Custom Comparison Functions in Python

This challenge focuses on creating custom comparison functions in Python, a powerful technique for sorting or comparing objects based on criteria beyond the default comparison operators. Understanding how to define these functions is crucial for working with complex data structures and implementing custom sorting logic. You'll be crafting functions that dictate how two objects are compared, enabling flexible and tailored sorting behavior.

Problem Description

You are tasked with creating a function that takes a list of dictionaries and a key as input. The function should return a new list containing the dictionaries sorted in ascending order based on the values associated with the specified key. The comparison should be done using a custom comparison function that you define. The dictionaries may contain values of different types (e.g., strings, numbers), so your comparison function needs to handle this gracefully.

Key Requirements:

• Input: A list of dictionaries and a string representing the key to sort by.
• Output: A new list containing the dictionaries sorted in ascending order based on the key's values. The original list should remain unchanged.
• Custom Comparison: You must define a comparison function that takes two values and returns:
  • A negative number if the first value is less than the second.
  • Zero if the first value is equal to the second.
  • A positive number if the first value is greater than the second.
• Type Handling: Your comparison function should handle different data types (strings, numbers, etc.) without raising errors. If types are incomparable (e.g., trying to compare a string and an integer), return 0.
• Error Handling: If the key does not exist in any of the dictionaries, return the original list unchanged.

Expected Behavior:

The function should sort the dictionaries based on the values associated with the provided key. If the key is missing in any dictionary, that dictionary should be placed at the end of the sorted list.

Examples

Example 1:

Input: [{'name': 'Alice', 'age': 30}, {'name': 'Bob', 'age': 25}, {'name': 'Charlie', 'age': 35}]
Key: 'age'
Output: [{'name': 'Bob', 'age': 25}, {'name': 'Alice', 'age': 30}, {'name': 'Charlie', 'age': 35}]
Explanation: The dictionaries are sorted in ascending order based on the 'age' key.

Example 2:

Input: [{'name': 'Alice', 'score': 90}, {'name': 'Bob', 'score': 80}, {'name': 'Charlie'}]
Key: 'score'
Output: [{'name': 'Bob', 'score': 80}, {'name': 'Alice', 'score': 90}, {'name': 'Charlie'}]
Explanation: The dictionaries are sorted based on the 'score' key. The dictionary without 'score' is placed at the end.

Example 3:

Input: [{'name': 'Alice', 'value': 'b'}, {'name': 'Bob', 'value': 'a'}, {'name': 'Charlie', 'value': 'c'}]
Key: 'value'
Output: [{'name': 'Bob', 'value': 'a'}, {'name': 'Alice', 'value': 'b'}, {'name': 'Charlie', 'value': 'c'}]
Explanation: The dictionaries are sorted alphabetically based on the 'value' key.

Constraints

• The input list will contain at least one dictionary.
• The key will be a string.
• The values associated with the key can be of any type.
• The length of the input list will be between 1 and 1000.
• The time complexity of your solution should be O(n log n), where n is the number of dictionaries in the input list.

Notes

Consider using the sorted() function with a custom key argument or the sort() method with a custom comparison function. Think about how to handle cases where the key is missing from a dictionary. The comparison function should be robust and handle different data types gracefully. Remember to return a new sorted list, not modify the original.