COS 126 Conditionals, Loops, Arrays Programming Assignment

The goal of this assignment is to write five short Java programs to gain practice with loops, conditionals, and arrays.
The goal of this assignment is to write five short Java programs to gain practice with loops and conditionals.
1. Bits. Write a program Bits.java that takes an integer command-line argument n and uses a while loop to compute the number of times you need to divide n by 2 until it is strictly less than 1. Print the error message "Illegal input" if n is negative.
 % java Bits 0 % java Bits 8 0 4 % java Bits 1 % java Bits 16 1 5 % java Bits 2 % java Bits 1000 2 10 % java Bits 4 % java Bits -23 3 Illegal input 

This computes the number of bits in the binary representation of n, which also equals 1 + floor(log2 n) when n is positive. This quantity arises in information theory and the analysis of algorithms.

2. Boolean and integer variables. Write a program Ordered.java that takes three integer command-line arguments, x, y, and z. Define a boolean variable whose value is true if the three values are either in strictly ascending order (x < y < z) or in strictly descending order (x > y > z), and false otherwise.
% java Ordered 10 17 49
true

% java Ordered 49 17 10
true

% java Ordered 10 49 17
false

3. Type conversion and conditionals.   Several different formats are used to represent color. For example, the primary format for LCD displays, digital cameras, and web pages—known as the RGB format—specifies the level of red (R), green (G), and blue (B) on an integer scale from 0 to 255. The primary format for publishing books and magazines—known as the CMYK format—specifies the level of cyan (C), magenta (M), yellow (Y), and black (K) on a real scale from 0.0 to 1.0.

Write a program RGBtoCMYK.java that converts from RGB format to CMYK format. Read three integers red, green, and blue from the command line, and print the input red, green, and blue, then print the equivalent CMYK values using these formulas:

\begin{align*} \textrm{white} \;&=\; \max\{\, \textrm{red}/255, \, \textrm{green}/255, \, \textrm{blue}/255 \, \} \\ \textrm{cyan} \;&=\; \Bigl( \textrm{white}-\frac{\textrm{red}}{255} \Bigr) \;/\; \textrm{white} \\ \textrm{magenta} \;&=\; \Bigl(\textrm{white}-\frac{\textrm{green}}{255}\Bigr) \;/\; \textrm{white} \\ \textrm{yellow} \;&=\; \Bigl(\textrm{white}-\frac{\textrm{blue}}{255}\Bigr) \;/\; \textrm{white} \\ \textrm{black} \;&=\; 1 - \textrm{white} \end{align*}

Hint. Math.max(x, y) returns the maximum of x and y.
 % java RGBtoCMYK 75 0 130 // indigo red = 75 green = 0 blue = 130 cyan = 0.423076923076923 magenta = 1.0 yellow = 0.0 black = 0.4901960784313726  % java RGBtoCMYK 255 143 0 // Princeton orange red = 255 green = 143 blue = 0 cyan = 0.0 magenta = 0.4392156862745098 yellow = 1.0 black = 0.0 

If the red, green, and blue values are each 0, the resulting color is black. Here is what your program should do:

% java RGBtoCMYK 0 0 0       // black
red     = 0
green   = 0
blue    = 0
cyan    = 0.0
magenta = 0.0
yellow  = 0.0
black   = 1.0

4. Noon snooze. Write a program NoonSnooze.java that takes an integer command-line argument snooze and prints the time of day (using a 12-hour clock) that is snooze minutes after 12:00pm (noon).
% java NoonSnooze 50
12:50pm

% java NoonSnooze 100
1:40pm

% java NoonSnooze 720
12:00am

% java NoonSnooze 11111
5:11am


Note: you may assume that snooze is a nonnegative integer.

Hint: use the integer division and remainder operators.

5. Checkerboard. Write a program Checkerboard.java that takes an integer command-line argument n, and uses two nested for loops to print an n-by-n "checkerboard" pattern like the one below: a total of n2 asterisks, where each row has 2n characters (alternating between asterisks and spaces).
 % java Checkerboard 4 % java Checkerboard 5 * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 

6. A drunkard's walk. A drunkard begins walking aimlessly, starting at a lamp post. At each time step, the drunkard forgets where he or she is, and takes one step at random, either north, east, south, or west, with probability 25%. How far will the drunkard be from the lamp post after N steps?

1. Write a program RandomWalker.java that takes an integer command-line argument n and simulates the motion of a random walker for n steps. Print the location of the random walker at each step (including the starting point), treating the starting point as the origin (0, 0). Also, print the square of the final distance from the origin.
% java RandomWalker 10             % java RandomWalker 20
(0, 0)                            (0, 0)
(0, -1)                           (0, 1)
(0, 0)                            (-1, 1)
(0, 1)                            (-1, 2)
(0, 2)                            (0, 2)
(-1, 2)                           (1, 2)
(-2, 2)                           (1, 3)
(-2, 1)                           (0, 3)
(-1, 1)                           (-1, 3)
(-2, 1)                           (-2, 3)
(-3, 1)                           (-3, 3)
squared distance = 10             (-3, 2)
(-4, 2)
(-4, 1)
(-3, 1)
(-3, 0)
(-4, 0)
(-4, -1)
(-3, -1)
(-3, -2)
(-3, -3)
squared distance = 18


2. Write a program RandomWalkers.java that takes two integer command-line arguments n and trials. In each of trials independent experiments, simulate a random walk of n steps and compute the squared distance. Output the mean squared distance (the average of the trials squared distances).
% java RandomWalkers 100 10000         % java RandomWalkers 400 2000
mean squared distance = 101.446         mean squared distance = 383.12

% java RandomWalkers 100 10000         % java RandomWalkers 800 5000
mean squared distance = 99.1674         mean squared distance = 811.8264

% java RandomWalkers 200 1000         % java RandomWalkers 1600 100000
mean squared distance = 195.75          mean squared distance = 1600.13064


As n increases, we expect the random walker to end up farther and farther away from the origin. But how much farther? Use RandomWalkers to formulate a hypothesis as to how the mean squared distance grows as a function of n. Use trials = 100,000 trials to get a sufficiently accurate estimate.

Note: you should assume that n is a nonnegative integer and that trials is a positive integer.

This process is a discrete version of a natural phenomenon known as Brownian motion. It serves as a scientific model for an astonishing range of physical processes from the dispersion of ink flowing in water, to the formation of polymer chains in chemistry, to cascades of neurons firing in the brain.

7. Dice and the Gaussian distribution. Write a program TenDice.java that takes an integer command-line argument n, and rolls 10 fair six-sided dice, n times. Use an integer array to tabulate the number of times each possible total (between 10 and 60) occurs. Then print a text histogram of the results, as illustrated below.
 % java TenDice 1000 10: 11: 12: 13: 14: 15: 16: 17: 18: * 19: **** 20: 21: *** 22: ****** 23: ******** 24: **************** 25: ************* 26: ********** 27: ********************************* 28: **************************************** 29: ********************************* 30: *************************************************** 31: ***************************************************************** 32: ******************************************************** 33: ************************************************************************************** 34: *********************************************************** 35: ********************************************************************* 36: *********************************************************************************** 37: ************************************************************** 38: ***************************************************************** 39: *************************************** 40: ***************************************************** 41: ************************************ 42: **************************** 43: ************************ 44: ************************ 45: ********* 46: *********** 47: ******* 48: *** 49: ** 50: 51: 52: * 53: 54: 55: 56: 57: 58: 59: 60: 

Note: you should assume that n is a nonnegative integer.

The central limit theorem, a key result in probability and statistics, asserts that the shape of the resulting histogram tends to the ubiquitous bell curve (Gaussian distribution) if the number of dice and rolls is large.

Program style and format. Is your header complete? Did you comment appropriately? Is your code indented consistently? Did you use descriptive variable names? Is your code littered with magic numbers? Did you follow the input and output specifications? Are there any redundant conditions? Did you click the Check All Submitted Files button? Follow the guidelines in the Assignment FAQ.

Submission. Submit the files Bits.java, NoonSnooze.java, Ordered.java, RGBtoCMYK.java, Checkerboard.java, RandomWalker.java, RandomWalkers.java, TenDice.java, and a completed readme.txt file.

Challenge for the bored. Implement NoonSnooze.java without using any if statements; also, handle negative snooze times.