CS 507

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CS 507 Mathematical Methods in Computer Science
Final Exam
Prof. Sung-Hyuk Cha
Spring of 2004
School of Computer Science Information Systems
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Print Your Name
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1. How many bit strings are there of length six
or less?
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2. Find the least number of cables required to
connect eight computers to four printers to
guarantee that four computers can directly access
four different printers.
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• How many permutations are there of the set
• a, b, c, d, e, f, g.

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4. How many bit strings of length 12 contain at
least three 1s?
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5. Find the coefficient of in
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6. What is the probability that a card selected
from a deck is an ace or a heart?
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7. What is the probability that a five-card
poker hand contains exactly one ace?
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8. What is the probability of the event that 1
precedes 3 when we randomly select a permutation
of 1, 2, 3?
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9-10. Suppose that we roll a die until a 6 comes
up. 9 What is the probability that we roll the
die n times? 10 What is the expected number
of times we roll the die?
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11. Which of the following (s) is (are) true?
a. The degree of a binary tree can be 0 or 1.
b. A binary search tree(BST) with nodes has
edges.
c. A tree with n nodes has exactly n -1 edges
d. The following postfix expression is true
4 7 3 - / 2 -2
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12. Is this tree a binary search tree?
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13. Build a binary search tree for be not
ashamed of mistakes and thus make them crimes.
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14. Given a binary search tree, draw the final
BST after these 2 operations insert 6 and
next insert 8.
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15. How many vertices and how many leaves does a
complete m-ary tree of height h have?
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16. Given a graph, select all valid topological
sorted lists.
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• (1 3 5 4 6 2)
• (1 4 3 5 6 2)
• (5 1 4 3 6 2)
• (5 3 1 4 6 2)

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4
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17. Given a graph how many nodes have their
degree 2?
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2
6
3
4
5
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18. Consider a directed unweighted graph
represented in an adjacent list. Show the graph
with the shortest path where 0 node is the source.
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5
4
1
1
2
2
3
3
5
6
4
0
3
5
3
6
2
1
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19. Represent adjacency matrix using graph.
a
b
c
d
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20. Consider a directed weighted graph, show the
graph with the shortest path where node is
the source.
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1
1
10
4
25
2
8
3
2
11
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