CS 2233 Discrete Mathematical Structures – Fall 08
10/15/08
5. Homework
Due 10/27/08 before class
Please refer to the corresponding exercise sections in the textbook (Rosen, 6th edition).
4.5 •(4 points) Use the loop invariant (I) : power = 2kto show that the code
below correctly computes 2nfor any n≥0. First, use induction to show
that (I) is indeed a loop invariant, and then draw conclusions for the
termination of the while loop.
int power_of_two(int n){
int power=1;
int k=0;
while(k<n){
// (I) power=2^k
k++;
power = power*2;
}
return power;
}
4.3 (page 308)
•(6 points) 8 a,b,c. First write down the first six elements of the sequence,
and then try to find a recursive definition. Do not forget the base case.
•(3 points) 12. Use (weak) induction.
•(2 points) 24 a,b.
4.4 (page 321)
•(2 points) 8
•(2 points) 10
c) (3 points) Use weak induction on nto prove that factorial(n) correctly
computes n!, when nis a non-negative integer.
int factorial(int n){
if(n==0)
return 1;
return factorial(n-1)*n;
}