The document is a post midterm exam for a data structures and algorithm analysis course, containing various types of questions worth a total of 100 points plus 10 bonus points. It includes questions on memory usage for data structures, sorting methods, definitions of big-o and big-omega, principles of stack and queue operations, breadth-first and depth-first search traversals, and constructing binary search trees. Additionally, it provides pseudocode for BFS and DFS algorithms and contains bonus questions related to mergesort and queue implementation.

1. Data Structures and Algorithm Analysis
Spring 2020 Post Midterm Exam – 100 points + 10 bonus
NAME:
1. How much memory will the following structures take up?
Hint: int takes 4 bytes, float takes 4 bytes, char takes 1 byte. – 9
points
a. struct Structure1 {int a,b,c,d,e[10]; float f;};
b. struct Structure2 {int a[12]; float b[5];};
c. struct Structure3 {char a[10][12][4], b[5][5], c[10];};
2. Show the steps when sorting (smallest to largest) the
following arrays of numbers using selection sort i.e. every time
a swap occurs, show what the current state of the array looks
like, including the final sorted array. – 12 points
a. [10, 2, 5, 8, 9, 1, 4, 7]

2. b. [7, 1, 3, 2, 5, 4, 8, 12, 9]
c. [8, 7, 6, 5, 4, 3, 2, 1]
d. [5, 3, 8, 1, 9, 4, 2, 6]

3. 3. Big-O: What is meant by f(n) = O(g(n))? Give the definition
and then explain what it means in your own terms. – 5 points
4. Big-Omega: What is meant by f(n) = Ω(g(n))? Give the
definition and then explain what it means in your own terms. –
5 points
5. Show that , make sure you use the definition and justify the
inequalities and constants used. - 4 points
6. Show that , make sure you use the definition and justify the
inequalities and constants used. - 4 points
7. Show that , make sure you use the definition and justify the

4. inequalities and constants used. - 4 points
8. Show that , make sure you use the definition and justify the
inequalities and constants used. - 4 points
9. Show that , make sure you use the definition and justify the
inequalities and constants used. - 4 points
10. What principle governs how you add/remove elements in a
stack? Spell it out and briefly explain. - 4 points
11. Briefly describe an application of a stack. - 4 points

5. 12. What principle governs how you add/remove elements in a
queue? Spell it out and briefly explain. - 4 points
13. Briefly describe an application of a queue. - 4 points
Consider the following graph (pseudocode for BFS and DFS
given on page 9):
14. Write the order in which the nodes would be visited in when
doing a breadth first search (BFS) traversal starting at node 4.
Also, write the distances from 4 to every other node. - 6 points
15. Write the order in which the nodes would be visited in when
doing a breadth first search (BFS) traversal starting at node 5.
Also, write the distances from 5 to every other node. - 6 points

6. Same graph (for your convenience):
16. Write the order in which the nodes would be visited in when
doing a depth first search (DFS) traversal starting at node 4
(order discovered or order off the stack). - 6 points
17. Write the order in which the nodes would be visited in when
doing a depth first search (DFS) traversal starting at node 5
(order discovered or order off the stack). - 6 points
18. Give the definition of a graph. - 5 points
19. Give the definition of a tree (from graph theory). - 4 points
BFS Pseudocode (for graph with n vertices):
Input: grapharray[n][n], source

7. queue<int> Q
int distance[n] (array to keep track of nodes distances (from
source), all values set to -1 except source which is set to 0 i.e. -
1 = not visited)
Q.push(source)
while(Q is not empty)
v = Q.front
Q.pop()
for each neighbor w of v
if distance[w] = -1
print w
distance[w] = distance[v]+1
Q.push(w)
end if
end for
end while
DFS Pseudocode (for graph with n vertices):
Input: grapharray[n][n], source
stack<int> S
int visited[n] (array to keep track of nodes visited, all values set
to 0 except source which is set to 1 i.e. 0 = not visited, 1 =
visited)
S.push(source)
while(S is not empty)

8. v = S.top
S.pop()
for each neighbor w of v
if visited[w] = 0
print w
visited[w] = 1
S.push(w)
end if
end for
end while
Bonus (4 points): Show all of the steps (splitting and merging)
when using mergesort to sort (smallest to largest) the following
array (they are the numbers 1 through 16):
[16, 1, 15, 2, 14, 3, 13, 4, 12, 5, 11, 6, 10, 7, 9, 8]

9. Bonus (2 points): describe how you could implement a queue
using 2 stacks.
Bonus (4 points) Draw the binary search tree that would be
constructed by inserting the following values in the exact order
given (starting with an empty tree i.e. first value will be the
first node in the tree): -
a. Binary Search Tree A: 8, 9, 2, 7, 1, 10, 3, 5, 6, 4

10. b. Binary Search Tree B: 10, 7, 9, 12, 4, 2, 5, 3, 1, 14, 11, 19,
13, 18, 20
11