CIS2500 Assignment 4 Question 2- Recursion Solution

2a. Recursive functions
• Implement the following functions using recursion (see the next page for examples) o Count up from 0 to n o Count down from 2n to 0 by 2 o nth, nth_sorted
§ this applies to Sorted Lists from Q1a o remove_nth, remove_nth_sorted
§ this applies to Sorted Lists from Q1a

2b. Greatest Common Divisor (GCD)
• Read up on the Euclidean Algorithm for solving GCD in Wikipedia o First Section: https://en.wikipedia.org/wiki/Euclidean_algorithm o Procedure: https://en.wikipedia.org/wiki/Euclidean_algorithm#Procedure o Example: https://en.wikipedia.org/wiki/Euclidean_algorithm#Worked_example o Using mod: https://en.wikipedia.org/wiki/Euclidean_algorithm#Euclidean_division o Implementations: https://en.wikipedia.org/wiki/Euclidean_algorithm#Implementations
• Examine the final implementation, which is recursive, and implement it in C o it should have the signature long gcd(long, long)
• This implementation (as yours should be) is naturally “tail recursive” o explain why it is tail recursive in the readme
o make sure your make file uses the appropriate gcc flag to run tail recursive code efficiently

To test question 2
Write a program called a4q2.c
• The program must read in a text file that contains a series of commands, one per line, with the name of the text file entered as a command line argument o Base this code on the code you used in q1a to implement command entries from a file o However, the code will need to be extended to allow for new commands that are detailed below
• Some of the questions in 2a use the Sorted_List data type with key_type as double and value_type as int, the same as a4q1a_int.c.
o So when compiling files containing Sorted_List functions in your make file, use –DINT
• All new commands for entry from the input file are listed on the next page

The assignment concludes with Question 3: Fraction ADT to be released early next week

List of Commands from the Input File
All commands from q1a should be made available as well as the following
• count_up n
o Prints the integers from 0 to n on a single line, comma separated, with 5 spaces before o Using the following commands count_up 4 the output should be
count_up from 0 to 4
0, 1, 2, 3, 4
• count_down n
o Same as count_up, but printing the integers down from 2n to 0 on by 2 o Using the following commands count_down 4 the output should be
count_down from 8 to 0 by 2
8, 6, 4, 2, 0
• nth n order o Displays the nth element in the list according to the order specified (inserted or key sort) on its own line as key value
§ Indented 5 spaces with 2 spaces between the key and the value
§ Firsts prints the command – see below for an example o Using the input from the append examples in q1a and the following commands print_all nth 1 INSERTED_ORDER nth 1 SORTED_ORDER the output should be
print_all: Insertion Order
3.27 1427
0.94 984
7.21 346
nth: n = 1, Insertion Order
0.94 984
nth: n = 1, Key Sort Order 3.27 1427
• remove_nth n order o removes the nth element in the list according to the order specified (inserted or key sort) and displays the removed element on its own line as key value
o Again using the input from the append examples in q1a For the commands
remove_nth 2 INSERTED_ORDER print_all
remove_nth 1 SORTED_ORDER print_all
the output should be
remove_nth: n = 2, Insertion Order
7.21 346
print_all: Insertion Order
3.27 1427
0.94 984
remove_nth: n = 1, Key Sort Order
3.27 1427
print_all: Insertion Order 0.94 984