CSC1001: Introduction to Computer Science

Programming Methodology

Assignment 2

Assignment description:

This assignment will be worth 8% of the final grade.

You should write your code for each question in a .py file (please name it using the question

name, e.g. q1.py). Please pack all your .py files into a single .zip file, name it using your

student ID (e.g. if your student ID is 123456, then the file should be named as 123456.zip),

and then submit the .zip file via Blackboard.

Please also write a text file, which provide the details about your code. (Note that the

report should be submitted as PDF) The report should be included in the .zip file as well.

Please note that, the teaching assistant may ask you to explain the meaning of your

program, to ensure that the codes are indeed written by yourself. Plagiarism will not be

tolerated. We may check your code using Blackboard.

This assignment is due on 5:00PM, 3 April (Saturday). For each day of late submission, you

will lose 10% of your mark in this assignment. If you submit more than three days later

than the deadline, you will receive zero in this assignment.

Question 1 (10% of this assignment):

(Math: approximate the square root) There are several techniques for implementing the

sqrt function in the math module. One such technique is known as the Babylonian function.

It approximates the square root of a number, n, by repeatedly performing a calculation

using the following formula:

nextGuess = (lastGuess + (n / lastGuess)) / 2

When nextGuess and lastGuess are almost identical, nextGuess is the approximated

square root. The initial guess can be any positive value (e.g., 1). This value will be the

starting value for lastGuess. If the difference between nextGuess and lastGuessis less than

a very small number, such as 0.0001, you can claim that nextGuess is the approximated

square root of n. If not, nextGuess becomes lastGuess and the approximation process

continues. Implement the following function that returns the square root of n.

def sqrt(n):

Write a program that prompts the user to enter a positive number and output the

approximation of its square root.

Question 2 (15% of this assignment):

(Emirp) An emirp (prime spelled backward) is a nonpalindromic prime number whose

reversal is also a prime. For example, both 17 and 71 are prime numbers, so 17 and 71 are

emirps. Write a program that displays the first 100 emirps. Display 10 numbers per line

and align the numbers properly, as follows:

Question 3 (15% of this assignment):

(Financial: credit card number validation) Credit card numbers follow certain patterns: It

must have between 13 and 16 digits, and the number must start with:

■ 4 for Visa cards

■ 5 for MasterCard credit cards

■ 37 for American Express cards

■ 6 for Discover cards

In 1954, Hans Luhn of IBM proposed an algorithm for validating credit card numbers. The

algorithm is useful to determine whether a card number is entered correctly or whether a

credit card is scanned correctly by a scanner. Credit card numbers are generated following

this validity check, commonly known as the Luhn check or the Mod 10 check, which can be

described as follows (for illustration, consider the card number 4388576018402626):

1. Double every second digit from right to left. If doubling of a digit results in a twodigit

number, add up the two digits to get a single-digit number.

2. Now add all single-digit numbers from Step 1.

4 + 4 + 8 + 2 + 3 + 1 + 7 + 8 = 37

3. Add all digits in the odd places from right to left in the card number.

6 + 6 + 0 + 8 + 0 + 7 + 8 + 3 = 38

4. Sum the results from Steps 2 and 3.

37 + 38 = 75

5. If the result from Step 4 is divisible by 10, the card number is valid; otherwise, it is

invalid. For example, the number 4388576018402626 is invalid, but the number

4388576018410707 is valid.

Write a program that prompts the user to enter a credit card number as an integer. Display

whether the number is valid or invalid. Design your program to use the following functions:

Question 4 (15% of this assignment):

(Anagrams) Write a function that checks whether two words are anagrams. Two words are

anagrams if they contain the same letters. For example, silent and listen are anagrams. The

header of the function is:

def isAnagram(s1, s2):

(Hint: Obtain two lists for the two strings. Sort the lists and check if two lists are identical.)

Write a test program that prompts the user to enter two strings and, if they are anagrams,

displays ‘is an anagram’; otherwise, it displays‘is not an anagram’. You don’t need to check

the existence of the words.

Question 5 (20% of this assignment):

(Game: locker puzzle) A school has 100 lockers and 100 students. All lockers are closed on

the first day of school. As the students enter, the first student, denoted S1, opens every

locker. Then the second student, S2, begins with the second locker, denoted L2, and closes

every other locker. (which means 1,3,5,7… are opened and 2,4,6,8… are closed.) Student

S3 begins with the third locker and changes every third locker (closes it if it was open, and

opens it if it was closed). Student S4 begins with locker L4 and changes every fourth locker.

Student S5 starts with L5 and changes every fifth locker, and so on, until student S100

changes L100.

After all the students have passed through the building and changed the lockers, which

lockers are open? Write a program to find your answer.

(Hint: Use a list of 100 Boolean elements, each of which indicates whether a locker is open

(True) or closed (False). Initially, all lockers are closed.)

Question 6 (25% of this assignment):

(Game: Eight Queens) The classic Eight Queens puzzle is to place eight queens on a

chessboard (8*8) such that no two queens can attack each other (i.e., no two queens are

in the same row, same column, or same diagonal). There are many possible solutions.

Write a program that displays one such solution. A sample output is shown below:

Note: you cannot just pre-define a solution and display it.

Please use algorithm to display a possible solution.

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