Home Work 11
The problems in this problem set cover lectures C13 and C14
1.
a. Define a robust algorithm to carry out integer division using repeated subtraction.
Your algorithm accepts two integers and returns the quotient and the remainder.
Hint: What are the preconditions and postconditions of your algorithm?
Precondtions: Two integers x,y
y is non-zero
Algorithm:
Set R to absolute_value(x)
Set Q to zero
While R >= absolute_value (y)
Increment Q
R := R- absolute_value(y)
If either x or y are negative
If both x and y are negative
Set R to –R
else
if x is negative
Set R to –R
Set Q to –Q
Display Q and R
Postconditions: Q contains the quotient
R contains the remainder
x = Q*y + R, abs(R) < abs(Q)
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