CSIS-385: Quiz 2 Name____________________________________
1. Which of the 7 algorithm properties is not
satisfied in the following algorithm?
Precision (or Input/Output not specified
correctly)
Input: two integers a and b.
Output: maximum of a and b.
max (a,b,c,d) {
compare a, b, c, and d;
return the one that’s the
biggest.
}
2. Which of the 7 algorithm properties is not
satisfied in the following algorithm?
Finiteness (or Correctness)
Input: an array of n integers
Output: True or False
True if there exist two adjacent
integers that are the same,
otherwise return false
adj_dup (A[], n) {
x = 0;
while (x < n-1) {
if (A[x] == A[x+1])
return true;
}
return false;
}
3. Express the exact number of operations
as a summation, then solve the summation.
for (x = 0 to n-1) {
3 operations; only count these operations
}
Answer:
)(33
1
nOn
n
x
4. Prove the following using Mathematical
Induction. You must use Mathematical
Induction! No other proof method will be
accepted. Show all three steps.
Step 1:
1122)1(2
2
1
1
x
Step 2: Assume this is true
n
x
nnx
1
2
2
Step 3:
1)1(2
2
1
1
nnx
n
x
1122)1(2
2
1
nnnxn
n
x
23)1(2
22
nnnnn
2323
22
nnnn
5. Express the exact number of operations as
a summation then solve the summation.
Hint: remember you can change the loop
bounds to an equivalent loop.
for (z = 0 to n-1) {
for (y = 1 to z) {
for (x = y to n) {
1 operation;
}
}
}
This loop is equivalent to
for (z = 1 to n)
for (y = 1 to z)
for (x = 1 to y)
1 operation;
n
z
n
z
z
y
n
z
z
y
y
x
zz
y
11 11 1 1
2
)1(
1
2
)1(
6
)12)(1(
2
1
2
1
11
2
nnnnn
zz
n
z
n
z
6
23
26
32
2
123223 nnnnnnnn