Description
1 Introduction
Consider a drunken sailor1
staggering about. Assume the sailor is initially located in the middle of a board
(plank) and can step either to the left or right. Given the board has a certain length and the sailor can take
a maximum number of steps, what is the probability he will fall off the board?
-3 -2 -1 0 1 2 3
1.1 The Odds of Falling
We are interested in determining the probability that the sailor will stagger (fall) off the board. A simple
method for determining the probability is to have a sailor do this many times (each time is considered an
experiment) and record the how often he falls. Of course, there is a limited supply of sailors in WinstonSalem area, so we’ll rely on simulating a staggering person. As done in lab 2, the probability of falling would
be the number of times the sailor falls divided by the total number of experiments performed. The more
experiments that are performed, the better the estimation.
The program will prompt the user for the board length (measured in steps), the maximum number of
steps to take, and the number of experiments. Note, the board length entered will be half of the actual length
minus one. Therefore if the user enters 3 for the board length, then the actual length is 7 (as seen above).
After the information is entered, your program will then run the number of experiments requested. For each
experiment, graphically display the steps of the sailor and the result. At the end of all the experiments,
display the total number of experiments, the number times the sailor fell, and the fall percentage (probability
estimation). An example of a board of length 3 (7 actual length), 5 maximum steps, and 2 experiments is
given below. Note this is only an example, not necessarily what you should expect.
✷ Terminal ✷✷
> ./lab3
Enter the board length, max number of steps and number of experiments -> 3 5 2
========
*
*
*
*
*
Sailor SAFE 🙂
========
*
*
*
Sailor FELL 🙁
After 2 experiments, sailor fell 1 time, fall percentage was 0.5%
1Of course the sailor is of age; regardless, we certainly don’t condone alcohol. Booooo alcohol! It only leads to staggering.
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2 Simulating a Drunken Stagger
Assume the board is divided into squares, where each square is a location the sailor can step. However,
remember the sailor can only move one square to the left or right per step. Assign each square a number,
where the middle square is zero, left squares are decreasing numbers, and right squares are increasing
numbers. This is seen in the figure on the first page.
The stagger of the sailor is simply randomly choosing a -1 or +1 per step and adding it to the current
position of the sailor (number of the square the sailor currently occupies). Remember the sailor will always
start a square zero (the middle of the board). If this number is ever less than the leftmost square, then the
sailor has fallen off the left edge. If this value is ever greater than the rightmost square, then the sailor has
fallen off the right edge. If the sailor has taken the maximum number of steps (specified by the user) and
remains on the board, then he has not fallen.
2.1 Programming Requirements for this Assignment
For this assignment, your program must at least consist of the following functions.
• readExperimentData is a function that will prompt the user and read the board length (measured in
steps), the maximum number of steps to take, and the number of experiments to make.
• drunkenWalk is a function that will simulate one complete experiment. The function should return if
the sailor fell.
• displayBoard is a function that will graphically display the current location of the sailor. The function
will print an underline (’ ’) for each board square except for the square where the sailor is located.
Print an asterisk (’*’) for the square where the sailor is located.
• outputExperimentStats is a function that will display the number of experiments, the number of
falls, and the percentage of falls.
• randStep is a function that will simulate a random step. The following function definition will simulate
a step by randomly generating the value -1 or +1, then returns the value using the function name.
int randStep()
{ return ( rand ()%2? -1:1); }
Where is the function rand() defined? It is defined in the cstdlib library, so you must add the
compiler directive #include to your program.
As a result, your main function will consist of variable declarations, function calls, and control structures
(loops). No output or input should be done in the main function.
3 Programming Points
You must adhere to all of the following points to receive credit for this lab assignment.
1. Create a directory Lab3 off of your CSC112 directory to store your program in a file called lab3.cpp
2. Your program must be modular in design and consist of the five functions described in Section 2.1.
3. Your main function can only consist of variable declarations, function calls, and control structures (no
input or output in the main function).
4. Your program must compile cleanly, no errors or warnings are allowed.
5. Pass variables appropriately. Only pass by reference when necessary.
6. Your program must adhere to documentation style and standards. Don’t forget function headers and
variable declarations.
7. Turn-in a print-out of your program source code (lab3.cpp). In addition, copy your program source
code to your Gade/Lab3 directory.
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