Mean of array using recursion

Given an array arr[] of integers, calculate the mean (average) using recursion.

Note: The mean of an array is the sum of its elements divided by the number of elements in the array.

Examples: 

Input: arr[] = [1, 2, 3, 4, 5]
Output: 3
Explanation: The sum of elements (15) divided by the number of elements (5) gives the mean: 3

Input: arr[] = [1, 2, 3]
Output: 2
Explanation: The sum of elements (6) divided by the number of elements (3) gives the mean: 2

[Approach] - Using Recursion - O(n) Time and O(n) Space

The idea is to compute the mean recursively by building it from smaller prefixes of the array.
Let mean(arr, n) represent the mean of the first n elements. We first calculate the mean of the first n−1 elements recursively. Since the mean of n−1 elements equals their sum divided by (n−1), multiplying it by (n−1) gives their total sum. We then add the nth element arr[n−1] to this sum and divide the result by n to obtain the mean of the first n elements.

The recursive formula for calculating the mean of an array is:

\text{mean}(arr, n) = \frac{\text{mean}(arr, n-1) \times (n-1) + arr[n-1]}{n}

//Driver Code Starts
#include <iostream>
#include <vector>
using namespace std;

//Driver Code Ends

// helper recursive function
double findMeanRec(vector<int>& arr, int n) {
    // Base case
    if (n == 1)
        return arr[0];

    // Recursive case
    return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n;
}

double findMean(vector<int>& arr) {
    return findMeanRec(arr, arr.size());
}

//Driver Code Starts

int main() {
    vector<int> arr = {1, 2, 3, 4, 5};
    cout << findMean(arr);
    return 0;
}
//Driver Code Ends

//Driver Code Starts
#include <stdio.h>

//Driver Code Ends

// helper recursive function
double findMeanRec(int arr[], int n){
    // Base case
    if (n == 1)
        return arr[0];

    // Recursive case
    return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n;
}

double findMean(int arr[], int n){
    return findMeanRec(arr, n);
}


//Driver Code Starts
int main(){
    int arr[] = {1, 2, 3, 4, 5};
    int n = sizeof(arr) / sizeof(arr[0]);
    printf("%f", findMean(arr, n));
    return 0;
}
//Driver Code Ends

//Driver Code Starts
import java.util.*;

//Driver Code Ends

class GfG {

// helper recursive function
static double findMeanRec(int[] arr, int n){
    // Base case
    if (n == 1)
        return arr[0];

    // Recursive case
    return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n;
}

static double findMean(int[] arr){
    return findMeanRec(arr, arr.length);
}

public static void main(String[] args){
    int[] arr = {1, 2, 3, 4, 5};
    System.out.println(findMean(arr));}
}

# helper recursive function
def findMeanRec(arr, n):
    # Base case
    if n == 1:
        return arr[0]

    # Recursive case
    return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n


def findMean(arr):
    return findMeanRec(arr, len(arr))

if __name__ == "__main__":
    arr = [1, 2, 3, 4, 5]
    print(findMean(arr))

//Driver Code Starts
using System;

//Driver Code Ends

class GfG{
    // helper recursive function
    static double findMeanRec(int[] arr, int n){
        // Base case
        if (n == 1)
            return arr[0];

        // Recursive case
        return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n;
    }

    static double findMean(int[] arr){
        return findMeanRec(arr, arr.Length);
    }

//Driver Code Starts

    static void Main(){
        int[] arr = {1, 2, 3, 4, 5};
        Console.WriteLine(findMean(arr));
    }
}
//Driver Code Ends

// helper recursive function
function findMeanRec(arr, n)
{
    // Base case
    if (n === 1)
        return arr[0];

    // Recursive case
    return (findMeanRec(arr, n - 1) * (n - 1) + arr[n - 1]) / n;
}

function findMean(arr)
{
    return findMeanRec(arr, arr.length);
}
// Driver Code
let arr = [1, 2, 3, 4, 5];
console.log(findMean(arr));

3