CP164 Final: Types of Recursion

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maroonmacaw543

14 Jun 2018

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Types of Recursion

When considering how to write a recursive algorithm, it is useful to know some basic

different approaches to recursion.

Fruitful Recursion

Fruitful recursion simply uses a function that returns one or more values. This is nothing

new to us - we have written many functions that return something. In the context of

recursion, however, this means that the recursion relies on the fact that each call returns a

value that will be used in the recursion.

We will demonstrate this approach by reversing the contents of a list. This algorithm solves

the problem by starting at the ends of the list, swapping the values at the ends, then

working inwards with the next pair of values until the middle of the list is reached and

there are no values left to swap. As part of these examples we will use a swap function to

'swap' two elements of a list:

def swap(data, i, j):

temp = data[i]

data[i] = data[j]

data[j] = temp

return

In this example, we reverse the contents of a Python list by changing slices of the list:

def rev_list_f(data):

n = len(data)

if n > 1:

swap(data, 0, n-1)

data[1:n - 1] = rev_list_f(data[1:n - 1])

return data

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Document Summary

When considering how to write a recursive algorithm, it is useful to know some basic different approaches to recursion. Fruitful recursion simply uses a function that returns one or more values. This is nothing new to us - we have written many functions that return something. In the context of recursion, however, this means that the recursion relies on the fact that each call returns a value that will be used in the recursion. We will demonstrate this approach by reversing the contents of a list. As part of these examples we will use a swap function to. "swap" two elements of a list: def swap(data, i, j): temp = data[i] data[i] = data[j] data[j] = temp return. In this example, we reverse the contents of a python list by changing slices of the list: def rev_list_f(data): n = len(data) if n > 1: swap(data, 0, n-1) data[1:n - 1] = rev_list_f(data[1:n - 1]) return data.

Related Questions

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

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

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CP164 Final: Types of Recursion

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