CSIS-385: Quiz 6 Name____________________________________
1. Given the following code:
fun(n) {
if (n == 0)
return;
else {
basic_op;
fun(n-1);
}
}
a. Exactly how many times it the basic
operation executed when n equal 3.
Answer: 3
b. What is the exact bound on the running
time, i.e., f(n)= (?)
Answer: f(n)= (n)
c. Explain how you figured out the running
time.
Answer:
c(n) = 1 + c(n-1);
c(0) = 0
Thus, c(n) =
1 + c(n-1) =
1 + 1 + c(n-2) =
1 + 1 + 1 + c(n-3) =
n + c(0) = n
Each time n is decremented, we do
one basic operation.
2. Given the following code:
fun(a, n) {
if (n == 1)
return a;
else {
m = fun(a,n/2);
return m*m; basic_op
}
}
a. What is the output of the algorithm
when n equals 4.
Answer: a4
b. What is the exact bound on the running
time, i.e., f(n)= (?)
Answer: f(n)= (log n)
c. Explain how you figured out the running
time.
Answer:
c(n) = 1 + c(n/2);
c(1) = 0
Thus, c(n) =
1 + c(n/1) =
1 + 1 + c(n/4) =
1 + 1 + 1 + c(n/8) =
log n + c(1) = log n
Each time n is divided by 2, we do one
basic operation. n can only be divided by
two log n times before n will equal 1.
