Tail recursion to calculate sum of array elements.

Given an array arr, we need to find the sum of its elements using Tail Recursion Method. We generally want to achieve tail recursion so that compilers can optimize the code. If the recursive call is the last statement, the compiler can optimize it by eliminating the need to store the parent call's state.

Examples: 

Input: arr = [1, 8, 9]
Output: 18
Explanation: The sum of the elements in the array [1, 8, 9] is 18.

Input: arr = [2, 55, 1, 7]
Output: 65

For the Normal Recursion Method, check out this guide: Sum of Array Elements Using Recursion

Approach:

• Extract arr[size - 1] and add it to the sum.
• Call the function again with size - 1 (excluding the last element).
• Instead of calculating the sum separately, pass the updated sum in each call.
• Keep reducing size until it reaches 0.
• Once all elements are added, return the accumulated sum as the result.

#include <bits/stdc++.h>
using namespace std;

// Function to calculate the sum of elements using Tail Recursion
int arrSum(vector<int> &arr, int n, int sum = 0)
{
    // Base Case
    if (n == 0)
        return sum;

    // Recursive call
    return arrSum(arr, n - 1, sum + arr[n - 1]);
}

int main()
{
    // Input array
    vector<int> arr = {2, 55, 1, 7};
    int n = arr.size();
    cout << arrSum(arr, n, 0) << endl;
    return 0;
}

class GfG {
    
    // Function to calculate the sum of elements using Tail Recursion
    static int arrSum(int[] arr, int n, int sum) {
        // Base Case
        if (n == 0)
            return sum;
        
        // Recursive call
        return arrSum(arr, n - 1, sum + arr[n - 1]);
    }

    public static void main(String[] args) {
        int arr[] = { 2, 55, 1, 7 };
        int n = arr.length;
        System.out.print(arrSum(arr, n, 0)); 
    }
}

def arrSum(arr, n, sum=0):
    # Base Case
    if n == 0:
        return sum

    # Recursive call
    return arrSum(arr, n - 1, sum + arr[n - 1])


# Driver code
arr = [2, 55, 1, 7]
n = len(arr)
print(arrSum(arr, n, 0))

using System;

class GfG {
    // Function to calculate the sum of elements using Tail
    // Recursion
    static int arrSum(int[] arr, int n, int sum)
    {
        // Base Case
        if (n == 0)
            return sum;

        // Recursive call
        return arrSum(arr, n - 1, sum + arr[n - 1]);
    }

    public static void Main()
    {
        int[] arr = { 2, 55, 1, 7 };
        int n = arr.Length;
        Console.WriteLine(arrSum(arr, n, 0));
    }
}

function arrSum(arr, n, sum = 0)
{
    // Base Case
    if (n === 0)
        return sum;

    // Recursive call
    return arrSum(arr, n - 1, sum + arr[n - 1]);
}

// Driver code
let arr = [ 2, 55, 1, 7 ];
let n = arr.length;
console.log(arrSum(arr, n, 0));

65

Time Complexity: O(n), where n is the length of array.
Auxiliary Space: O(n), due to recursive function calls stored in the call stack.