The Hailstone Sequence II

For this homework, we'll be modifying homework 6 by adding another option for the user to choose:

H - view a Histogram of chain lengths for a range

Do NOT modify your original hw6.py file. Instead make a copy of your hw6.py file in your hw7 directory named hw7.py

The Task

We'll be using some of the methods from the graphics library to draw a histogram of chain lengths for a range of values. This histogram will be drawn in a window. How big should the window be ? It depends on the user's input.

Thoughts
• How wide does the window have to be ?
• We can't let the user choose a long range of numbers or else the window would have to be too wide or our bars too thin. So let's always have a range of 10 values and just let the user pick the starting value.
• How will we know the highest bar in the histogram ?
• Just like in the tic-tac-toe example from lecture, we'll create a a window that is 500 x 500, let's title it "Histogram of Chain Lengths". Then we can use the setCoords method to have the coordinates match our data.
• So what should the height of the y-axis be? The length of the longest chain plus some room for the labels at the bottom where n is shown.
• How wide should the x-axis be? We want to show bars for 10 values and histograms look better if there is some space between the bars AND we'll need some space on the left for the lengths to be printed. Let's try 20.

The Modifications

First, the obvious modifications are :

• Since we're going to be using some methods from the graphics library, add
  from graphics import * to the top your hw7.py file.
• Modify your printMenu() function so that it has this additional choice:
  
  H - view a Histogram of chain lengths for a range
  
  
• If it doesn't already, modify your hailstone() function so that it returns the length of n's chain.
• We're going to be storing these returned lengths into a list by using the list method append. First we have to start with an empty list, then use the append method whose form is <listName>.append(x) Here's the code :

        # initialize variables  
        longestLength = 1
        lengthList = []

        # restrict the range to 10 values
        for n in range (start, start + 10):
            length = hailstone(n)
            lengthList.append(length)
            # code for finding longestLength here

• Add another elif that will make a call to a new function named drawHistogram() when the user has entered 'h' or 'H'. You'll have to pass it the starting value of the range, start, the longestLength of a chain for the values in this range, and lengthList, the list of lengths of the chains.

Now that you have everything set up, write the function drawHistogram()

Specifications for drawHistogram()

• The title of the window should be: "Histogram of Chain Lengths".
• The value of n should be printed beneath each of the histogram's bars.
• Labels showing the lengths should be printed on the left side. See the sample histograms for what's expected. Notice that the length labels along the left side change as the longest length of the chains change for different ranges.
• The bars should be filled with a color different than the background color.
• Since we want to allow the user to draw histograms for more than one range of numbers during the running of the program, we'll want to close the window after having enough time to view it. You should close the window after 10 seconds. You'll need to use sleep() to do this.
• All handling of the graphics window should be done within the drawHistogram() function. In fact, since the window is opened in this function, it is local to this function. Trying to close the window in main() will cause an error when run.

Sample Histograms

Here's the histogram for the range 2 to 11 :

Here's the histogram for the range 16 to 25 :

Submitting Your Work

After you've finished your assignment, use the submit command to turn it in.

• You must be logged into your account.
• You must be in the same directory as the file you're trying to submit.
• At the Linux prompt, type

  submit cs201 HW7 hw7.py

Don't forget to watch for the confirmation that submit worked correctly. Specifically, the confirmation will say:

Submitting hw7.py...OK

If not, try again.

You can check your submission by entering
submitls cs201 HW7
You should see the name of the file that you just submitted, in this case, hw7.py.