Exercises

The following exercises provide you with the opportunity to practice with recursion. The solutions to these exercises are found in the section .

The following function prints every other number from a low number to a high number. For example, if low is 0 and high is 10, it would print:
0
2
4
6
8
10

Identify the base case in the function:
def print_every_other(low, high):
if low > high:
return

print(low)
print_every_other(low + 2, high)
My kid was playing with my computer and changed my factorial function so that it computes factorial based on (n - 2) instead of (n - 1). He also changed number <= 1 to number == 1. Predict what will happen when we run factorial(10) using this function:
def factorial(number):
if number == 1:
return 1
else:
return number * factorial(number - 2)
Following is a function in which we pass in two numbers called low and high. The function returns the sum of all the numbers from low to high. For example, if low is 1 and high is 10, the function will return the sum of all numbers from 1 to 10, which is 55. However, our code is missing the base case and will run indefinitely! Fix the code by adding the correct base case:
def sum(low, high):
return high + sum(low, high - 1)

Here’s an array containing both numbers and arrays, which in turn contain numbers and arrays:

Write a recursive function that prints all the numbers (and just numbers).

	def print_every_other(low, high):
	if low > high:
	return

	print(low)
	print_every_other(low + 2, high)

	def factorial(number):
	if number == 1:
	return 1
	else:
	return number * factorial(number - 2)

	def sum(low, high):
	return high + sum(low, high - 1)