15-112 Fundamentals of Programming

For this homework, there is no starter file. You have to create your own .py file and submit it to Autolab. You can take a previous starter file and modify it appropriately.

Please add your name, Andrew id, and section at the top of the file.

Write test functions for each function you write.

IMPORTANT: All the code above the #ignore_rest line is autograded, and all the code below it is ignored. Make sure you put all test functions below #ignore_rest.

From now on you will be graded on style. For this homework, however, style deductions are half-weighted, so the maximum number of points you can lose on style is 5 (out of 100). Please see here for the style rubric.

You may not use recursion, sets, dictionaries or any other constructs that we have not yet covered in class.

You will have 3 submissions on Autolab for this homework.

Questions

1. This question is for fun and will not be graded. First, read a bit about Fermat's Last Theorem here. In 1769, Leonhard Euler proposed a generalization of Fermat's Last Theorem. He conjectured that for n > 2, at least n nth powers are needed to obtain a sum that is itself an nth power. Euler's conjecture stood until 1967! Now you can disprove it yourself in just minutes. Write a function called disproveEuler() that returns a tuple of non-zero integers (a, b, c, d, e) such that a**5 + b**5 + c**5 + d**5 = e**5. Hint: You don't need to try values larger than 150.


2. Study the following examples first. Make sure you understand how they work.

   def drawRectangle(rows, cols):
       for i in range(rows):
           for j in range(cols):
               print("*", end="")
           print()
   
   drawRectangle(3, 4)
   print()
   
   def drawChessBoard(n):
       for i in range(n):
           for j in range(n):
               if((i+j) % 2 == 0):
                   print("W", end="")
               else:
                   print("B", end="")
           print()
   
   drawChessBoard(8)
   print()
   
   def drawTriangle1(rows):
       for i in range(rows):
           for j in range(i+1):
               print("*", end="")
           print()
   
   drawTriangle1(4)
   print()
   
   def drawTriangle2(rows):
       for i in range(rows):
           for j in range(rows-i-1):
               print(" ", end="")
           for k in range(i+1):
               print("*", end="")
           print()
   
   drawTriangle2(4)
   print()
   
   # This one works the same way as the one above.
   def drawTriangle2(rows):
       for i in range(1, rows+1):
           for j in range(1, rows+1):
               if(i+j > rows):
                   print("*", end="")
               else:
                   print(" ", end="")
           print()
   
   drawTriangle2(4)
   print()
   
   def drawO(n):
       for i in range(-n,n+1):
           for j in range(-n,n+1):
               if(i**2 + j**2 <= n**2):
                   print("* ", end="")
               else:
                   print("  ", end="")
           print()
   
   drawO(16)
   

   
   Write a function called myTriangle(height) that takes a non-negative integer height as input, and returns the string that when printed, produces a triangle of the given height. The shape of the triangle is illustrated below.
   

   # If height = 3, the shape should be:
   #   *
   #  ***
   # *****
   #
   # If height = 4, the shape should be:
   #    *
   #   ***
   #  *****
   # *******
   # 
   # Here are a couple of test cases you can use:
   assert(myTriangle(0) == "")
   assert(myTriangle(3) == "  *  \n *** \n*****")
   

   
   Next, write a function called myX(n) that takes a non-negative integer n as input, and returns the string that when printed, produces a (2n+1) by (2n+1) X-shape as illustrated below.
   

   # If n = 2, the shape should be:
   # *   *
   #  * * 
   #   *  
   #  * * 
   # *   *
   #
   # The corresponding test case is:
   assert(myX(2) == "*   *\n * * \n  *  \n * * \n*   *")
   

   
   


3. doPigStrategyAnalysis from here.