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The student's solution demonstrates a good understanding of pandas operations to solve the problem of finding the nth highest salary. Here are some detailed observations:

  1. Correctness:

    • Both functions handle the case where N is out of bounds (either too large or negative) by returning None, which is correct.
    • The second_highest_salary function correctly handles cases where there are fewer than 2 unique salaries.
    • The approach of using drop_duplicates() followed by sorting and selecting the nth element is a valid approach.
  2. Time Complexity:

    • The time complexity is dominated by the sorting operation, which is O(n log n) where n is the number of unique salaries.
    • This is optimal for this type of problem as we need to sort to find the nth highest value.
  3. Space Complexity:

    • The space complexity is O(n) for storing the unique salaries, which is reasonable.
    • No unnecessary copies of the dataframe are made.
  4. Code Quality:

    • The code is generally clean and readable.
    • Variable names could be more descriptive (e.g., 'df' could be 'unique_salaries').
    • The functions could benefit from docstrings explaining their purpose and parameters.
    • The solution could be made more consistent between the two functions (one uses chaining while the other uses intermediate variables).
  5. Efficiency:

    • The solution is already quite efficient for the problem.
    • One potential optimization would be to use nlargest() instead of sort+head for better readability and potentially better performance in some cases.
    • The second function could be simplified to use the same approach as the first function for consistency.

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