The exam is open book: you may consult your notes, books, even computer
programs that you have written before. But all the work should be yours.
Show all your work: you may get partial credit. Add extra sheets if
necessary.
-
(10 points) Given the following code:
struct SpecialNode{
int info;
SpecialNode* parent;
SpecialNode* child;
};
main()
{
SpecialNode a1, a2, a3, a4;
SpecialNode* b;
b = &a1;
a1.info = 1; a2.info = 2; a3.info = 3; a4.info = 4;
a1.parent = new SpecialNode;
a2.parent = &a1;
a3.parent = &a2;
a4.parent = &a1;
b->parent->parent = NULL;
b->parent->info = 0;
b->child = &a2;
}
-
(2 points) Draw a "box and arrow" structure corresponding to the set of
SpecialNode's created by this program and fill in all the information and
pointers as done by the program.
-
(2 points) Write a C++ statement to set to 10 the value of the info field
of the parent of a1.
-
(2 points) Write a C++ statement to change the parent of a3 to be a4.
-
(4 points) Write C++ statements to set the children of all the
nodes accessible through the pointer b to be the newly created node.
-
(34 points) Given the following structure definition:
struct Node{
int a;
Node* b;
Node* c;
};
and the following definitions of variables:
BNode n1, *n2, n3[5];
BNode* n4[10];
Which of the following is a valid C++ expression? (2 points each) Cross
the invalid expressions.
-
n1 -> b
-
n1.b
-
n2.c
-
n2->c
-
n1.b.c
-
n1.b -> c
-
n2.b -> c
-
n2->b ->b
-
n2-> b . c
-
n3[2].a
-
n3[2].a ->a
-
n3[2].a.c
-
n3[2]->c->b
-
n4[5].b->c
-
n4[5]->b->c->c
-
n4[5]->b->c->c->a
-
n4[2]->c->b->b.c
-
(12 points) Write a short recursive C++ function (NOT a whole
program!!!) to compute the depth of a node of a binary tree.
The depth of a node is the length of the longest path from the node
to a leaf which is a descendent of the node.
The program should use the representation of a tree as a pointer
to a tree node, where a tree node is a C++ structure defined as:
struct TNode{
int data;
TNode* left;
TNode* right;
}
Name your function depth. It should take as argument a
tree and return an integer.
- (10 points) Trace the stack behavior for the following recursive function
call. What is the value printed in the main function?
main()
{
cout << f(2,2);
}
int f(int a, int b)
{
if (a==0 || b== 0) return 1;
return f(a-1,b)+f(a,b-1);
}
- (5 points)
Describe the structure (header file) of a templated C++ class for a binary
search tree with a generic type of data in the tree
node. In the testdriver, you will test it for two data types
(e.g. int and char).
Assuming that the file is called Tree.h, the
corresponding implementation file is Tree.cpp and the testdriver
is testTree.cpp, describe which file is included in which one,
and give the structure of the Makefile for compiling this code.
- (5 points)
Write a short C++ function to delete a node in a binary tree. The
node is given as a parameter to the function by a pointer called
current. Your function should deallocate all nodes that
would otherwise become inaccessible. Describe the complete code,
do not simply invoke some function you know of from one of the
homework assignments.
-
(8 points) Given the graph:
-
(2 points)Write the adjacency list representation for the graph, with each
adjacency list sorted increasingly by the vertex number.
-
(3 points) Starting from vertex 1, list the vertices of the graph in the
postfix order in which they are visited by a depth-first search algorithm.
-
(3 points) Starting at vertex 1, list the vertices in the order in which
they are visited by a breadth-first search algorithm.
-
(6 points) Given the following binary tree:
Write down the vertices of the tree in preorder (2 points), inorder
(2 points) and postorder (2 points).
-
(10 points) Sort the list of numbers {5, 7, 2, 6, 8, 4, 1, 3, 9} using
binary search trees.
-
Step 1:construct the binary search tree.
-
Step 2: traverse the tree in the appropriate order (and specify which one).
Enjoy your summer :-)
Ileana