11 Recursion Function Examples for Practice (Easiest 😎 to Hardest🤯)

Solve These Problems To Get Expert At Recursion Function

If you are new to Python and struggle to get your hands dirty with Recursive functions, you must try to solve the problems listed in this article. The article is sorted from easy to challenging levels. By solving each problem, you get ready and confident to solve the next challenge. Let’s dive in 🤿

If you are entirely new or not confident with the basics of a recursive function, then you should check  the blog  Recursive Function Explained – Understand recursion with functions in Python intuitively.

Factorial of a Number

In the “Introduction to the Recursive function” blog, you will learn recursive functions with the factorial problem.

Factorial of a Number

Fibonacci Sequence

The most famous formulas in mathematics are the Fibonacci sequence. Each number in the sequence is the sum of the two numbers that precede it. Therefore, sequence looks like: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.

What is Fibonacci Sequence and its working using illustration
Wrt functions, the sequence Fn of Fibonacci numbers is defined by the recurrence relation.
Fn = Fn-1 + Fn-2

with seed values

F0 = 0 and F1 = 1

Both factorial and Fibonacci are what we call Primitive Recursions, which means that we can also do them in “for” loops. However, there are some functions that are completely recursive, i.e we must do them recursively.

def fib(n) :
    if n==0 :
        return 0
    elif n ==1 :
        return 1
    else :
        return fib(n-1) +fib(n-2)



Sum of Digits of a Number

It is used to find the sum of digits of a number using recursion.

Sum of Digits working with illustration

def sumDigits(no):
    if no == 0:
        return 0
    else :
        return int(no % 10) + sumDigits(int(no / 10))


 Sum of the First n Natural Numbers

In this problem, we are simply adding 1 to n natural numbers.

Sum of the First n Natural Numbers working using illustration
Sum of the First n Natural Numbers

Likewise, we can find the sum of odd or even numbers.

def sumnums(n):
    if n == 1:
        return 1
    return n + sumnums(n - 1)


Power of a Number

The product of multiplying a number by itself is called Power. Usually, with a Base number and an Exponent, the Power is expressed. The exponent refers to a small number written above and to the right of the base number. It depicts how many times the base number is multiplied.

Power of a Number’s working using illustration

def power(num, topwr):
    if topwr == 0:
        return 1
        return num * power(num, topwr - 1)

print('{} to the power of {} is {}'.format(4, 7, power(4, 7)))
print('{} to the power of {} is {}'.format(2, 8, power(2, 8)))

Least Common Multiple(LCM) of 2 Numbers

The least common multiple(LCM) of a number is the smallest number that is the product of two or more numbers.

What is LCM and its working using illustration

def LCM(a, b):
  t = a % b
  if t == 0:
        return a
  return a * LCM(b, t) / t

print(LCM(2, 5))

Greatest Common Divisor(GCD) of 2 Numbers

The most significant positive number is the GCD of two or more integers that each of the integers is divisible, i.e., it is the most significant number that divides both of them. Thus, simply factorizing both numbers and multiplying common prime factors will give GCD.

What is GCD and its working using illustration

def GCD(a, b):
    low = min(a, b)
    high = max(a, b)

    if low == 0:
        return high
    elif low == 1:
        return 1
        return GCD(low, high%low)


 Merge Sort

The most efficient sorting algorithm is Merge sort. It works on the principle of Divide and Conquers. Merge sort repeatedly breaks down a list into several sublists until each sublist consists of a single element and merges those sublists in a manner that results in a sorted list.

What is Merge Sort and its working using illustration

def merge_sort(inp_arr):
    size = len(inp_arr)
    if size > 1:
        middle = size // 2
        left_arr = inp_arr[:middle]
        right_arr = inp_arr[middle:]


        p = 0
        q = 0
        r = 0

        left_size = len(left_arr)
        right_size = len(right_arr)
        while p < left_size and q < right_size:
            if left_arr[p] < right_arr[q]:
                inp_arr[r] = left_arr[p]
                p += 1
                inp_arr[r] = right_arr[q]
                q += 1

            r += 1

        while p < left_size:
            inp_arr[r] = left_arr[p]
            p += 1
            r += 1

        while q < right_size:
            inp_arr[r] = right_arr[q]
            q += 1
            r += 1

inp_arr = [8, 3, 5, 1, 2, 7, 6, 9]
print("Input Array :\n")
print("Sorted Array :\n")

Tower of Hanoi

A mathematical puzzle where we have three rods and n disks is known as the Tower of Hanoi. Here the puzzle is to move the entire stack to another rod, obeying the following simple rules:

  1. At a time, one disk can move.
  2. It works by taking the upper disk from one stack and placing it on top of another stack, i.e., a disk can move if it is the uppermost disk on a stack.
  3. A larger disk can not be put on top of a smaller disk.

Transferring the top n-1 disks from the source rod to the Auxiliary rod can again be thought of as a fresh problem and can be solved in the same manner.

What is Tower of Hanoi and its working using illustration
def TowerOfHanoi(n, source, destination, auxiliary):
    if n == 1:
        print("Move disk 1 from source", source, "to destination", destination)
    TowerOfHanoi(n - 1, source, auxiliary, destination)
    print("Move disk", n, "from source", source, "to destination", destination)
    TowerOfHanoi(n - 1, auxiliary, destination, source)

n = 4
TowerOfHanoi(n, 'A', 'B', 'C')

Reverse a string

As per the title, it reverses the original string, i.e., modifying the original string and arranging it in a reverse manner, starting from the last character to the first character.

Reverse a string’s working using illustration
def reverse(string):
    if len(string) == 0:
        return string
        return reverse(string[1:]) + string[0]

reverseme = 'Desserts'

reverseme = 'Knits'

reverseme = 'Regal'

reverseme = 'Pupils'

reverseme = 'Smart'

reverseme = 'Pals'

reverseme = 'Straw'

reverseme = 'Time'

reverseme = 'Star'

Pascals Triangle

Pascal’s Triangle can be seen as the triangle of numbers where each number is the sum of the above two (except for the edges, which are all “1”)

What is Pascals Triangle and its working using illustration
def pascal(n):
    if n == 1:
        return [1]
        line = [1]
        previous_line = pascal(n-1)
        for i in range(len(previous_line)-1):
            line.append(previous_line[i] + previous_line[i+1])
        line += [1]
    return line


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