CSC236H5 Lecture Notes - Lecture 1: Empty String, Subset, Empty Set

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22 Dec 2019

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Consider strings made up only of the characters 0 and 1; these are binary strings. A binary palindrome is a palindrome that is also a binary string. Let f (n) be the number of binary palindromes of length 2n, for n 0. The only length-0 string is the empty string, and that is a palindrome. So, we have 1 = 20 palindrome of length 0, as required. We want to prove this for n + 1, which is length 2n + 2. A string of length 2n + 2 has a 0 at the beginning and end, or a 1 at the beginning and end, with 2n symbols in between. The predicate here is p (n) : f (n) = 2n. We must prove that n 0, p (n). When n = 0, the length of our binary strings is 2n = 2 0 = 0, so we must show that there are 20 = 1 palindromes of length 0.

Related Questions

1.Write a function encipher(s, n) that takes as inputs an arbitrary string s and a non-negative integer n between 0 and 25, and that returns a new string in which the letters in s have been "rotated" by n characters forward in the alphabet, wrapping around as needed. For example:

>>> encipher('hello', 1) result: 'ifmmp'

>>> encipher('hello', 2) result: 'jgnnq'

>>> encipher('hello', 4) result: 'lipps'

Upper-case letters should be "rotated" to upper-case letters, even if you need to wrap around. For example:

>>> encipher('XYZ', 3)

result: 'ABC'

Lower-case letters should be "rotated" to lower-case letters:

>>> encipher('xyz', 3)

result: 'abc'

Non-alphabetic characters should be left unchanged:

>>> encipher('#caesar!', 2)

result: '#ecguct!'

Hints/reminders:

You can use the built-in functions ord and chr convert from single-character strings to integers and back:

>>> ord('a')

result: 97

>>> chr(97)

result: 'a'

You can use the following test to determine if a character is between 'a' and 'z' in the alphabet:

if 'a' <= c <= 'z':

A similar test will work for upper-case letters.

We recommend writing a helper function rot(c, n) that rotates a single character c forward by n spots in the alphabet. We have given you a template for this helper function in ps3pr3.py that checks to ensure that c is a single-character string. We wrote rot13(c) in lecture; rot(c, n) will be very close to rot13(c)! You can test your rot(c, n) as follows:

>>> rot('a', 1)

result: 'b'

>>> rot('y', 2)

result: 'a'

>>> rot('A', 3)

result: 'D'

>>> rot('Y', 3)

result: 'B'

>>> rot('!', 4)

result: '!'

Once you have rot(c, n), you can write a recursive encipher function.

Once you think you have everything working, here are three more examples to try:

>>> encipher('xyza', 1)

result: 'yzab'

>>> encipher('Z A', 2)

result: 'B C'

>>> encipher('Caesar cipher? I prefer Caesar salad.', 25)

result: 'Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.'

2.Write a function decipher(s) that takes as input an arbitrary string s that has already been enciphered by having its characters "rotated" by some amount (possibly 0). decipher should return, to the best of its ability, the original English string, which will be some rotation (possibly 0) of the input string s. For example:

>>> decipher('Bzdrzq bhogdq? H oqdedq Bzdrzq rzkzc.')

result: 'Caesar cipher? I prefer Caesar salad.'

Here are two more examples:

>>> decipher('Hu lkbjhapvu pz doha ylthpuz hmaly dl mvynla lclyfaopun dl ohcl slhyulk.')

result: 'An education is what remains after we forget everything we have learned.'

>>> decipher('python')

result: 'eniwdc'

------------------------------------

def rot(c, n):
""" your docstring goes here """
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

def letter_prob(c):
""" if c is the space character (' ') or an alphabetic character,
returns c's monogram probability (for English);
returns 1.0 for any other character.
adapted from:

"""
# check to ensure that c is a single character
assert(type(c) == str and len(c) == 1)

if c == ' ': return 0.1904
if c == 'e' or c == 'E': return 0.1017
if c == 't' or c == 'T': return 0.0737
if c == 'a' or c == 'A': return 0.0661
if c == 'o' or c == 'O': return 0.0610
if c == 'i' or c == 'I': return 0.0562
if c == 'n' or c == 'N': return 0.0557
if c == 'h' or c == 'H': return 0.0542
if c == 's' or c == 'S': return 0.0508
if c == 'r' or c == 'R': return 0.0458
if c == 'd' or c == 'D': return 0.0369
if c == 'l' or c == 'L': return 0.0325
if c == 'u' or c == 'U': return 0.0228
if c == 'm' or c == 'M': return 0.0205
if c == 'c' or c == 'C': return 0.0192
if c == 'w' or c == 'W': return 0.0190
if c == 'f' or c == 'F': return 0.0175
if c == 'y' or c == 'Y': return 0.0165
if c == 'g' or c == 'G': return 0.0161
if c == 'p' or c == 'P': return 0.0131
if c == 'b' or c == 'B': return 0.0115
if c == 'v' or c == 'V': return 0.0088
if c == 'k' or c == 'K': return 0.0066
if c == 'x' or c == 'X': return 0.0014
if c == 'j' or c == 'J': return 0.0008
if c == 'q' or c == 'Q': return 0.0008
if c == 'z' or c == 'Z': return 0.0005
return 1.0

olivemink636

Given the following main program

#main
a = [5,2,9,6,3] doubleList(a) print a

Implement the function named doubleList that takes one list argument and modifies the list so that each element in the list is doubled. The statement print(a) in the main program will then have to print [10,4,18,12,6]
Given the following main program

#main
a = [5,2,9,6,3]
b = reversedList(a) print b
print a

Implement the function named reversedList that takes one list argument and returns a list that contains the elements in the list argument in reverse order. The statement print(b) in the main program will then have to print [3,6,9,2,5]. The statement print(a) must print the original list [5,2,9,6,3] unaffected. This means your function should not modify the list argument.
Given the following main program

#main
a = [5,2,9,6,3] reverseList(a) print a

Implement the function named reverseList that takes one list argument and reverses the list so that the modified list contains the same elements in reverse order. The statement print(a) in the main program will then have to print [3,6,9,2,5]
What is the return value of the functions doubleList, reversedList and reverseList in questions 1, 2, and 3 above?

Given the following main program

#main
a = [5,2,9,6,3]
b = evenElements(a) print b

Implement the function named evenElements that takes one list argument and returns a list that contains the elements in the list argument that are even integers. The statement print(b) in the main program will then have to print [2,6]. What is the return value of the function? Your function should not modify the list argument.
Given the following main program

#main
a = [5, 2, 9, 6, 3, 7, 19, 4, 8, 17, 21, 20, 15] removeOddElements(a)
print a

Implement the function named removeOddElements that takes one list argument and modifies the list so that all odd integers in the list are removed. The statement print(a) in the main program will then have to print [2,6,4,8,20]. What is the return value of the function?
Part A
#Main program A=[5,8,2,0,-5,3] n=-5
answer = isFound(A, n) if answer == True:

print "The integer is found in the list" else:

print "The integer is not found in the list."

Consider the main program shown above. Write a Python function named isFound that takes a list of integers and an integer as arguments and returns True if the integer is found in the list; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, you must write a loop to go through the elements of the list.

Part B

Give the following main program

#main
A = [5,2,9,6,3]
B = [2,4,3,9,7,1,6,5]
flag = isList1InList2(A, B) if flag:

print "The list", A, "is contained in the list", B else:

print "The list", A, "is not contained in the list", B

Implement the function named isList1InList2 that takes two list arguments and returns True if and only if each element of the first list argument are found in the second list argument; otherwise it returns False.

Remark: You are NOT allowed to use the in operator or any other built in function when you write this function. Instead, if you wish, you can use the function you wrote in Part A.

For the lists shown in the main program, your function must return True because each element of list A is found in list B.

A given List is known as Palindrome List if the reverse of the List contains the same elements in the same order of the original List. For example the List of integers [2, 5, 0, 3, 3, 0, 5, 2] is a Palindrome because the reverse of the List which is [2, 5, 0, 3, 3, 0, 5, 2] contains the same elements in the same order as the given List. However the List [1, 2, '2', 1] is not Palindrome because its reverse which is [1, '2', 2, 1] does not contain the same elements in the same order as the given List.

Write a Python function named isPalindrome that takes a List as argument and returns True if the argument is a Palindrome List; otherwise it returns False. You don't need to write the main program; just write the function. If you would like to test your function, then it is ok to write the main program too but you will not get any mark for the main program.
Given your function in question #7 above, what is the output of the following code: a=[]

b = [5,2,9,6,3]

print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code:

a=[]
b=[]
print isList1InList2(a,b)
Given your function in question #7 above, what is the output of the following code: a = [5,2,9,6,3]

b=[]

print isList1InList2(a,b)

Given the following main program

#main
a=[]
n = readListElements(a)
print "The user entered", n, "elements to the list" print a

Implement the function named readListElements that takes one list argument and modifies the list by repeatedly asking the user to enter integer values and then appending them to the list. The process stops when the user enters -1000. The stopping value -1000 should not be appended to the list. Moreover your function must count the appended elements and return it. Example if the user enters the integers 31, -4, 9, 1,-1000 then your function must modify the list a to a = [31, -4, 9, 1] and return the number elements added which is 4.
Write a function named createRandomList that takes an integer argument n and returns a list with n elements. The elements must be random numbers in the range [0,100]

Given the following main program:

#main

   n = int(input("How many elements do you want in your list? "))
   a = createList(n)
   s1 = sumOfElementsAtEvenIndexes(a)
   print s1

   s2 = sumOfElementsAtOddIndexes(a)
   print s2
   s3 = sumOfAllElements1(a)
   print s3

   s4 = sumOfEvenElements(a)
   print s4
   s5 = sumOfOddElements(a)
   print s5

   s6 = sumOfAllElements2(a)
   print s6
   if (s3 != s6):

         print "Something is wrong in your program."
   else:

         print "Looks like you have done a good job."

Implement the functions as follows:

createList: returns a list object with n elements. The elements are generated randomly so that each element is in the range [15,45]
sumOfElementsAtEvenIndexes: returns the sum of the elements at even indexes. Use a for loop or a while loop.
sumOfElementsAtOddIndexes: returns the sum of the elements at odd indexes. Use a for loop or a while loop.
sumOfAllElements_A: returns the sum of all the elements in the list using the functionssumOfElementsAtEvenIndexes and sumOfElementsAtOddIndexes. Here you are NOT allowed to use any loop; instead make function calls as described.
sumOfEvenElements: returns the sum of the even integer elements in the list. Use a for loop or a while loop.
sumOfOddElements: returns the sum of the odd integer elements in the list. Use a for loop or a while loop.
sumOfAllElementsB: returns the sum of all the elements in the list using the functions sumOfEvenElements and sumOfOddElements. Here you are NOT allowed to use any loop; instead make function calls as described.

17. Most data compression algorithms like winzip, gzip, lzip and etc are based on the frequency distribution of characters in a given string. Write a function named getFreqDistribution that takes a string argument and returns a LIST that has length 26 such that the first element of the list is the number of appearance of 'a' or 'A' in the string, the second element is number of appearance of 'b' or 'B', and so on so forth.

I'm studying python 2 and have a lot of troubles with solving these homework questions.

grayelk171

Section 3 - Programming Questions 7. Role playing video games (RPGs) form a loosely defined genre of video games in which the player controls a small number of game characters. These characters form a group of adventurers whose purpose is to fulfill one or many quests. A common feature of RPGs is that the group of adventurers can collect various items and keep them for future me, sach items are added to the player's inventory. In this question, you will write classes which could be used to manage a player's inventory in an RPG. Part 1 Write a class called Item. An Item object represents an entire category of items carried by a group of adventurers, and each Item object has the following attributes: • The description of the items in this category (a String) The quantity of tems in this category that the group of adventurers is currently carrying can int). For example, suppose the group of adventurers is carrying 50 Heal Potions and 10 Life Potions. The SO Heal Pations would he represented by a single Item object, the value of the description attribute of this item object would be the string "Heal Potion, and the value of the quantity attribute of this Item object woukl be 50. The 10 Life Potions would also be represented by a single Item object, which is different from the Ttem object representing the Heal Potions. The value of the description attribute of this second Ttem object would he Life Potion", and the value of the quantity attribute of this second liem object would be 10. The Item class MUST provide the following INSTANCE methods, note that in the method descrip tions below, the phrase "this Item" means the item on which the method in question is called • A constructor, which takes as its only parameter a string representing the description attribute of the newly created Item. This constructor sets the quantity attribute of the newly created Item to 1. • A method called get Description(), which takes no parameters and returns a string representing the value of the description attribute of this Item • A method called getQuantity O. which takes no parameters and returns an int represent ing the value of the quantity attribute of this Item • A method called set Quantity), which takes a value of type int as its only parameter and returns nothing. This method changes the value of the quantity attribute of this Item so that its new value is equal to the int value this method accepts as parameter, this happens regardless of what the value of the int parameter is, even if it represents a sensical value Note that you MUST respect proper encapsulation practices that is, the attributes and methods of your class MUST he declared using the proper visibility modifiers. Part 2 Write a class called Inventory, which represents the inventory of a group of adventures. An Inventory object has only one attributes a collection of items, which specifies all the types of items that a group of adventurers is currently carrying along with the mumber of items of each type that the group is carrying Inventory objects MUST keep track of the items being carried by adventurers using a PLAIN ARRAY of Items, you MUST NOT se ArrayLists (or any other class which is part of the the Java Collection Framework such as Linkedin.ist) within the Inventory class under ANY circumstances. Each position in the array contains cither • The address of an Item object in memory, an Item is considered to be in the Inventory if and only if its address in memory is stored in the array . null Fach Item object in the inventory MUST appear exactly once in this array, in other words, there MUST NOT be any duplicate elements in the array under ANY circumstances, whether these dupli cates are deep copies or aliases The Inventory class MUST provide the following INSTANCE methods, note that an actual im plementation used in an RPG would provide additional methods, in particular methods to add an item to the Inventory. Also note that in the method descriptions below, the phrase "this inventory" means "the Inventory on which the method in question is called • A constructor, which takes a value of type int as its only parameter, and initializes the newly created Inventory so that the number of item types it can store is equal to the value of the parameter. The number of item types which can be stored in the Inventory is fixed during instantiation, and can never change during the lifetime of the Inventory object • A method called get.Capacity (), which takes no parameters and returns a value of type int representing the capacity of this Inventory (that is, the number of different item types which can be stored in this Inventory). • A method called getItem(), which takes a value of type int as its only parameter, and returns the Item Nered at the commenpanding position in the array holding the Items stond in this Inventory, this method returns null if the element at the position specified by the parameter value is null or if the parameter represents an invalid index in this array. • A method called consumeOne(), which takes as its only parameter a string represent ing the description of an item, and returns a value of type boolean. The method searches the inventory for an item whose description is equal to the parameter String, with the comparison being performed in a case-INSENSITIVE manner. If no such Ttem exists in the inventory, the method returns false, and the state of the Inventory does not change. On the other hand, if such an Item exist in the inventory, the method returns true and modifies the state of the Inventory as follows: -If the quantity attribute of the item is greater than or equal to 2, then its value is reduced by 1. -If the quantity attribute of the Item is equal to 1, then the item is removed from the Inventory. Note that removing an Item can be done by simply assigning null to the amay position that contains it. The state of the array before and after calling this method can consist of addresses of Item objects interspersed with null elements. For example, in an Inventory whose capacity is 20, it is possible that the array contains the addresses of Item objects al positions 3 and 17. while the other amay position contains null. This implies that the method does NOT have to "compact the array so that the addresses of all the actual tem objects appear at the beginning of the array while all the null elements appear at the end. You MAY assume that the string parameter is not null; in other words, your method does not have to handle cases in which the string parameter is indeed null Akmal notes • You MUST respect proper encapulation practices, that is the attributes and methods of your class MUST be declared using the proper visibility modifiers. • Y MUNT call the methods you were asked to write in the previous part to retrieve the descrip tion and quantity attributes of an Item object, or to change the quantity attribute of an Item object. You MAY me that the item class has been implemented correctly, even if you did not successfully complete the previous part WRITE YOUR Inventory CLASS IN THE SPACE BELOW:

CSC236H5 Lecture Notes - Lecture 1: Empty String, Subset, Empty Set

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