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Mean of Array After Removing Some Elements

Difficulty: Easy

Problem Description

Given an integer array arr, return the mean of the remaining integers after removing the smallest 5% and the largest 5% of the elements.

Key Insights

  • To compute the mean after removing elements, we must first sort the array.
  • The number of elements to remove is calculated as 5% of the total length of the array.
  • After removing the specified elements, we can calculate the mean from the remaining elements.
  • The answer must have a high precision, within 10^-5 of the actual mean.

Space and Time Complexity

Time Complexity: O(n log n) - due to sorting the array. Space Complexity: O(1) - if we sort in place, or O(n) if we use a separate array for sorted elements.

Solution

The solution involves sorting the array and determining the number of elements to remove based on the length of the array. Once the smallest and largest 5% of the elements are removed, we calculate the mean of the remaining elements. The mean is computed as the sum of the remaining elements divided by their count.

Code Solutions

def mean_after_removal(arr):
    arr.sort()  # Sort the array
    n = len(arr)
    to_remove = n // 20  # Calculate number of elements to remove (5% of n)
    
    # Remove the smallest and largest 5%
    remaining = arr[to_remove:n - to_remove]
    
    # Calculate the mean of the remaining elements
    return sum(remaining) / len(remaining)
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