Description
1 Assignment Goals
1. Produce an application with more than one class, appropriately split into multiple files.
2. Learn how to use a constructor to produce a semantically valid non-trivial data structure.
3. Learn how to use classes and objects to model a physical structure.
4. Learn how to driver program to exercise and test a class.
5. Learn how to code within a prescribed and restricted subset of the language.
2 Think-A-Dot
2.1 Some history
Think-a-Dot is a mathematical toy introduced by E.S.R. Inc. in the 1960’s.
http://www.jaapsch.net/puzzles/images/thinkadot.jpg
It is covered by U.S. patent 3,388,483, issued June 18, 1968 to Joseph A. Weisbecker. (See Fig. 1.)
2 Problem Set 3
Figure 1: U.S. patent 3,388,483, issued June 18, 1968 to Joseph A. Weisbecker.
Figure 2: Looking inside a slightly-modified box.
Handout #5—September 26, 2018 3
Ask some questions:
1. What is the structure of the machine? (See Figure 3.)
2. Starting from the all-yellow pattern, can one drop in marbles so as to make it all blue?
3. If so, can one get back to the all-yellow pattern?
4. How many of the 2
8 = 256 possible patterns can one reach from the initial state (all-yellow)?
5. Given that pattern s2 is reachable from pattern s1, how many marbles are needed? (Call this
the directed distance from s1 to s2.)
6. Is the distance from s1 to s2 always the same as the distance from s2 to s1?
7. What is the largest distance between any pair of states for which the distance is defined?
Figure 3: Structure of the machine.
Binary Counter
Eight balls through hole C will cause gates 7–5–3
to behave like a binary counter and cycle through
all eight possibilities.
Gates to the above and left (1, 2, 4, 6) are not
affected.
4 Problem Set 3
How can you get to a particular pattern?
Starting from all yellow, how can one reach this goal?
Here’s one solution:
−→
−→
−→
Handout #5—September 26, 2018 5
2.2 Further references
Google returns many hits for the search term “think-a-dot”.
1. Some of the early pre-E.S.R. Think-a-Dot history.
2. A realistic Think-a-Dot simulator that you can play with, written Scratch. This shows the
original unmodified dot pattern that appears when the device is tipped to the right.
3. A Think-a-Dot-inspired electronic game from 2002.
4. Some of the mathematical theory behind Think-a-Dot (from Wikipedia, Think-a-Dot).
(a) Schwartz, Benjamin L. (1967), “Mathematical theory of Think-a-Dot”, Mathematics
Magazine, 40 (4): 187193, doi:10.2307/2688674, MR 1571696.
(b) Beidler, John A. (1973), “Think-a-Dot revisited”, Mathematics Magazine, 46: 128136,
doi:10.2307/2687967, MR 0379077.
(c) Gemignani, Michael (1979), “Think-a-Dot: a useful generalization”, Mathematics Magazine, 52 (2): 110112, doi:10.2307/2689850, MR 1572295.
3 Problem
You are to model a Think-a-Dot device and its behavior through a collection of C++ classes. You
are also to write a command tad that allows a user to interact with your simulated Think-a-Dot
device. User inputs are single letters commands. All command letters are case insensitive, so ‘Q’
and ‘q’ for example have the same effect. The commands are:
• ‘A’, ‘B’, ‘C’ simulate the action of the machine when a ball is dropped in hole ‘A’, ‘B’, or ‘C’,
respectively.
• ‘L’, ‘R’ cause the gates to be reset to all point the same way – all to the left or all to the right,
respectively.
• The flip-flops should be colored as shown for the modified box in Figure 2.
• ‘P’ prints the state of the machine using three lines of text, e.g.,
R L R
L L
L L L
• ‘H’ prints a brief version of these instructions.
• ‘Q’ exits the program.
Your program will prompt the user to enter a command letter, check it for validity, and print the
hole at which the ball exits the machine (hole ‘P’ or ‘Q’ as shown in Fig. 3).
4 Programming Notes
You will define and implement three classes: ThinkADot, FlipFlop, and Game. Class
ThinkADot models the Think-A-Dot device. FlipFlop models a single flip-flop within the
Think-a-Dot. Game controls the user-interaction with the Think-A-Dot. It prompts the user to get
command letters (from cin) and to print results (to cout). It interacts with the Think-A-Dot to
determine how the device responds to the various operations that can be performed on it.
6 Problem Set 3
Class Game should have a public function play() that starts the game. play() first creates
a ThinkADot object where the flip-flops are colored as shown in Figure 2. It then enters the
interactive loop that prompts the user for a command letter and performs the corresponding action.
Class FlipFlop models a single flip-flop. The state of a flip-flop is either “left” or “right”
and should be represented by an enum type. (See 08-brackets Token class for an example.) There
should be a print() function that just prints a single letter ‘L’ or ‘R’ according to the current state
of the flip-flop. There should also be a function flip() that flips the state from “left” to “right”
or vice versa and returns the side of the flip-flop (“left” or “right”) the ball is on when leaving the
flip-flop. Thus, if the flip-flop is in the “left”-leaning state initially, the ball will pass to the right,
and the new state will be “right”.
For this class, it is okay to have public functions getState() and setState() to be used
by member functions of class ThinkADot. A superior design would nest the entire FlipFlop
class inside of the ThinkADot class, but for this assignment, FlipFlop should be a separate
class at the same level as the others. (We will get to nested classes later in the course.)
Class ThinkADot models the device. It has a private array (not a vector) of eight FlipFlop
objects that store the current state of each of the eight flip-flops. Its constructor should initialize all of
the flip-flops to the “left” position, the same as the ‘L’ command. It has public functions reset(),
play(), and print() that carry out the actions ‘A’, ‘B’, ‘C’, ‘L’, and ‘R’ (with appropriate
parameters) that can be performed on the device. The flip-flop states must be accessible only from
these required member functions. In particular, there should be no getter or setter functions for the
flip-flops.
The file main.cpp will have the same form as in PS1. The global function run() should only
have two lines – one to instantiate Game and the other to call the Game object’s play() function.
4.1 Computing the next state
The tricky part of this assignment is how to update the state when a ball is dropped through one of
the three holes ‘A’, ‘B’, or ‘C’. Referring to Figure 2, you can see seven channels through which
the ball can pass. If we number them from 0 through 6, starting at the left, then we see that a ball
dropped in hole ‘A’ enters channel 1. After passing through the first flip-flop it moves to either
channel 0 or to channel 2, depending on the state of the flip-flop. If it goes to channel 0, it drops
straight through to the bottom and comes out on the left side. If it goes to channel 2, it encounters
the first flip-flop in the second row. After passing through it, the ball enters channel 1 or 3, etc.
Your code should trace the path of a ball through the machine as described above, flipping each
of the flip-flops encountered on the way, and recording the last channel the ball was in. Clearly that
will be channel 1, 3, 5, or 7. If it’s 1 or 3, the ball exits the machine through hold ‘P’. Otherwise, it
exits through hole ‘Q’. Note that it would be ambiguous where the ball exits if it were coming from
channel 4, but that is not possible.
4.2 No-no’s
There are many ways to implement a Think-a-Dot. For this assignment, you must do it as described
above. Here are a few no-no’s, not because they’re necessarily wrong but because I want you to
learn the particular techniques described above.
1. Don’t use new or delete.
2. Don’t use any Standard Library container functions such as vector.
3. Don’t use a table lookup to find the next state.
Handout #5—September 26, 2018 7
4. Don’t use nested classes.
5. Don’t use language features that have not been presented in lecture or in any of the class
examples. Don’t use prohibited features such as non-const global variables or goto’s.
If you think you need to violate any of these restricts, please ask me for help.
5 Grading Rubric
Your assignment will be graded according to the scale given in Figure 4 (see below).
# Pts. Item
1. 1 All relevant standards from PS1 are followed regarding submission, identification of authorship on all files, and so forth.
2. 1 A well-formed Makefile or makefile is submitted that specifies compiler
options -O1 -g -Wall -std=c++17.
3. 1 Running make successfully compiles and links the project and results in an
executable file tad.
4. 1 tad smoothly interacts with the user. Clean, easily understood user prompts
and help messages are given.
5. 2 Bad user inputs are handled gracefully and do not result in fatal errors.
6. 6 All of the functionality in section 3 is correctly implemented. In particular, each
of the eight command letters works properly in both upper and lower case and
carries out its assigned action correctly.
7. 3 The structure of the program matches the specification and restrictions given in
in section 4. No dynamic storage is used.
8. 1 Each function definition is preceded by a comment that describes clearly what
it does.
9. 4 The program shows good style. All functions are clean and concise. Inline initializations, functions, and const are used where appropriate. Variable names
are appropriate to the context. Programs are consistently indented according to
the course indenting style. Each class has a separate .hpp file and, if needed, a
separate .cpp file.
20 Total points.
Figure 4: Grading rubric.
