5. Recursively Reverse a List Mke a recursive function that reverses a list. For example, given [1, 2, 3, 4], the function would return this list [4, 3, 2, 1]. It does not print anything.
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5. Recursively Reverse a List
Mke a recursive function that reverses a list. For example, given [1, 2, 3, 4], the function
would return this list [4, 3, 2, 1]. It does not print anything.
Instruction is below
Practice writing recursive functions in python3
Make the five recursive functions described below in python3 by using the starter code recursive_functions.py. For each function, figure out how to solve it conceptually : write down the base case (when recursion stops) and how each recursive function-call moves towards the base case. The functions should not print anything (except you may add temporary print statements to help debug them).
You can test your program by using the provided program test_recursive_functions.py. Don't edit the test program. Put it into the same directory (folder) with your recursive_functions.py and run it. It will import your functions as a module, test your functions, and tell you when each function is returning correct results.
1. Factorial
In math, if you have a number n, the factorial function (written n!) computes
n x (n-1) x (n-2) x (n-3) x ... x 1. For example:
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0! is defined to be 1
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1! = 1
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2! = 2 x 1=2
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3! = 3 x 2 x 1=6
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4! = 4 x 3 x 2 x 1 = 24
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5! = 5 x 4 x 3 x 2 x 1 = 120
Add your code to the provided function signature so it computes the factorial of the integer it is given. You may not use math.factorial() in your function.
2. Recursively Sum
Make a recursive function that takes an integer argument n and returns the sum of the
integers from 1 to n. E.g., if n=10, the function should return 55 (1 + 2 + 3 + . . . 10).
3. Recursively Sum List
Make a recursive function sumlist_recursively(l) that accepts a list of numbers as an argument, and returns the sum of all the numbers in the list. E.g., if the function is passed the list [1, 4, 8, 3, 0, 16], it should return 32.
4. Recursively Multiply
Make a recursive function that multiplies its two integer arguments (x and y) recursively. The function should return the value of x times y. Hint: multiplication can be performed as repeated addition, for example.:
7 x 4 = 4 + 4 + 4 + 4 + 4 + 4 + 4 = 28
5. Recursively Reverse a List
Mke a recursive function that reverses a list. For example, given [1, 2, 3, 4], the function
would return this list [4, 3, 2, 1]. It does not print anything.
starter code recursive_function.py:
def factorial(n):
pass # replace this line with your lines of recursive code
def sum_recursively(n):
pass # replace this line with your lines of recursive code
def sumlist_recursively(l):
pass # replace this line with your lines of recursive code
def multiply_recursively(n, m):
pass # replace this line with your lines of recursive code
def reverse_recursively(l):
pass # replace this line with your lines of recursive code
test_recursive_functions.py:
import recursive_functions
import math
def main():
# Test factorial
print('Testing factorial.')
assert recursive_functions.factorial(0) == 1
assert recursive_functions.factorial(1) == math.factorial(1) == 1
assert recursive_functions.factorial(2) == math.factorial(2) == 2
assert recursive_functions.factorial(5) == math.factorial(5) == 120
assert recursive_functions.factorial(7) == math.factorial(7) == 5040
print('All tests pass for `factorial` (✿◠‿◠)\n')
# Test sum_recursively
print('Testing sum_recursively.')
assert recursive_functions.sum_recursively(0) == 0
assert recursive_functions.sum_recursively(1) == sum(range(1+1)) == 1
assert recursive_functions.sum_recursively(2) == sum(range(2+1)) == 3
assert recursive_functions.sum_recursively(10) == sum(range(10+1)) == 55
print('All tests pass for `sum_recursively` (✿◠‿◠) ')
# Test sumlist_recursively(l)
print('Testing sumlist_recursively.')
assert recursive_functions.sumlist_recursively([1,2,3]) == sum([1,2,3])
assert recursive_functions.sumlist_recursively([42,16,99,102,1]) == sum([42,16,99,102,1])
assert recursive_functions.sumlist_recursively([17,13,9,5,1]) == sum([17,13,9,5,1])
print('All tests pass for r_sumlist (✿◠‿◠)\n')
# Test multiply_recursively
print('Testing multiply_recursively.')
assert recursive_functions.multiply_recursively(5, 1) == 5*1 == 5
assert recursive_functions.multiply_recursively(7, 4) == 7*4 == 28
print('All tests pass for `multiply_recursively` (✿◠‿◠)\n')
# Test reverse_recursively
print('Testing reverse_recursively.')
assert recursive_functions.reverse_recursively([1, 2, 3, 4]) == [4, 3, 2, 1]
life = ['born', 'grow up', 'grow old']
assert recursive_functions.reverse_recursively(life) == ['grow old', 'grow up', 'born']
print('All tests pass for `reverse_recursively` (✿◠‿◠)\n')
main()
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