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For problem1.py (department_highest_salary):

  1. Correctness: The solution appears correct for finding employees with the highest salary in each department. It merges the tables, calculates max salary per department, and filters employees matching that salary.
  2. Time Complexity: O(n log n) due to the merge and groupby operations.
  3. Space Complexity: O(n) for storing the merged DataFrame.
  4. Code Quality: The code is concise but could benefit from more descriptive variable names (e.g., 'max_sal' could be 'max_salary_per_dept'). The column renaming at the end is clear.
  5. Efficiency: The solution is efficient, though using transform() might be slightly less optimal than other approaches like idxmax().

For problem2.py (order_scores):

  1. Correctness: The solution correctly sorts scores and assigns dense ranks.
  2. Time Complexity: O(n log n) for sorting and O(n) for ranking, so overall O(n log n).
  3. Space Complexity: O(n) for storing the sorted and ranked DataFrame.
  4. Code Quality: The code is clean and straightforward. The use of dense ranking is appropriate here.
  5. Efficiency: The solution is efficient, though the method could be specified more explicitly (e.g., 'dense' ranking).

General suggestions:

  1. Add docstrings to explain function purposes and return values.
  2. Consider adding comments for complex operations.
  3. For problem1.py, consider handling edge cases like empty DataFrames or departments with no employees.
  4. Consistent formatting (e.g., spaces around operators) would improve readability.

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