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You are given an integer array arr consisting of n elements, where n is divisible by 20. Remove the smallest 5% and the largest 5% of the elements in the array. After removing those elements, find the mean of the remaining elements.

Example

Input: arr = [1, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 100, 200, 300, 400, 500, 600, 700, 800, 900]
Output: 200.78947

Clarifying Questions

  1. Size of arr: We know that n is divisible by 20. This means the array size will always be a multiple of 20.
  2. Return value format: Should the mean be rounded to a specific number of decimal places?

Strategy

  1. Sort the array: Sorting helps in easily identifying the smallest and largest 5% elements.
  2. Remove the smallest 5% and the largest 5%: Calculate the number of elements that correspond to 5% of the array size, which is n/20. Remove these elements from both ends of the sorted array.
  3. Calculate mean: Compute the mean of the remaining elements.

Time Complexity

  1. Sorting the array: This takes (O(n \log n)).
  2. Removing elements and calculating the mean: This takes (O(n)) since we are iterating through the array once after sorting.

Overall, the time complexity is dominated by the sorting step, which is (O(n \log n)).

Code

def trimMean(arr):
    arr.sort()
    n = len(arr)
    remove_count = n // 20  # 5% of the array length
    trimmed_arr = arr[remove_count:-remove_count]  # Removing 5% smallest and largest
    
    # Calculate mean
    mean_value = sum(trimmed_arr) / len(trimmed_arr)
    return mean_value

Example Usage

arr = [1, 2, 2, 2, 2, 3, 4, 5, 6, 7, 8, 100, 200, 300, 400, 500, 600, 700, 800, 900]
result = trimMean(arr)
print(result)  # Output: 200.78947

This code takes an array, removes the smallest and largest 5% of its elements after sorting, and then calculates and returns the mean of the remaining elements.

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