76 lines
3.0 KiB
Markdown
76 lines
3.0 KiB
Markdown
# [1792] Maximum Average Pass Ratio
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## 題目資訊
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- **難度**: Medium
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- **標籤**: Array, Greedy, Heap(Priority Queue)
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- **題目連結**: [LeetCode](https://leetcode.com/problems/maximum-average-pass-ratio/)
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- **練習日期**: 2025-09-01
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## 題目描述
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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.
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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.
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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 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.
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Return the *maximum* possible average pass ratio after assigning the `extraStudents` students. Answers within `10-5` of the actual answer will be accepted.
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## 解題思路
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### 初步分析
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- 這題主要考察什麼概念?
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- 貪心算法，找出每次分配學生，通過率可以提升至最高
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- Pass Ratio = pass / total
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- Average Pass Ratio = sum of pass ration / number of class
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### 解法概述
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1. **暴力解法**:
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- 思路：
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- 每次分配一個學生看哪個班級提升率會最高
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- leetcode 這邊會 time limit exceeded
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- 時間複雜度：O(N)
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- 空間複雜度：O(N)
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2. **最佳解法**:
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- 思路：
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- Priority Queue(Max Heap) 存每個班級潛在
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- 時間複雜度：O(?)
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- 空間複雜度：O(?)
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## 測試案例
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### 範例輸入輸出
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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 be equal to (3/4 + 3/5 + 2/2) / 3 = 0.78333.
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```
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### 邊界情況
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- 1 <= classes.length <= 10^5
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- classes[i].length == 2
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- 1 <= passi <= totali <= 10^5
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- 1 <= extraStudents <= 10^5
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## 學習筆記
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### 今天學到什麼？
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- 第一次使用 Priority Queue
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- 第一次使用 Unit Test
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### 遇到的困難
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- 可能要再了解 Priority Queue 更多實際用途
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### 改善方向
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-
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### 相關題目
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- [#1627](https://leetcode.com/problems/graph-connectivity-with-threshold/description/) Graph Connectivity With Threshold
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- [#1728](https://leetcode.com/problems/cat-and-mouse-ii/description/) Cat and Mouse II
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- [#3440](https://leetcode.com/problems/reschedule-meetings-for-maximum-free-time-ii/description/) Reschedule Meetings for Maximum Free Time II
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---
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**總結**:
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1. 貪心策略，每次都選擇當下收益最大解
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2. 練習使用Priority Queue 快速找到最大收益
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