# 15-112 Spring 2016 Homework 4 Due Sunday, 7-Feb, at 10pm

• This hw is SOLO. See the syllabus for details.
• There is no starter file this week. Remember: all the code above the #ignore_rest line is autograded, and all the code below it is ignored.
• Starting this week, you may use lists, but (as usual) you may not use constructs we have not yet covered (sets, maps, recursion, etc), unless explicitly allowed below.
• This week you may only make up to 7 submissions max to Autolab. As usual, only your last one counts.
• This week onwards, style is fully-weighted, up to 10 points.

1. lookAndSay(a) [15 pts]
First, read about look-and-say numbers here. Then, write the function lookAndSay(a) that takes a list of numbers and returns a list of numbers that results from "reading off" the initial list using the look-and-say method, using tuples for each (count, value) pair. For example:
```  lookAndSay([]) == []
lookAndSay([1,1,1]) == [(3,1)]
lookAndSay([-1,2,7]) == [(1,-1),(1,2),(1,7)]
lookAndSay([3,3,8,-10,-10,-10]) == [(2,3),(1,8),(3,-10)]
```

2. inverseLookAndSay(a) [10 pts]
Write the function inverseLookAndSay(a) that does the inverse of the previous problem, so that, in general:
```  inverseLookAndSay(lookAndSay(a)) == a
```
Or, in particular:
```  inverseLookAndSay([(2,3),(1,8),(3,-10)]) == [3,3,8,-10,-10,-10]
```

3. solvesCryptarithm(puzzle, solution) [20 pts]
Background: a cryptarithm is a puzzle where we start with a simple arithmetic statement but then we replace all the digits with letters (where the same digit is replaced by the same letter each time). We will limit such puzzles to strings the form "A+B=C" (no spaces), where A, B, and C are positive integers. For example, "SEND+MORE=MONEY" is such a puzzle. The goal of the puzzle is to find an assignment of digits to the letters to make the math work out properly. For example, if we assign 0 to "O", 1 to "M", 2 to "Y", 5 to "E", 6 to "N", 7 to "D", 8 to "R", and 9 to "S" we get:
```    S E N D       9 5 6 7
+ M O R E     + 1 0 8 5
---------     ---------
M O N E Y     1 0 6 5 2
```
And so we see that this assignment does in fact solve the problem! Now, we need a way to encode a possible solution. For that, we will use a single string where the index of the letter corresponds to the digit it represents. Thus, the string "OMY--ENDRS" represents the assignments listed above (the dashes are for unassigned digits).

With this in mind, write the function solvesCryptarithm(puzzle, solution) that takes two strings, a puzzle (such as "SEND+MORE=MONEY") and a proposed solution (such as "OMY--ENDRS"). Your function should return True if substituting the digits from the solution back into the puzzle results in a mathematically correct addition problem, and False otherwise. You do not have to check whether a letter occurs more than once in the proposed solution, but you do have to verify that all the letters in the puzzle occur somewhere in the solution (of course). You may not use the eval() function. Also, you almost surely will want to write at least one well-chosen helper function.

4. bestScrabbleScore(dictionary, letterScores, hand) [20 pts]
Background: In a Scrabble-like game, players each have a hand, which is a list of lowercase letters. There is also a dictionary, which is a list of legal words (all in lowercase letters). And there is a list of letterScores, which is length 26, where letterScores[i] contains the point value for the ith character in the alphabet (so letterScores contains the point value for 'a'). Players can use some or all of the tiles in their hand and arrange them in any order to form words. The point value for a word is 0 if it is not in the dictionary, otherwise it is the sum of the point values of each letter in the word, according to the letterScores list (pretty much as it works in actual Scrabble).

In case you are interested, here is a list of the actual letterScores for Scrabble:
```   letterScores = [
#  a, b, c, d, e, f, g, h, i, j, k, l, m
1, 3, 3, 2, 1, 4, 2, 4, 1, 8, 5, 1, 3,
#  n, o, p, q, r, s, t, u, v, w, x, y, z
1, 1, 3,10, 1, 1, 1, 1, 4, 4, 8, 4,10
]
```
Note that your function must work for any list of letterScores as is provided by the caller.

With this in mind, write the function bestScrabbleScore(dictionary, letterScores, hand) that takes 3 lists -- dictionary (a list of lowercase words), letterScores (a list of 26 integers), and hand (a list of lowercase characters) -- and returns a tuple of the highest-scoring word in the dictionary that can be formed by some arrangement of some subset of letters in the hand, followed by its score. In the case of a tie, the first element of the tuple should instead be a list of all such words in the order they appear in the dictionary. If no such words exist, return None.

Note: there is no fixed dictionary here. Each time we call the function, we may provide a different dictionary! It may contain 100 words or perhaps 100,00 words.

Write the function drawCirclePattern(n) that takes one parameter, a positive int, and displays a graphics window, inside of which it draws the nxn version of this picture: While the image above shows two circle patterns, you only need to draw one at a time. For example, the left image above was drawn with 10 rows (and 10 columns), and the right image with 5 rows (and 5 columns). The pattern consists of "buttons" (or perhaps "bullseyes"), where each button is really several circles drawn on top of each other. Each circle in a "button" has a radius 2/3rds as large as the next-larger circle, which continues until the radius is less than 1. As for the color of each button, here are the rules to follow:

Rule 1: Starting from the left-top corner, every 4th diagonal is entirely red.
Rule 2: For the non-red buttons, starting from the top row, every 3rd row is entirely green.
Rule 3: For the non-red and non-green buttons, starting from the second-to-leftmost column, every 2nd column is entirely yellow.
Rule 4: Any non-red, non-green, and non-yellow button is blue.

Note that these rules can be fairly easily implemented using a single if-elif-elif-else statement. Inside that statement, you might want to set a variable, say one named "color", based on each of these four conditions. Then you could draw with fill=color.

Note: The drawing should mostly fill the window, and the 10x10 case should be about the same size as the 10x10 case in the image above, but the exact dimensions of the drawing are up to you.

6. runSimpleTortoiseProgram(program, winWidth=500, winHeight=500) [25 pts] [manually-graded]
In addition to the Tkinter which we all know and love, Python usually comes with another graphics package called "Turtle Graphics", which you can read about here. We will definitely not be using turtle graphics in this problem (and you may not do so in your solution!), but we will instead implement a small turtle-like (or maybe turtle-inspired) graphics language of our own. We'll call it Tortoise Graphics.

First, we need to understand how Tortoise Graphics programs work. Your tortoise starts in the middle of the screen, heading to the right. You can direct your tortoise with the following commands:

• color name
Set the drawing color to the given name, which is entered without quotes, and which can be "red", "blue", "green", or any other color that Tkinter understands. It can also be "none", meaning to not draw.

• move n
Move n pixels straight ahead, where n is a non-negative integer, while drawing a 4-pixel-wide line in the current drawing color. If the drawing color is "none", just move straight ahead without drawing (that is, just change the tortoise's location).

• left n
Turn n degrees to the left, without moving, where n is a non-negative integer.

• right n
Turn n degrees to the right, without moving, where n is a non-negative integer.

Commands are given one-per-line. Lines can also contain comments, denoted by the hash sign (#), and everything from there to the end-of-line is ignored. Blank lines and lines containing only whitespace and/or comments are also ignored.

With this in mind, write the function runSimpleTortoiseProgram(program, winWidth=500, winHeight=500) that takes a program as specified above and runs it, displaying a window (which is 500x500 by default) with the resulting drawing from running that program. Your function should also display the tortoise program in that window, in a 10-point font, in gray text, running down the left-hand side of the window (say 10 pixels from the left edge). Don't worry if the program is longer than can fit in the window (no need to scroll or otherwise deal with this). Also, you are not responsible for any syntax errors or runtime errors in the tortoise program.

For example, this call:
``````runSimpleTortoiseProgram("""
# This is a simple tortoise program
color blue
move 50

left 90

color red
move 100

color none # turns off drawing
move 50

right 45

color green # drawing is on again
move 50

right 45

color orange
move 50

right 90

color purple
move 100
""", 300, 400)
``````

produces this result in a 300x400 window: And this call:
``````runSimpleTortoiseProgram("""
# Y
color red
right 45
move 50
right 45
move 50
right 180
move 50
right 45
move 50
color none # space
right 45
move 25

# E
color green
right 90
move 85
left 90
move 50
right 180
move 50
right 90
move 42
right 90
move 50
right 180
move 50
right 90
move 43
right 90
move 50  # space
color none
move 25

# S
color blue
move 50
left 180
move 50
left 90
move 43
left 90
move 50
right 90
move 42
right 90
move 50
""")
``````

produces this result in a 500x500 window: 7. Bonus/Optional: drawSpiral(winWidth, winHeight) [2 pts] [manually-graded]
Similarly to the drawCirclePattern problem above, write an animation named drawSpiral(winWidth, winHeight) that takes two ints and creates a window of the given dimensions, and then draws this picture (to fill the window as completely as possible): Here, you will draw both sides of the picture (the larger and smaller spirals), along with the title text (drawSpiral) and the boxes around the spirals.

As for the image, each side will be a spiral (or really a series of spiral arms). The spiral arms must be created by drawing a series of circles (the only thing drawn to create the spirals in this exercise are small circles). There should be 28 arms, each arm composed of 32 circles. Each arm spirals, or bends, such that the outermost circle in the arm is drawn pi/4 radians (45 degrees) beyond the innermost circle in that same arm. Hint: You will have to use basic trigonometry here! Also, try to make the color gradients work as indicated (think rgbString).

8. Bonus/Optional: runSimpleProgram(program, args) [4 pts]
First, carefully watch this video that describes this problem:

Then, write the function runSimpleProgram(program, args) that works as described in the video, taking a legal program (do not worry about syntax or runtime errors, as we will not test for those cases) and runs it with the given args, and returns the result.

Here are the legal expressions in this language:

• [Non-negative Integer]
Any non-negative integer, such as 0 or 123, is a legal expression.

• A[N]
The letter A followed by a non-negative integer, such as A0 or A123, is a legal expression, and refers to the given argument. A0 is the value at index 0 of the supplied args list. It is an error to set arg values, and it is an error to get arg values that are not supplied. And you may ignore these errors, as we will not test for them!

• L[N]
The letter L followed by a non-negative integer, such as L0 or L123, is a legal expression, and refers to the given local variable. It is ok to get an unassigned local variable, in which case its value should be 0.

• [operator] [operand1] [operand2]
This language allows so-called prefix expressions, where the operator precedes the operands. The operator can be either + or -, and the operands must each be one of the legal expression types listed above (non-negative integer, A[N] or L[N]).

And here are the legal statements in this language (noting that statements occur one per line, and leading and trailing whitespace is ignored):

• ! comment

• L[N] [expr]
Lines that start with L[N] are assignment statements, and are followed by the expression (as described above) to be stored into the given local variable. For example: ``` L5 - L2 42 ``` This line assigns (L2 - 42) into L5.

• [label]:
Lines that contain only a lowercase word followed by a colon are labels, which are ignored except for when they are targets of jump statements.

• JMP [label]
This is a jump statement, and control is transferred to the line number where the given label is located. It is an error for such a label to not exist, and you may ignore that error.

• JMP+ [expr] [label]
This is a conditional jump, and control is transferred to the line number where the given label is located only if the given expression is positive. Otherwise, the statement is ignored.

• JMP0 [expr] [label]
This is another kind of conditional jump, and control is transferred only if the given expression is 0.

• RTN [expr]
This is a return statement, and the given expression is returned.

Hints:
1. Do not try to translate the program into Python! Even if you could do so, it is not allowed here. Instead, you are going to write a so-called interpreter. Just keep track of the local variables, and move line-by-line through the program, simulating the execution of the line as appropriate.
2. You will find it useful to keep track of the current line number.
3. How long do you run the program? Until you hit a RTN statement! You may assume that will always eventually happen.
4. We used strip, split, and splitlines in our sample solution, though you of course may solve this how you wish.

Finally, here is a sample test function for you. You surely will want to add some addition test cases. In fact, a hint would be to build your function incrementally, starting with the simplest test cases you can think up, which use the fewest expression and statement syntax rules. Then add more test cases as you implement more of the language.
def testRunSimpleProgram(): print("Testing runSimpleProgram()...", end="") largest = """! largest: Returns max(A0, A1) L0 - A0 A1 JMP+ L0 a0 RTN A1 a0: RTN A0""" assert(runSimpleProgram(largest, [5, 6]) == 6) assert(runSimpleProgram(largest, [6, 5]) == 6) sumToN = """! SumToN: Returns 1 + ... + A0 ! L0 is a counter, L1 is the result L0 0 L1 0 loop: L2 - L0 A0 JMP0 L2 done L0 + L0 1 L1 + L1 L0 JMP loop done: RTN L1""" assert(runSimpleProgram(sumToN, ) == 1+2+3+4+5) assert(runSimpleProgram(sumToN, ) == 10*11//2) print("Passed!")