nth Order Statistic

The nth order statistic of a set of values refers to the n-th smallest value in the ordered list. For example, given the set {5, 2, 8, 3, 9}, the 3rd order statistic would be 5, since if we order the set it becomes {2, 3, 5, 8, 9} and the 3rd smallest value is 5.

Some key properties of nth order statistics:

The minimum of a set is the 1st order statistic
The maximum is the nth order statistic, where n is the number of elements in the set
The median is the (n+1)/2 th order statistic if n is odd, or the mean of the n/2 th and (n/2 + 1)th order statistics if n is even

Example in Java:

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import java.util.Arrays; 

public class OrderStatistic {

  public static int findNthStatistic(int[] arr, int n) {
    Arrays.sort(arr);
    return arr[n-1]; 
  }

  public static void main(String[] args) {
    int[] arr = {5, 2, 8, 3, 9}; 
    int third = findNthStatistic(arr, 3); 
    System.out.println(third); // Prints 5
  }

}

Example in C++:

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#include <algorithm>
#include <iostream>
#include <vector>

int findNthStatistic(std::vector<int> arr, int n) {
  std::sort(arr.begin(), arr.end());
  return arr[n-1];
}

int main() {
  
  std::vector<int> arr = {5, 2, 8, 3, 9};
  int third = findNthStatistic(arr, 3);
  
  std::cout << third << "\n"; // Prints 5

  return 0;
}

Example in Python:

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def find_nth_statistic(arr, n):
  arr.sort()
  return arr[n-1]

arr = [5, 2, 8, 3, 9]
third = find_nth_statistic(arr, 3)
print(third) # Prints 5

The nth order statistic of a set is its largest element, assuming the set has n elements. Simply put, it’s the maximum value in the set. Finding the nth order statistic is a basic operation and has multiple ways to be calculated. Methods range from straightforward looping through the dataset to more complex data structures like heaps. The core idea is that the nth order statistic gives you an upper bound of the dataset.

Java Code

In Java, finding the nth order statistic can be as straightforward as iterating through an array to find the maximum value:

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public class NthOrderStatistic {
    public static int findMaximum(int[] arr) {
        int max = Integer.MIN_VALUE;

        for (int num : arr) {
            if (num > max) {
                max = num;
            }
        }

        return max;
    }

    public static void main(String[] args) {
        int[] array = {5, 3, 9, 1, 4};
        int maximum = findMaximum(array);
        System.out.println("The maximum is: " + maximum);
    }
}

findMaximum initializes max to Integer.MIN_VALUE.
It scans each element in the array and updates max whenever a larger number is found.

C++ Code

In C++, you can also find the nth order statistic by iterating through the elements:

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#include <iostream>
#include <algorithm>
#include <climits>

int findMaximum(int arr[], int size) {
    int max = INT_MIN;

    for (int i = 0; i < size; ++i) {
        max = std::max(max, arr[i]);
    }

    return max;
}

int main() {
    int arr[] = {5, 3, 9, 1, 4};
    int max = findMaximum(arr, 5);
    std::cout << "The maximum is: " << max << std::endl;
}

findMaximum initializes max to INT_MIN.
The function iterates through the array to update max whenever a larger value is found.

Python Code

Python provides built-in methods for finding the maximum, but a custom function can also be implemented:

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def find_maximum(arr):
    max_val = float('-inf')

    for num in arr:
        if num > max_val:
            max_val = num

    return max_val

if __name__ == "__main__":
    arr = [5, 3, 9, 1, 4]
    maximum = find_maximum(arr)
    print(f"The maximum is: {maximum}")

find_maximum initializes max_val to float('-inf').
It iterates through the list and updates max_val whenever a larger element is found.

Each of these implementations shows a simple way to find the nth order statistic, the largest value, in a set of integers using Java, C++, and Python.