Lecture "Recursion", exercise 1

[essepuntato]

Define a recursive function def exponentiation(base_number, exponent) for implementing the exponentiation operation. Test (by implementing the related test case) it on the following inputs: 3⁴, 17¹, and 2⁰.

[ereuhl]

def exponentiation(base_number, exponent):
    if exponent == 0:
        return 1
    elif exponent == 1:
        return base_number
    elif exponent == 2:
        return  base_number*base_number
    else:
        return base_number*exponentiation(base_number, exponent-1)

def test_exponentiation(base_number, exponent, expected):
    result = exponentiation(base_number, exponent)
    if result == expected:
        return True
    else:
        return False

print(test_exponentiation(3, 4, 81)) # True
print(test_exponentiation(17, 1, 17)) # True
print(test_exponentiation(2, 0, 1)) # True

[arcangelo7]

def test_exponentiation(base_number, exponent, expected):
    if exponentiation(base_number, exponent) == expected:
        return True
    else:
        return False

def exponentiation(base_number, exponent):
    if exponent == 0:
        return 1
    elif exponent == 1:
        return base_number
    elif exponent == 2:
        return base_number * base_number
    else:
        return base_number * exponentiation(base_number, exponent - 1)

print(test_exponentiation(3, 4, 81)) # True
print(test_exponentiation(17, 1, 17)) # True
print(test_exponentiation(2, 0, 1)) # True

[Vince2992]

[FrancescoFernicola]

Here I am considering the value of 0^0 in algebra, namely 0^0=1. If we were to consider it from the point of view of mathematical analysis, we would have to leave it undefined, but then I wouldn't really know how to implement the recursive element.

def test_exponentiation(base_number, exponent, expected):
    result = exponentiation(base_number, exponent)
    if result == expected:
        return True
    else:
        return False

def exponentiation(base_number, exponent):
    if exponent == 0:
        return 1
    else:
        return base_number * exponentiation(base_number, exponent - 1)

print(test_exponentiation(3, 4, 81)) #True
print(test_exponentiation(17, 1, 17))  #True
print(test_exponentiation(2, 0, 1))  #True
print(test_exponentiation(0, 0, 1))  #True
print(test_exponentiation(1, 0, 1))  #True
print(test_exponentiation(0, 2, 0))  #True

[arimuti]

[aschimmenti]

True True True

[essepuntato]

Hi all,

please find attached my personal solution – also available online:

# Test case for the algorithm
def test_exponentation(base_number, exponent, expected):
    result = exponentation(base_number, exponent)
    if expected == result:
        return True
    else:
        return False

# Code of the algorithm
def exponentation(base_number, exponent):
    if exponent == 0:
        return 1
    else:
        return base_number * exponentation(base_number, exponent - 1)

print(test_exponentation(3, 4, 81))
print(test_exponentation(17, 1, 17))
print(test_exponentation(2, 0, 1))
print(test_exponentation(0, 15, 0))
print(test_exponentation(0, 0, 1))