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Given an array of integers arr, where each integer is not necessarily unique, perform a “rank transform” of the array. The rank of each element is its position in the list of unique values sorted in ascending order. The smallest element receives a rank of 1, the second smallest a rank of 2, and so on.

Example

Clarifying Questions

  1. Q: Are there any constraints on the values of integers in the array? A: No, the integers can be any value within the range of typical 32-bit integers.
  2. Q: If the array is empty, what should be the result? A: The result should be an empty array.
  3. Q: Are negative integers allowed? A: Yes, negative integers are allowed.

Strategy

  1. Create a sorted list of unique elements from arr:
    • This allows us to determine the rank of each unique element.
  2. Create a mapping from element to its rank:
    • Iterate through the sorted list and assign ranks starting from 1.
  3. Transform the original array using this mapping:
    • Replace each element in the original array with its corresponding rank.

Code

def arrayRankTransform(arr):
    if not arr:
        return []

    # Step 1: Get the sorted list of unique elements
    sorted_unique = sorted(set(arr))

    # Step 2: Create a rank mapping
    rank_map = {val: rank + 1 for rank, val in enumerate(sorted_unique)}

    # Step 3: Transform the original array to its rank representation
    return [rank_map[val] for val in arr]

# Example usage
arr = [40, 10, 20, 30]
print(arrayRankTransform(arr))  # Output: [4, 1, 2, 3]

Time Complexity

The time complexity of this solution is:

  1. O(n log n) for sorting the unique elements, where n is the number of elements in the input array.
  2. O(n) for creating the rank map and transforming the original array.

Thus, the overall time complexity is O(n log n) due to the sorting step. The space complexity is O(n) due to the storage of the rank_map and the unique sorted values.

If there are further specific constraints or requirements, please let me know!

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