Compute the rank as a percentage

# Table: Students
#
# +---------------+------+
# | Column Name   | Type |
# +---------------+------+
# | student_id    | int  |
# | department_id | int  |
# | mark          | int  |
# +---------------+------+
# student_id contains unique values.
# Each row of this table indicates a student's ID, the ID of the department in which the student enrolled, and their mark in the exam.
#
#
#
# Write a solution to report the rank of each student in their department as a percentage, where the rank as a percentage is computed using the following formula: (student_rank_in_the_department - 1) * 100 / (the_number_of_students_in_the_department - 1). The percentage should be rounded to 2 decimal places. student_rank_in_the_department is determined by descending mark, such that the student with the highest mark is rank 1. If two students get the same mark, they also get the same rank.
#
# Return the result table in any order.
#
# The result format is in the following example.
#
# Example 1:
# Input:
# Students table:
# +------------+---------------+------+
# | student_id | department_id | mark |
# +------------+---------------+------+
# | 2          | 2             | 650  |
# | 8          | 2             | 650  |
# | 7          | 1             | 920  |
# | 1          | 1             | 610  |
# | 3          | 1             | 530  |
# +------------+---------------+------+
# Output:
# +------------+---------------+------------+
# | student_id | department_id | percentage |
# +------------+---------------+------------+
# | 7          | 1             | 0.0        |
# | 1          | 1             | 50.0       |
# | 3          | 1             | 100.0      |
# | 2          | 2             | 0.0        |
# | 8          | 2             | 0.0        |
# +------------+---------------+------------+
# Explanation:
# For Department 1:
# - Student 7: percentage = (1 - 1) * 100 / (3 - 1) = 0.0
# - Student 1: percentage = (2 - 1) * 100 / (3 - 1) = 50.0
# - Student 3: percentage = (3 - 1) * 100 / (3 - 1) = 100.0
# For Department 2:
# - Student 2: percentage = (1 - 1) * 100 / (2 - 1) = 0.0
# - Student 8: percentage = (1 - 1) * 100 / (2 - 1) = 0.0

import pandas as pd
import numpy as np


def compute_rating(students: pd.DataFrame) -> pd.DataFrame:
  students["rank"] = students.groupby("department_id")["mark"].rank(
    method="min", ascending=False
  )
  dept_count = students.groupby("department_id")["student_id"].transform("count")
  students["percentage"] = np.where(
    dept_count <= 1,
    0.0,
    ((students["rank"] - 1) * 100 / (dept_count - 1)).round(2),
  )
  result = students[["student_id", "department_id", "percentage"]]
  return result.sort_values(["department_id", "percentage"]).reset_index(drop=True)