CPSC120B
Fundamentals of Computer Science I

Lab 26

Histograms

Write a function called count_values(a_dictionary, a_value), which takes a dictionary and some value as parameters. Your function should return the number of occurances of a_value as a value in a_dictionary. For this exercise, DO NOT USE THE count method to solve this problem.. 






Histogram



  Histograms allow us to visualize the distribution of some data set.
  For example, We could visualize the distribution of the birth months
  of children:




  
  




  Where the purple bars are the expected distributions based on month
  lengths, and the blue bars are the actual, observed distributions
  from some data set.  In a previous lab,
  we had the
  opportunity to use this information to change the probability
  distributions for computing the birthday paradox.  Today, We will
  generate a histogram that could possibly be used to break
  a substitution cipher.




Details



  Create a function called print_histogram(text) in a
  file called histogram.py.  The function should print a
  sorted (in descending order) histogram that represents the number of
  occurrences of the characters in text.  You will use a
  dictionary to represent this histogram, with the keys of the
  dictionary as characters and the values of the dictionary as
  integers.




Sample Test Cases



  
    

      Function Parameters
      Expected Output
    

  
  
    

      hello
      
        
l: ##
h: #
o: #
e: #
        

      		
    

    

      This is a test!
      
        
s: ###
 : ###
i: ##
t: ##
T: #
h: #
a: #
e: #
!: #
        

      		
    

  




Hint




  
  

    
    
      
  1. 
        
    
          Create a function called
          compute_histogram(text).  The function should
          return a dictionary that represents a histogram of the
          number of occurrences of the characters in text.
          The keys of the dictionary should be characters and the
          values of the dictionary should be integers.
        
    
        
    
	  You are going to follow the accumulator pattern for this
	  activity.  However, you aren't going to have a single
	  accumulator.  You are going to have multiple accumulators
	  all stored in a dictionary.  This dictionary is your
	  histogram that you are going to return.
        
    
        
    
          The for loop should iterate over each of the characters
          in text.  For each character, increment the value
          of the character's entry in the dictionary.  Note, you must
          handle the special case of the character not already having an
          entry in the dictionary.
        
    
      
    2. 
      
  2. 
        
    
          To print the histogram in descending order, first find the
          entry with the largest value in the dictionary.  Use the
          dictionary values method and the
          built-in max function to find the largest
          value.
        
    
        
    
          Create a function reverse_lookup(dictionary,
          value) that returns the key of an entry
          in dictionary that has the
          value value.  Note, there may be more than one
          key with the specified value, in this case it doesn't matter
          which key associated with the value is returned.
        
    
        
    
          Use the reverse_lookup function to print the
          character with the largest value in the dictionary.  And use
          the * operator to print the appropriate number
          of # characters.  Then use the del
          operator to delete the entry from the histogram dictionary.
          Repeat this process for the next largest value until the
          dictionary is empty.
        
    
      
    3. 
  





 




Challenge



  A substitution cipher is a non-linear cipher that relies on a
  "look-up" table (the key for the cipher) in order to accomplish the
  encryption.  It avoids the problems of the Caesar cipher, because
  the mapping from plain-text character to cipher-text character is
  not a linear function; you have to figure out each character
  individually in a substitution cipher.




  If something is known about the plain-text, we can make an attempt
  at figuring out the entirety of the mapping.  Suppose it is known
  that the plain-text was written in English.  We know the
  distribution of characters in the English language:




  
  



  If we take the most commonly occurring character from the
  cipher-text, chances are it is the encrypted version of 'e'.  The
  second most common character is probably the encrypted version of
  't'.  The third most common is probably the encrypted version of
  'a', and so on.




  You are provided with the
  module ciphers.py,
  which includes functions encode_substitution(plain_text,
  key) and
  decode_substitution(cipher_text, key, ordered).  Create
  a program in a file called
  hack_substitution.py.  This program should read in a
  cipher-text string, and attempt to decode the string using the
  sequence of the most commonly occurring characters.  Try your
  program on this
  encoded file.  You can redirect a file to your program by using the
  "<" operator at the command line.



  $ python3 hack_substitution.py < encoded.txt




  How well does it work?  Can you at least read some words?  Why does
  this not work out exactly correctly?





Submission


Please show your source code and run your programs for the instructor or lab assistant. Only a programs that have perfect style and flawless functionality will be accepted as complete.