Instructions for diamonds

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This task will help you think about how functions can be used to store and replay code, and how parameters can make that process even more flexible. With the right approach, the entire printed pattern can be produced by a program that only includes a single line of code which uses the print function.

Your goal is straightforward: In the provided file, define a zero-parameter function named diamondPattern. When diamondPattern is invoked, it should print the pattern of digits shown in this example.

Notice that the starter code contains the following variable definitions:

# pre-defined strings
zero  = '     '
one   = '  1  '
two   = ' 2 2 '
three = '3 3 3'
empty = ''

By combining only these strings and no others, diamondPattern must print out the pattern shown in the example. You must also have no more than 10 places in your program where the print function is called. Of course, because those lines of code may be run several times if they are in a function which is called more than once, your code will end up calling print exactly 40 times, once for each line of the output pattern.

You will need to define some of your own functions besides just diamondPattern to solve this problem, and it is up to you how to define those functions. As a minimum requirement, your diamondPattern function must itself contain at least two function calls to other custom functions you have defined (this could be two calls to a single other function, or two calls to two different functions, as long as there are two different function calls). In addition, your diamondPattern function may not call print directly (i.e., calls to print may appear in helper functions called by diamondPattern, but not within diamondPattern itself).

Notes

• Remember that every function you write must include a documentation string (docstring) that describes what it does.

• There are possible solutions where one of the provided strings may not be necessary.

• You may concatenate the provided strings to form larger strings, but you are not allowed to create any new strings delimited by quotation marks. You may not use the newline character '\n'.

• In this problem, you are not allowed to use features of Python that we have not studied yet, even if you know them. In particular, you are not allowed to use conditionals (i.e., if statements) or loops (i.e., for loops or while loops).

• You may not define any functions within other functions. This isn't a useful thing to do in any case. Each of your functions should be defined one-by-one without any indentation before the 'def'.

• For a perfect score, you must also make no more than 8 function calls of any kind within the diamondPattern function itself (though the functions that it calls may make more).

• As an extra goal, you may call print in no more than 5 places throughout your file, rather than 10.

• This problem has many possible solutions. There is a particularly elegant solution that calls print in only one place. While we don't require you to do this, you might want to challenge yourselves.

• To check whether your pattern is correct, you can call it in the shell by typing diamondPattern() and hitting enter. We have also provided a test case in the test_diamonds.py file. When you run that file, you should see the following text appear in red:

  ✓ test_diamonds.py:24
  

  If your pattern is not correct, you will see an explanation of where the first difference was found (or what the error was if there was an error).

Hints

The goal of this problem is two-fold: to recognize patterns, and to write functions that can generate these patterns and combine them together to produce the complete pattern. We strongly recommend that you spend some time thinking about how to break the drawing into different patterns that can be captured by simple functions. If you are having difficulty recognizing patterns, we have a diagram to help you with this process. Access the diagram only after pondering on the pattern on your own.

  1         1         1         1  
 2 2       2 2       2 2       2 2 
3 3 3     3 3 3     3 3 3     3 3 3
 2 2       2 2       2 2       2 2 
  1         1         1         1  

       1         1         1         1  
      2 2       2 2       2 2       2 2 
     3 3 3     3 3 3     3 3 3     3 3 3
      2 2       2 2       2 2       2 2 
       1         1         1         1  

  1         1         1         1  
 2 2       2 2       2 2       2 2 
3 3 3     3 3 3     3 3 3     3 3 3
 2 2       2 2       2 2       2 2 
  1         1         1         1  
       1         1         1         1  
      2 2       2 2       2 2       2 2 
     3 3 3     3 3 3     3 3 3     3 3 3
      2 2       2 2       2 2       2 2 
       1         1         1         1  

  1         1         1         1  
 2 2       2 2       2 2       2 2 
3 3 3     3 3 3     3 3 3     3 3 3
 2 2       2 2       2 2       2 2 
  1         1         1         1  
       1         1         1         1  
      2 2       2 2       2 2       2 2 
     3 3 3     3 3 3     3 3 3     3 3 3
      2 2       2 2       2 2       2 2 
       1         1         1         1  
  1         1         1         1  
 2 2       2 2       2 2       2 2 
3 3 3     3 3 3     3 3 3     3 3 3
 2 2       2 2       2 2       2 2 
  1         1         1         1  
       1         1         1         1  
      2 2       2 2       2 2       2 2 
     3 3 3     3 3 3     3 3 3     3 3 3
      2 2       2 2       2 2       2 2 
       1         1         1         1