First Order Statistic

The first order statistic of a dataset is the smallest value in the dataset. Algorithmically, it refers to finding the minimum element in a collection efficiently.

Java example:

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int findMin(int[] arr) {
  int min = arr[0];
  for (int i = 1; i < arr.length; i++) {
    if (arr[i] < min) {
      min = arr[i]; 
    }
  }
  return min; 
}

C++ example:

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int findMin(vector<int> arr) {
  int min = arr[0];
  for (int i = 1; i < arr.size(); i++) {
    if (arr[i] < min) {
      min = arr[i];
    }
  }
  return min;
}

Python example:

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def find_min(arr):
  min = arr[0]
  
  for i in range(1, len(arr)):
    if arr[i] < min:
      min = arr[i]

  return min

The first order statistic provides useful insight into datasets and distributions when efficient algorithms are used. It has applications in selection algorithms and density estimation.

Some efficient algorithms to find the first order statistic are minimum heaps and randomized quickselect. The minimum can be found in O(n) expected time.

The first order statistic of a set is the smallest element in that set. It’s the minimum value. Finding the first order statistic is a fundamental operation, and there are various ways to do it, from simply scanning the whole array to using more complex data structures like heaps. The key takeaway is that the first order statistic is crucial for understanding the lower bound of a dataset.

Java Code

In Java, the first order statistic can be found using a simple for loop:

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public class FirstOrderStatistic {
    public static int findMinimum(int[] arr) {
        int min = Integer.MAX_VALUE;

        for (int num : arr) {
            if (num < min) {
                min = num;
            }
        }

        return min;
    }

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

1. findMinimum initializes min to Integer.MAX_VALUE.
2. It scans each element and updates min whenever a smaller number is found.

C++ Code

In C++, you can find the first order statistic using a simple for loop:

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

int findMinimum(int arr[], int size) {
    int min = INT_MAX;

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

    return min;
}

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

1. findMinimum initializes min to INT_MAX.
2. The function iterates through the array, updating min whenever a smaller value is found.

Python Code

In Python, the min() function or a for loop can be used to find the first order statistic:

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def find_minimum(arr):
    min_val = float('inf')

    for num in arr:
        if num < min_val:
            min_val = num

    return min_val

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

1. find_minimum initializes min_val to float('inf').
2. The function then iterates through the list, updating min_val when a smaller element is found.

These implementations illustrate straightforward ways to find the first order statistic, or the minimum value, in a set of integers in Java, C++, and Python.