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Pre-lab 01 An Amazing Programming Problem

This Pre-lab must be completed before you write the WhichWay program.

Table of Contents

The Original Problem

Draw a Flowchart

Square Naming Convention

Shortest Path Solution

Build a Truth Table

Draw your Flowchart - Solution for a Fully "Deterministic" Maze

Pre-lab Assignment

Find Your Target Square

How to Find Your Path

Design Methodology for a “Non-deterministic” Maze

A Modular Solution

Step-by-Step Instructions

Deliverable for Pre-Lab 1

Checklist

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The Original Problem The problem we will be trying to solve for the semester was originally taken from a puzzle book.

Here is the problem as defined by the puzzle book.

“In the forest, you will find beehives and more importantly honeycombs. Along the path

are bees. The number of bees at any given location is indicated by a number. There are

a few ways your bear can travel to the forest. Your aim is to teach your bear how to

make his way to the forest while encountering as few bees as possible”

Take a few minutes and see if you can solve the puzzle.

Figure 1 The Maze

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Draw a Flowchart Now let’s see if you can translate your path through the maze into a flowchart.

1. Assume the hungry Bear is initially pointing north with his knapsack. In the knapsack is a

blank notepad with a pencil and eraser. The length of each step is exactly one square.

2. Draw your solution as a flowchart named WhichWay. Here is how your flowchart will fit

within the main flowchart.

Figure 2 Top level flowchart of maze problem.

You may only use the following unconditional, conditional, and notepad instructions.

Actuators and corresponding unconditional instructions

1. Take a step You may only use this instruction once as shown in the flowchart above

(Figure 2).

2. Turn left

3. Turn right

4. Turn around

5. Count and record the number of bees in your notepad. You may only use this single

instruction once in your WhichWay flowchart for the Shortest Path as shown in Figure 4.

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Sensors and corresponding conditional instructions

1. Did you hit a wall?

2. Can your left paw touch a wall?

3. Can your right paw touch a wall?

4. Are you in the forest? You may only use the single instruction included in the example

WhichWay flowchart for the Shortest Path (Figure 4).

5. Do you see any bees? You may only use the single instruction included in the example

WhichWay flowchart for the Shortest Path (Figure 4).

6. Are you thinking of a number {not equal, less than, greater than or equal} to 0?

7. Is the number on page N of the notepad {not equal, less than, greater than or equal} to

some constant?

Notepad operations

The bear can remember 8-bit unsigned and 1-bit (binary) numbers. The bear records a number

in his notepad. He can only save one number per page. You may assign a descriptive name to

a page (ex. bees), simple use the page number (page1), or think of it as a variable (X). In the

following example X = 0.

C++ Equivalent Instructions

1. Erase page X. page0 = 0;

2. Increment the number on a page. increment page0;

Nodes

The following two instructions are included in the provided flowchart (Figure 4) and may only be

used once.

1. Start

2. Stop

Tips and Tricks

● You may not need all the instructions provided.

● Although not required, you can use subroutines.

Take a few minutes to see if you can sketch-out your flowchart. If you don’t know where to start;

don’t worry, in the next few sections I will step you through how to write your own flowchart.

Square Naming Convention Here is a standardized naming convention to help you define the decision points in any maze. In

order to provide a design example, the following maze identifies the squares (i.e., intersections)

where the bear needs to make a decision for the shortest path solution.

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Figure 3 Shortest path solution with intersections identified.

Squares are numbered by concatenating the binary values (yes = 1, no = 0) for the answers to

the following three questions (sensor inputs).

Can your left paw touch a wall? - Did you hit a wall? - Can your right paw touch a wall?

The answers to these three questions provide all the information that our bear can know about

any given square. Let’s look at a few examples to see how this works. After taking the first step

the bear can touch a wall with his left paw (1), has not hit a wall (0), and cannot touch a wall

with its right paw (0). For our convention this would correspond to input condition 4 = 1002. As

seen in the illustration I have therefore numbered this square 4. Assuming the bear turns left;

after taking another step the bear finds himself in a hallway where his left and right paws touch

a wall and he does not hit a wall. This corresponds to square 5 (1012). Although you could write

a 5 in this square, for the sake of brevity, I left it blank (your bear walks down a lot of hallways).

Notice that the numbers are based on the direction the bear is facing and not a universal

reference point, like facing north. This corresponds to the fact that within the maze our bear has

no idea where north, or any direction for that matter, is (our bear forgot his compass). So, let’s

continue to the next intersection. Here the bears left paw cannot touch a wall (0), he does not hit

a wall (0), and his right paw can touch a wall (1). We therefore would write a 1 (0012) in this

square. Continuing in this fashion all intersections are identified for our minimum solution.

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Shortest Path Solution

Using the naming convention and the shortest path through the maze presented in the last

section, lets design a solution for the shortest path.

Build a Truth Table

Here are all the possible squares our bear could encounter and a short description of the

situation he is facing.

Table 1 Shortest Path Solution

For your minimum solution your bear should encounter squares 1, 3, 4, 5, and 6. Once again we

did not include in our illustration situations where the bear has no choice (3 = left corner, 6 =

right corner, and 5 = hallway).

Draw your Flowchart - Solution for a Fully "Deterministic" Maze

A fully deterministic maze is one where for any given intersection the bear will always (it is

predetermined) take the same action. For example; for your puzzle solution, whenever the bear

encounters intersection 4 he will always turn right. For a non-deterministic maze he may turn

right one time and turn left another. If you look at our shortest solution to the maze you will

discover that it is fully deterministic, and so it lends itself to this simple solution.

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Figure 4 Shortest Path Solution

It is always a good idea to check your answer (or mine) to see if it actually teaches the bear how

to count the bees and find the shortest path out of the maze.

Once you have your flowchart, implementation in the C programming language or Assembly is

fairly straight forward.

Pre-lab Assignment In subsequent labs we will be working with the same bear in the same maze; however you will

all be mapping out and trying to teach your bear how to follow a different path. To help everyone

plot a unique path, you will need to locate your target square.

Find Your Target Square Write down the last four digits of your student ID and two 2-digit numbers. These digits will

provide the coordinates (row and column) of your target square. For example, if the last four

digits of your student ID were 7386, your two 2-digit numbers would be 73 and 86. Divide using

long division each number by 20 and write the remainder down. In our example, 20 divides into

73 three times with a remainder of 13 and into 86 four times with a remainder of 6. Next convert

both numbers into a base 16 (hexadecimal) number. For our example, 13 = 0x0D (where 0x

simple means a number in hexadecimal) and 6 = 0x06. Your target square would therefore be in

row 0x0D and column 0x06.

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How to Find Your Path Find a path through the maze such that:

1. The bear goes through the target square.

2. The bear must get lost at least once. Specifically, he must at some point turn-around.

This is typically, but does not need to be, at a dead end.

3. There are any number of paths that can take your bear through the target square, get

lost, and into the forest, you now want to find the one that results in the numbers of bees

encountered being closest to but not exceeding 15 (inclusive).

4. Finally, the maze must be non-deterministic. This means that at some intersection along

the path the bear will need to take a different action. For example, the first time he

encounters a T-intersection he turns left and the second time he turns right. The good

news is that, if your path meets the first three criteria, the odds are extremely high that it

will be non-deterministic.

Lets look at how you can develop a flowchart for your unique path.

Design Methodology for a “Non-deterministic” Maze As previously mentioned, most maze solutions are non-deterministic. The phrase “not fully

deterministic” means, while one set of input conditions in one part of the maze will determine

one action (go straight), in another part of the maze the exact same conditions will require a

different action (turn right). By looking at your truth-table you can recognize a “non-deterministic”

path as having two or more 1’s in the same row. A quick inspection of my truth table reveals

that, for the shortest path solution (Figure 4), the bear follows a fully deterministic path.

Specifically, for any given intersection the bear will always take the same action. For example, if

the bear’s left paw is touching a wall (1), he does not hit a wall (0), and his right paw is not

touching a wall (0), then the bear will always turn right. Following is one path that I will use to

illustrate how to solve a non-deterministic maze.

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Figure 5 Non-deterministic path example

Let’s begin by looking at the sequential actions that must be taken as we encounter each

intersection.

Table 2 Sensor input combinations and actions for non-deterministic path example.

The good news is that with the exception of square number 1 all other actions are deterministic.

The bad news is that only when we encounter room 1 after the second time do we start turning

left. To solve this more difficult problem, we will create a binary tree that allows us to resolve all

8 squares, allowing us to then take any action needed. This binary tree can now be easily

translated into C++ or Assembly.

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Figure 6 Flowchart showing binary tree solution to nondeterministic path example.

A Modular Solution

A more modular solution separates the identification of the square (referred to as a room) from

the action to be taken. Identification of the room is placed into a C++ or Assembly subroutine

which returns the room number. The calling program must then determine the action to be taken

based on the room number returned. The flowchart for the room subroutine is provide here and

once again easily implemented in C++ using if or switch conditional instructions as discussed in

the next lab.

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Figure 7 Flowchart of WhichRoom Subroutine

Step-by-Step Instructions Here are step-by-step instructions for solving your maze.

Begin by making a copy (electronic or paper) of the maze and drawing your bear’s path through

the maze. When you are happy with your new path, follow the methodology previously

discussed to build your truth table. Verify that your path meets the design criteria (intersects

target square while encountering the minimum number of bees). Remember, your target square

may not be along the original solution path.

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It is now time to teach your bear how to navigate the new path by writing a flow chart. To

accomplish your goal you will need to apply everything you have learned so far plus add a few

Notepad operations. The notepad pages (i.e., variables) are used to determine which path your

bear should take when he enters an intersection in which more than one action is possible. For,

example the first time he enters intersection 1 you may want the bear to go straight, while the

second time he encounters intersection 1 you want him to turn left. To resolve this conflict you

would record in your notepad how many times intersections 1 had been encountered and then

check your notepad before taking any action.

In addition to previously stated conditions, your solution must also meet the following negative

criteria.

1. Your solution may not use a variable (notepad) to simply count how many steps the bear

has taken in order to make a decision.

2. Your solution should use a variable(s) and not the number of bees encountered to help it

make a decision.

Deliverable for Pre-Lab 1 Turn in the following material on the following pages (i.e., no more, no less). All work must be

typed or neatly done in ink.

Page 1

At the top of the page provide the last four digits of your student ID and describe how you

calculated your target square. Include in your discussion how the resulting path met the design

requirements defined in the pre-lab. For example how many paths did you consider before

choosing your final path - how close did you come to 15.

Page 2

Next, using your favorite illustration (Visio, Illustrator, or Photoshop) program or the drawing

tools included with your favorite Office program (PowerPoint, Excel, and Word) mark your target

square with an X and illustrate your bear’s path through the maze (including the sensor input

combinations and actions table). Also include on this page a table of “Sensor input combinations

and actions” similar to Table 2.

Many drawing programs allow you to import a bitmap file, in this case the maze. You can find a

bitmap and vector formatted picture of the Maze in the Lab_02 folder (theMaze.bmp and

theMaze.ai). Once imported draw your path, typically using the line tool. Next, number your

intersections (but not corners or hallways) as illustrated in Figure 5 “Nondeterministic path

example.”

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Page 3

Again using your favorite drawing program, draw the flowchart for programming problem.

Your flowchart should resemble the one included with the lab and only use the provided

instructions. Artwork of the sample flowchart is included in Microsoft Visio format in the Lab_02

folder.

All labs should represent your own work - DO NOT COPY.

Checklist 1. Your pre-lab report includes a title page (Page 0) with your picture (one that will allow

me to match a name with a face). Title information includes lab number, your name,

today’s date, and the day your lab meets (Monday or Tuesday)

2. Pages are in the order specified (see Deliverable)

3. You do not have any extra pages

4. You describe how you arrived at your path.

5. Maze is not copied from another student (zero points)

6. Path is computer drawn.

7. Maze Path meets specified requirements.

8. Intersections are not drawn by hand and appear as shown in the example.

9. Intersection are numbered

10. Intersections are numbered correctly

11. Truth table

12. Truth table is on the same page as the maze

13. Truth table is typed

14. Truth table matches the maze

15. Flowchart

16. Flowchart matches your truth table

17. Flowchart is correct