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Recursive Practice Problems with Solutions

Tail recursion to calculate sum of array elements.

Last Updated : 17 Mar, 2025

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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.

C++

#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; }

Java

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));      } }

Python

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))

C#

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));     } }

JavaScript

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));

Output

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.

Recursive Practice Problems with Solutions

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Article Tags :

DSA
Recursion
tail-recursion

Practice Tags :

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