Project 2: Algorithms in Pseudocode
Assigned: Wednesday February 6th
Due: Friday February 15th 11:00PM
Project type: individual
This project contains 5 problems. Each problem is weighted equally. Each problem has multiple
questions, and each question is weighted equally.
Instructions
1. You have to write your answers in THIS file. You can write your answers to each problem
question right after the corresponding question, or you can write them altogether
starting at a new page in the end of this document. In this case, remember to use Qxx
ANSWER at the beginning of your answers to question xx.
Turnin instructions
You will turn-in your project using the turn-in command you used in the labs.
Hence, on your UNIX account on the lore machine, create a directory project2 using the
following commands:
$ cd
$ cd CS177
$ mkdir project2
To submit your project2 from the LWSN lab, refer to the instructions you got in Lab2.
For project2, enter the following commands on your lore account:
$ cd
$ cd CS177
$ turnin –v -c cs177=COMMON -p project2 project2
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CS177 Spring 13 –Project2
IMPORTANT – WORKING FROM HOME:
You can also work at home and then transfer remotely your project1 (i.e. THIS file with your
answers) to your UNIX account, and then turn-in it using the instructions above. Please read the
document http://courses.cs.purdue.edu/_media/cs17700:spring13:remoteturnin-s13.pdf.
Please note that this document describes how to turn-in a python file. However you can transfer and
turn-in a MS Word file too.
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CS177 Spring 13 –Project2
1. Reversing a 1-D array. Given an array A of length n, write an algorithm that outputs an
array B that has the elements of A in reverse order. For example, if A = {2, 3, 0, 1, 5}, (n
is 5), then B should be {5, 1, 0, 3, 2}. Hint: the algorithm traverses B and sets each
element to the corresponding element in A.
a. Give a brief step by step description of the algorithm.
b. Give a pseudo-code description of the algorithm.
c. Trace the algorithm for A = {1, 3, 2, 4, 0}, n = 5.
d. What is the algorithm running time? Explain.
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2. Searching for a given string in an array. Given an array A of length n that stores
characters and an array B of length m that also stores characters, write an algorithm
that prints out “yes” if B is found in A and “no” if B is not found in A. For example if A is
“Today was a cold day.” and B is “old”, the algorithm should print out “yes”, as B is a
substring of A. Hint: traverse A from the beginning and for each element (i.e. letter) in A
check if B is in A starting at that element.
a. Give a brief step by step description of the algorithm.
b. Give a pseudo-code description of the algorithm.
c. Trace the algorithm for A = “black cat”, n = 9, and B = “at”, m = 2.
d. What is the algorithm running time? Explain.
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3. Mirror along a vertical axis. Given the following image of size wxh (e.g. 7 rows by x 6
columns), give an algorithm that mirror the image along a vertical axis.
10
10
20
15
15
30
30
20
30
40
25
25
40
40
30
35
40
18
18
50
50
40
20
10
18
18
11
11
50
30
20
15
15
13
13
60
35
10
15
15
12
12
Input image
a.
b.
c.
d.
What is the output of the algorithm on the following image?
Give a brief step by step description of the algorithm.
Give a pseudo-code description of the algorithm.
What is the algorithm running time? Explain.
Hint:
The visual effect of mirroring an image along a vertical axis is depicted below:
Input image
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Output image
CS177 Spring 13 –Project2
4. Summing up values stored at the leafs of a binary tree. CountBTR is a recursive
algorithm for counting the nodes in a binary tree, see lecture notes. Modify the
algorithm to compute the sum of all the numbers stored at the leafs of a binary tree T. T
stores a number at each node. Hint: a node doesn’t count as 1 anymore, but rather as 0
if the node is an internal node, or as V if the node is a leaf, where V is the number stores
at the leaf.
a. Give a brief step by step description of the algorithm.
b. Give a pseudo-code description of the algorithm.
c. What is the algorithm running time, assuming that the binary tree stores n
nodes? Explain.
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5. Fast searching in sorted array. Given an array of integers A sorted in descending order
and an integer B, describe a fast algorithm that finds if B is in A, where n is the length of
A. Hint: check B against the middle element of A, A[n/2]; if B is greater than A[n/2],
continue your search in the left half of A, else continue your search in the right half of A.
a. Give a high-level step-by-step description of algorithm.
b. Give a pseudo-code description of the algorithm.
c. Trace the algorithm for A = {1, 3, 4, 6, 7, 7, 9, 12, 19, 22, 30, 100}, B = 1, then for
B = 100, then for B = 9.
d. Explain why the running time is log2n. Hint: how many times can a number be
divided by 2 before you get 1? If log2n = a, then n = 2a.
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CS177 Spring 13 –Project2