// LeetCode 1792: Maximum Average Pass Ratio
// 難度: Medium
// 日期: 2025-09-01

using System;
using System.Collections.Generic;
using System.Linq;

public class Solution
{
    public double MaxAverageRatio(int[][] classes, int extraStudents)
    {
        // use priority queue
        var pq = new PriorityQueue<ClassInfo, double>();

        // 初始化：將所有班級加入優先佇列 
        for (int i = 0; i < classes.Length; i++)
        {
            int pass = classes[i][0];
            int total = classes[i][1];

            double gain = CalculateGain(pass, total);

            pq.Enqueue(new ClassInfo(pass, total), -gain);
        }

        for (int i = 0; i < extraStudents; i++)
        {
            var classInfo = pq.Dequeue();

            classInfo.Pass++;
            classInfo.Total++;

            double newGain = CalculateGain(classInfo.Pass, classInfo.Total);
            pq.Enqueue(classInfo, -newGain);
        }

        double totalRatio = 0;
        while (pq.Count > 0)
        {
            var classInfo = pq.Dequeue();
            totalRatio += (double)classInfo.Pass / classInfo.Total;
        }

        return totalRatio / classes.Length;
    }

    public double MaxAverageRatioByBruteForce(int[][] classes, int extraStudents)
    {
        var n = classes.Length;
        var pass = new int[n];
        var total = new int[n];

        for (var i = 0; i < n; i++)
        {
            pass[i] = classes[i][0];
            total[i] = classes[i][1];
        }

        for (int student = 0; student < extraStudents; student++)
        {
            int bestClass = -1;
            double maxInprovement = 0;

            for (int i = 0; i < n; i++)
            {
                double currentAvg = CalculateAvergaeRatio(pass, total);

                pass[i]++;
                total[i]++;

                double newAvg = CalculateAvergaeRatio(pass, total);
                double improvement = newAvg - currentAvg;

                pass[i]--;
                total[i]--;

                if (improvement > maxInprovement)
                {
                    maxInprovement = improvement;
                    bestClass = i;
                }
            }

            if (bestClass != -1)
            {
                pass[bestClass]++;
                total[bestClass]++;
            }
        }

        return CalculateAvergaeRatio(pass, total);
    }

    private double CalculateGain(int pass, int total)
    {
        // 計算提升率
        return (double)(pass + 1) / (total + 1) - (double)pass / total;
    }

    private double CalculateAvergaeRatio(int[] pass, int[] total)
    {
        double sum = 0;
        for (var i = 0; i < pass.Length; i++)
        {
            sum += (double)pass[i] / total[i];
        }
        return sum / pass.Length;
    }
}

public class ClassInfo
{
    public int Pass { get; set; }
    public int Total { get; set; }

    public ClassInfo(int pass, int total)
    {
        Pass = pass;
        Total = total;
    }
}

// 測試程式
public class Program
{
    public static void Main()
    {
        Solution solution = new Solution();

        // TestCase
        TestCase1(solution);
        TestCase2(solution);
    }

    static void TestCase1(Solution solution)
    {
        // Input: 
        int[][] classes = new int[][]
        {
            new int[] {1, 2},
            new int[] {3, 5},
            new int[] {2, 2}
        };
        int extraStudents = 2;

        Console.WriteLine("Test 1: ");
        Console.WriteLine($"classes: [{string.Join("], [", classes.Select(c => string.Join(", ", c)))}]");
        Console.WriteLine($"extraStudents: {extraStudents}");

        // Expected: 
        Console.WriteLine("Expect: ");
        Console.WriteLine($"output: 0.78333");

        // Actual: 
        Console.WriteLine("Actual: ");
        Console.WriteLine($"Brute Force: {solution.MaxAverageRatioByBruteForce(classes, extraStudents):F6}");
        Console.WriteLine($"Priority Queue: {solution.MaxAverageRatio(classes, extraStudents):F6}");
    }


    static void TestCase2(Solution solution)
    {
        // Input: 
        int[][] classes = new int[][]
        {
            new int[] {2, 4},
            new int[] {3, 9},
            new int[] {4, 5},
            new int[] {2, 10}
        };
        int extraStudents = 4;

        Console.WriteLine("Test 2: ");
        Console.WriteLine($"classes: [{string.Join("], [", classes.Select(c => string.Join(", ", c)))}]");
        Console.WriteLine($"extraStudents: {extraStudents}");

        // Expected: 
        Console.WriteLine("Expect: ");
        Console.WriteLine($"output: 0.53485");

        // Actual: 
        Console.WriteLine("Actual: ");
        Console.WriteLine($"Brute Force: {solution.MaxAverageRatioByBruteForce(classes, extraStudents):F6}");
        Console.WriteLine($"Priority Queue: {solution.MaxAverageRatio(classes, extraStudents):F6}");
    }
}