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Python Programs - Recursion Functions

Recursive function to compute sum of first N numbers - Python Program

Example 1 :

Python 
def sum_n(n):
    """Return sum of first n natural numbers."""
    if n == 0:
        return 0
    return n + sum_n(n-1)

print(sum_n(5))

Output

 
OUTPUT  :
15

Example 2 : Advanced Program

Python 
def recursive_sum_n(n):
    """
    Calculates the sum of the first N natural numbers recursively.

    Args:
        n (int): The number up to which the sum is calculated. 
                 Must be a non-negative integer.

    Returns:
        int: The sum of the first N natural numbers.
    """
    if n <= 1:  # Base case: if n is 0 or 1, return n
        return n
    else:  # Recursive step: add n to the sum of (n-1) numbers
        return n + recursive_sum_n(n - 1)

# Example Usage:
num = int(input("Enter a number  : "))
if num < 0:
    print("Please enter a non-negative number.")
else:
    result = recursive_sum_n(num)
    print(f"The sum of the first {num} natural numbers is: {result}")

num_two = 10
if num_two < 0:
    print("Please enter a non-negative number.")
else:
    result_two = recursive_sum_n(num_two)
    print(f"The sum of the first {num_two} natural numbers is: {result_two}")

Output

 
OUTPUT  :
Enter a number  : 5
The sum of the first 5 natural numbers is: 15
The sum of the first 10 natural numbers is: 55

Explanation:

 

The recursive_sum_n(n) function calculates the sum of the first n natural numbers using recursion.

  • Base Case:

The function first checks for the base case: if n <= 1: return n. This is crucial for stopping the recursion. If n is 0, the sum is 0. If n is 1, the sum is 1. This condition prevents infinite recursion.

  • Recursive Step:

If n is greater than 1, the function executes the recursive step: return n + recursive_sum_n(n - 1). In this step, the function adds the current value of n to the result of calling itself with n-1. This effectively breaks down the problem into smaller, similar subproblems. For example, recursive_sum_n(5) becomes 5 + recursive_sum_n(4), which then becomes 5 + (4 + recursive_sum_n(3)), and so on, until the base case (recursive_sum_n(1)) is reached. The results are then accumulated back up the call stack to provide the final sum.

 

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