The Islamic University of Gaza ECOM 3011: Discrete Mathematic

Faculty of Engineering Instructor: Pro. Mohammed Al Hanjouri

Department of Computer Engineering T.A.: Eng. Ahmed M Bader El-Din

Lab 2

Eng. Ahmed M Bader El-Din November 24, 2018

Part 1 : Operations OF sets

Part 1: Write code to receive two sets and print the sets, union, intersection, Cartesian product, power of the 1st one, and the difference (1st – 2nd)?

1- Union :

2- Intersection :

3- Difference :

------------------------------------------- Output ---------------------------------------------

A: [0, 1, 2, 3] B: [2, 3, 4, 5] Union of two Set [0, 1, 2, 3] and [2, 3, 4, 5] in Java is [0, 1, 2, 3, 4, 5] Intersection of two Set [0, 1, 2, 3] and [2, 3, 4, 5] in Java is [2, 3] Difference of two Set [0, 1, 2, 3] and [2, 3, 4, 5] in Java is [0, 1] Cartesian Product between two Set [[0, 2], [0, 3], [0, 4], [0, 5], [1, 2], [1, 3], [1, 4], [1, 5], [2], [2, 3], [2, 4], [2, 5], [2, 3], [3], [3, 4], [3, 5]]

4- Set Power

set P(S) of a set S is the set of all subsets of S

E.g. S = {a, b, c} then P(s) = {{}, {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, {a, b, c}}. If S has n

elements in it then P(s) will have 2^n elements.

Algorithm:

----------------------------------------- Input ------------------------------------------

1- Set [], set_size

---------------------------------------- Procedure -------------------------------------

1. Get the size of power set

powet_set_size = POW (2, set_size)

2. Loop for counter from 0 to pow_set_size

(a) Loop for i = 0 to set_size

(i) If ith bit in counter is set

Print ith element from set for this subset

(b) Print separator for subsets i.e., newline

---------------------------------------- Example --------------------------------------

Set = [a, b, c]

power_set_size = POW (2, 3) = 8

Run for binary counter = 000 to 111

Value of Counter Subset

000 -> Empty set

001 -> a

010 -> b

011 -> ab

100 -> c

101 -> ac

110 -> bc

111 -> abc

------------------------------------------ Code ------------------------------------------

------------------------------------------- Output ---------------------------------------------

a b ab c ac bc abc BUILD SUCCESSFUL (total time: 0 seconds)

Q1) Can you now get this output?

Power Set

[[], [a], [b], [a, b], [c], [a, c], [b, c], [a, b, c]]

Part 2: Write code to import names from two Excel sheets and merge both (union)?

------------------------------------------- Output ---------------------------------------------

run: First set : [A, B, C] Second set : [B, D, F] New List : [A, B, C, D, F] BUILD SUCCESSFUL (total time: 1 second)

HW#2:

The Caesar cipher shifts all the letters in a piece of text by a certain number of

places. The key for this cipher is a letter, which represents the number of

place for the shift. Therefore, for example, a key D means “shift 3 places" and

a key M means, “shift 12 places". Note that a key A means “do not shift" and a

key Z can either mean “shift 25 places" or “shift one place backwards". For

example, the word “CAESAR” with a shift P becomes “RPTHPG”.

- Write Algorithm for Caesar Cipher (Input, Procedure) and give example for

your algorithm.

- Write code for Caesar's cipher.