Integer Division¶
What is being divided is called the dividend, which is divided by the divisor, and the result is called the quotient. In the example, 20 is the dividend, 5 is the divisor, and 4 is the quotient.
Write an integer division algorithm that will calculate print out quoutient q and remainder r so:
Prove the loop invariant of the algorithm.
In [1]:
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# m: dividend
# n: divisor
# q: quotient
# r: remainder
def integer_division(m, n):
q = 0
r = m
while r >= n:
q = q + 1
r = r - n
print("number =", m)
print("divisor =", n)
print("quotient =", q)
print("remainder =", r)
print("----------------------------------------")
# m: dividend
# n: divisor
# q: quotient
# r: remainder
def integer_division(m, n):
q = 0
r = m
while r >= n:
q = q + 1
r = r - n
print("number =", m)
print("divisor =", n)
print("quotient =", q)
print("remainder =", r)
print("----------------------------------------")
Testing out algorithm with examples¶
In [2]:
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integer_division(5,2)
integer_division(7,5)
integer_division(9,4)
integer_division(5,2)
integer_division(7,5)
integer_division(9,4)
number = 5 divisor = 2 quotient = 2 remainder = 1 ---------------------------------------- number = 7 divisor = 5 quotient = 1 remainder = 2 ---------------------------------------- number = 9 divisor = 4 quotient = 2 remainder = 1 ----------------------------------------