# [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) 存每個班級潛在
   - 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？
- 第一次使用 Priority Queue
- 第一次使用 Unit Test

### 遇到的困難
- 可能要再了解 Priority Queue 更多實際用途

### 改善方向
- 

### 相關題目
- [#1627](https://leetcode.com/problems/graph-connectivity-with-threshold/description/) Graph Connectivity With Threshold
- [#1728](https://leetcode.com/problems/cat-and-mouse-ii/description/) Cat and Mouse II
- [#3440](https://leetcode.com/problems/reschedule-meetings-for-maximum-free-time-ii/description/) Reschedule Meetings for Maximum Free Time II

---
**總結**:
1. 貪心策略，每次都選擇當下收益最大解
2. 練習使用Priority Queue 快速找到最大收益