Download docx

CSE 2320 - Spring 2015
Exam 2
Time: 80 mins
Name:
.
Student ID:
.
Total exam points: 100.
Question
1
2
3
4
5
6
7
Total
Points
Out of
15
18
10
10
17
15
15
100
If you have the smallest doubt about what a question asks of you, or whether or not
you can use certain code, ASK US! (Even if you think that it is a really silly
question).
For any programming question you are free to write additional helper functions if
you want to.
Exam questions are on both sides.
1
Question 1 (15 points)
We define a function F(N), for integers N >= 0, as follows:
 F(0) = 2
 If N is an integer greater than 0, F(N) = F(N-1) + F(floor(N/2)) + 3*N.
a) (5 points) Compute the value for F(N) shown below. SHOW YOUR
WORK. Hint: read the whole problem first.
F(4) = …
F(3) = …
F(2) = …
F(1) = …
2
b) (10 points) Is it possible to write a function in C that computes F(N) in O(Ν)
time? If not, why not? If yes, write the function.
3
Question 2 – 18 points
Consider this recursive function foo(N):
int foo(int N)
{
if (N <= 2) return 2;
return foo(N-1) * (foo(N-1) + 3) - foo(N-1) + 4;
}
Use the function definition as is. There is no error.
a) (6 points) Draw the tree that shows the function calls performed in order to
compute foo(5) (the root will be foo(5) and it will have a child for each
recursive call.)
b) (6 points) Use that tree to compute the number of function calls (that is, the
number of nodes in the tree). SHOW YOUR WORK. (Continue on the next
page if needed)
4
c) (6 points) Is it possible to re-implement this function so that it has running
time O(N)? If not, why not? If yes, write this O(N) implementation of foo in
C.
5
Question 3 – 10 points
Questions a) and b) below are independent of each other.
a) (5 points) An undirected graph G of 7 vertices contains 10 edges (note: we do
NOT count edges from A to B and from B to A as two edges, we count them as a
single edge). Does this graph:
 Definitely contain a cycle (i.e., two vertices connected by multiple paths).
 Definitely NOT contain a cycle
 Possibly contain a cycle, possibly not contain one
Choose one of these three answers, and justify your choice.
6
b) (5 points) A graph G of 7 vertices contains 10 edges. Does this graph:
 Definitely contain a pair of vertices NOT connected by any path
 Definitely NOT contain a pair of vertices NOT connected by any path
 Possibly contain a pair of vertices NOT connected by any path, or possibly
NOT contain such a pair.
Choose one of these three answers, and justify your choice.
7
Question 4 – 10 points
Write a function int longest(char* S) that takes a string, S, and returns
the length of the longest name in that string. You can assume that S will be
composed of names concatenated together. A name will start with an uppercase
letter. You can assume that all the characters in S are letters (no spaces).
E.g. for “JaneBobMarcus” it should return 6 (the length of Marcus),
for “TomMatthewGarry” it should return 7 and
for “TommatthewGarry” it should return 10 (length of Tommatthew – since
matthew starts with lowercase m, it will not be considered a new name)
8
Question 5 – 17 points
The tree below has root 9 (the nodes are shown as squares).
9
1
4
3
8
2
a) (3 points) List the nodes in inorder:
b) (3 points) List the nodes in preorder:
c) (3 points) List the nodes in postorder:
9
d) (8 points) In the following sequence of numbers a 0 means a NULL node
and a non-zero number means an actual node in the tree. Build a binary tree
from these numbers s.t. if we list the nodes of your tree in preorder and we
show a 0 for every NULL node, we will produce the same sequence of
numbers. For example 3,0,0 would produce a tree that has root 3 and no
children (both children are NULL). For clarity, in your tree, show the 0’s as
well.
7, 2, 0, 1, 6, 0, 0, 0, 3, 5, 8, 0, 0, 0, 0
10
Question 6 – 15 points A binary tree structure is defined as follows:
struct Tree
{
int item;
struct Tree * left_child;
struct Tree * right_child;
}
If a left child or right child does not exist, the corresponding member variable is set
to NULL.
Write a recursive function int positive(struct Tree * tree) that returns 0 if there is
at least one node that has a negative integer and 1 otherwise (all the nodes have
integers that are greater than or equal to 0). (Your program should not crash.)
11
Question 7 – 15 points A binary tree structure is defined as follows:
struct Tree
{
int item;
struct Tree * left_child;
struct Tree * right_child;
}
If a left child or right child does not exist, the corresponding member variable is set
to NULL.
Write a function int print_level(struct Tree * tree) that prints the nodes in
LEVEL-ORDER, but for each node, IT ALSO PRINTS THE LEVEL. Your
program should not crash.
If it is easier, you can assume you already have implementations for lists, stacks
and queues of integers that you can use in your function.
Partial credit will be given if only printing in level-order (without showing the
level numer)
E.g. for the tree below it will print, in this order: R–0, E–1, S–1, U–2, L–2, T–3
R
S
E
U
L
T
12
13
14