp[1] + 1;
            double total = temp[2] + 1;
            double delta = profit(pass, total);
            heap.offer(new double[] {delta, pass, total});
            extraStudents--;
        }
        double average = 0d;
        while (!heap.isEmpty()) {
            double[] temp = heap.poll();
            average += temp[1] / temp[2];
        }
        return average / classes.length;
    }

    // O(1)
    private double profit(double a, double b) {
        return (a + 1) / (b + 1) - a / b;
    }
}