📚 Maximum Average Pass Ratio (LeetCode Problem 1792)

A school has multiple classes of students, and each class will have a final exam. Your task is to distribute a given number of extra brilliant students across these classes to maximize the average pass ratio. Here's how it works:

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Problem Description

You are given:

1. classes:

A 2D array where each entry is of the form classes[i] = [passi, totali]:

• passi: The number of students in the class who are guaranteed to pass.
• totali: The total number of students in the class.

2. extraStudents:

An integer representing the number of extra students you can assign to any class. These students are guaranteed to pass in the class they're assigned to.

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Definitions:

• Pass Ratio of a Class:
  The ratio of passing students to total students:

$$\text{Pass Ratio} = \frac{\text{passi}}{\text{totali}}$$

• Average Pass Ratio Across All Classes:
  The sum of pass ratios of all classes divided by the total number of classes.

$$\text{Average Pass Ratio} = \frac{\sum \left( \frac{\text{passi}}{\text{totali}} \right)}{n}$$

• where 𝑛 is the total number of classes.

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Goal: Distribute the extraStudents in a way that maximizes the average pass ratio across all classes.

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🧪 Test Cases:

Example 1:

Input: classes = [[1, 2], [3, 5], [2, 2]];              extraStudents = 2;

Output: 0.78333;

Example 2:

Input:
classes = [[2, 4], [3, 9], [4, 5], [2, 10]]
extraStudents = 4

Output:
0.53485

✅ Constraints:

$$1 \leq \text{classes.length} \leq 10^5$$ $$\text{classes}[i].\text{length} == 2$$ $$1 \leq \text{passi} \leq \text{totali} \leq 10^5$$ $$1 \leq \text{extraStudents} \leq 10^5$$