diff --git a/problems/1792-maximum-average-pass-ratio/README.md b/problems/1792-maximum-average-pass-ratio/README.md new file mode 100644 index 0000000..7a3e56b --- /dev/null +++ b/problems/1792-maximum-average-pass-ratio/README.md @@ -0,0 +1,71 @@ +# [1792] Maximum Average Pass Ratio + +## 題目資訊 +- **難度**: Medium +- **標籤**: Array, Greedy, Heap(Priority Queue) +- **題目連結**: [LeetCode](https://leetcode.com/problems/maximum-average-pass-ratio/) +- **練習日期**: 2025-09-01 + +## 題目描述 +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. + +## 解題思路 + +### 初步分析 +- 這題主要考察什麼概念? + - 貪心算法，找出每次分配學生，通過率可以提升至最高 +- Pass Ratio = pass / total +- Average Pass Ratio = sum of pass ration / number of class + +### 解法概述 +1. **暴力解法**: + - 思路： + - 每次分配一個學生看哪個班級提升率會最高 + - leetcode 這邊會 time limit exceeded + - 時間複雜度：O(N) + - 空間複雜度：O(N) + +2. **最佳解法**: + - 思路： + - Priority Queue(Max Heap) 存每個班級淺在 + - 時間複雜度：O(?) + - 空間複雜度：O(?) + +## 測試案例 + +### 範例輸入輸出 +``` +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. +``` + +### 邊界情況 +- 1 <= classes.length <= 10^5 +- classes[i].length == 2 +- 1 <= passi <= totali <= 10^5 +- 1 <= extraStudents <= 10^5 + +## 學習筆記 + +### 今天學到什麼？ +- + +### 遇到的困難 +- + +### 改善方向 +- + +### 相關題目 +- [題目編號] 題目名稱 - 相似概念 +- [題目編號] 題目名稱 - 進階版本 + +--- +**總結**: 這題的核心概念是...，適合練習...技巧。 diff --git a/problems/1792-maximum-average-pass-ratio/csharp/Program.cs b/problems/1792-maximum-average-pass-ratio/csharp/Program.cs new file mode 100644 index 0000000..bd54a7b --- /dev/null +++ b/problems/1792-maximum-average-pass-ratio/csharp/Program.cs @@ -0,0 +1,130 @@ +// 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 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 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; + } +} + +// 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($"output: {solution.MaxAverageRatio(classes, extraStudents):F6}"); + } + + + static void TestCase2(Solution solution) + { + // Input: + int[][] classes = new int[][] + { + new int[] {2, 4}, + new int[] {3, 9}, + new int[] {4, 5}, + new int[] {2, 10} + }; + int extraStudents = 4; + + Console.WriteLine("Test 2: "); + Console.WriteLine($"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($"Brute Force: {solution.MaxAverageRatioByBruteForce(classes, extraStudents):F6}"); + //Console.WriteLine($"output: {solution.MaxAverageRatio(classes, extraStudents):F6}"); + } +} diff --git a/problems/1792-maximum-average-pass-ratio/csharp/csharp.csproj b/problems/1792-maximum-average-pass-ratio/csharp/csharp.csproj new file mode 100644 index 0000000..2150e37 --- /dev/null +++ b/problems/1792-maximum-average-pass-ratio/csharp/csharp.csproj @@ -0,0 +1,10 @@ + + + + Exe + net8.0 + enable + enable + + +