# Homework Two: Recursion, Searching, and Sorting Algorithms Solution

I. Arrays (20pts)

1. Exercise One (10pts) Design and implement and algorithm that compare two strings and check if they are reversed. For instance, if the two strings are google and elgoog, then the method returns 1. If the two strings are “data”, “ata” then the method returns 0. The algorithm should ignore white spaces, lower/upper cases.

Specify the running time of your algorithm in terms of Big-O notation. Attach Exercise One.doc that explains the running time.

2. Exercise Two (10pts) Design and implement an algorithm that takes a set of strings. Then, for every three consecutive strings (assuming the list of strings is larger than 3 and the number of strings in your sentence is a multiple of 3) leave only the shortest of the three. In case two string among the three are of the same length then you leave the first one.

For instance, consider the following set of strings: “Other entries include a historic district in Charlottesville Virginia cut-flower greenhouse complex” à “Other a in complex”

Specify the running time of your algorithm in terms of Big-O notation. Attach Exercise Two.doc that explains the running time.

II. Recursion (50pts)

1. (10pts) Design and implement a binary recursive algorithm that finds the maximum number in array of size n.

2. (20pts) Design and implement a recursive algorithm that returns the number of zeroes in the binary representation of N.

In this exercise the input to the algorithm must be an integer N. Your algorithm should not calculate the binary representation of N but recursively finds the number of zeroes in the binary representation of N. You are NOT allowed to use arrays.

3. (20pts)Implement a recursive algorithm that checks if word is A palindrome.

A palindrom is a word or number that is identical when read both forwards and backwards. Please ignore all punctuation. Some simple palindromes include kayak radar dad

III. Sorting (60pts)

3.1. Provide your own implementation of the six algorithms mentioned bellow. You must provide your own code. Code copied form the internet or modified will be result into a Zero grade for the entire homework.

Provide a table (attached in a word document) where you compare the running time of the sorting algorithms mentioned bellow in terms of best case and worst case running time.

1. Bubble Sort Non-Recursive (5pts)

2. Bubble Sort Recursive (5pts)

3. Selection Sort (Non-recursive) (5pts)

4. Insertion Sort (Non-recursive) (5pts)

5. Merge Sort (Recursive) (5pts)

6. Quick Sort (Recursive) (5pts)

4

77

98

30

20

50

77

22

49

2

3.2 Consider the array mentioned above, show a step by step illustration (either by hand or written in a word document) of applying the sorting algorithms mentioned to the array.

Include all your answers for this HW into a zip file.

1. Exercise One (10pts) Design and implement and algorithm that compare two strings and check if they are reversed. For instance, if the two strings are google and elgoog, then the method returns 1. If the two strings are “data”, “ata” then the method returns 0. The algorithm should ignore white spaces, lower/upper cases.

Specify the running time of your algorithm in terms of Big-O notation. Attach Exercise One.doc that explains the running time.

2. Exercise Two (10pts) Design and implement an algorithm that takes a set of strings. Then, for every three consecutive strings (assuming the list of strings is larger than 3 and the number of strings in your sentence is a multiple of 3) leave only the shortest of the three. In case two string among the three are of the same length then you leave the first one.

For instance, consider the following set of strings: “Other entries include a historic district in Charlottesville Virginia cut-flower greenhouse complex” à “Other a in complex”

Specify the running time of your algorithm in terms of Big-O notation. Attach Exercise Two.doc that explains the running time.

II. Recursion (50pts)

1. (10pts) Design and implement a binary recursive algorithm that finds the maximum number in array of size n.

2. (20pts) Design and implement a recursive algorithm that returns the number of zeroes in the binary representation of N.

In this exercise the input to the algorithm must be an integer N. Your algorithm should not calculate the binary representation of N but recursively finds the number of zeroes in the binary representation of N. You are NOT allowed to use arrays.

3. (20pts)Implement a recursive algorithm that checks if word is A palindrome.

A palindrom is a word or number that is identical when read both forwards and backwards. Please ignore all punctuation. Some simple palindromes include kayak radar dad

III. Sorting (60pts)

3.1. Provide your own implementation of the six algorithms mentioned bellow. You must provide your own code. Code copied form the internet or modified will be result into a Zero grade for the entire homework.

Provide a table (attached in a word document) where you compare the running time of the sorting algorithms mentioned bellow in terms of best case and worst case running time.

1. Bubble Sort Non-Recursive (5pts)

2. Bubble Sort Recursive (5pts)

3. Selection Sort (Non-recursive) (5pts)

4. Insertion Sort (Non-recursive) (5pts)

5. Merge Sort (Recursive) (5pts)

6. Quick Sort (Recursive) (5pts)

4

77

98

30

20

50

77

22

49

2

3.2 Consider the array mentioned above, show a step by step illustration (either by hand or written in a word document) of applying the sorting algorithms mentioned to the array.

Include all your answers for this HW into a zip file.

You'll get 1 file (4.4MB)