1.5   Input and Output

In this section we extend the set of simple abstractions (command-line input and standard output) that we have been using as the interface between our Java programs and the outside world to include standard input, standard draw, and standard audio. Standard input makes it convenient for us to write programs that process arbitrary amounts of input and to interact with our programs; standard draw makes it possible for us to work with graphics; and standard audio adds sound.

Bird's-eye view.

A Java program takes input values from the command line and prints a string of characters as output. By default, both command-line input and standard output are associated with the application that takes commands (the one in which you have been typing the java and javac commands). We use the generic term terminal window to refer to this application.

• Command-line input. All classes have a main() method that takes a String array as argument. That array is the sequence of command-line arguments that we type, provided to Java by the operating system. By convention, both Java and the operating system process the arguments as strings, so if we intend for an argument to be a number, we use a method such as Integer.parseInt() to convert it from String to the appropriate type.
• Standard output. To print output values in our programs, we have been using System.out.println(). Java sends the results to an abstract stream of characters known as standard output. By default, the operating system connects standard output to the terminal window - all of the output in our programs so far has been appearing in the terminal window.

RandomSeq.java uses this model: It takes a command-line argument N and produces an output sequence of random numbers between 0 and 1.

To complete our programming model, we add the following libraries:

• Standard input. Read numbers and strings from the user.
• Standard draw. Plot graphics.
• Standard audio. Create sound.

To use these libraries, download StdIn.java, StdOut.java, StdDraw.java, and StdAudio.java into the same directory as your program.

Standard output.

Java's print() and println() methods, invoked with System.out, implement the standard output abstraction that we need, but to treat standard input and standard output in a uniform manner, we use the methods defined in the following API:

The print() and println() methods are the ones that you have been using. The printf() method gives us more control over the appearance of the output.

• Formatted printing basics. In its simplest form, printf() takes two arguments. The first argument, a string, contains a format that describes how the second argument is to be converted to a string for output.

  

  Formats begin with % and end with a one-letter conversion code. The following table summarizes the most frequently used codes:

  

  This API documents all of the printf() conventions.
• Format string. The first argument of printf() is called the format string. Any part of the format string that is not part of a format is passed through to the output, with the format replaced by the argument value (converted to a string as specified). See the textbook for details.
• Multiple arguments. The printf() function can take more than two arguments. In this case, the format string will have a format specifier for each argument, perhaps separated by other characters to pass through to the output.

Standard input.

Our StdIn library supports an abstract data stream that may be empty or can contain a sequence of values separated by whitespace. Each value is a String or a value from one of Java's primitive types. One of the key features of the standard input stream is that your program consumes values when it reads them. Once your program has read a value, it cannot back up and read it again. The library is defined by the following API:

We now consider several examples in detail.

• Typing input. When you use the java command to invoke a Java program from the command line, you actually are doing three things: (i) issuing a command to start executing your program, (ii) specifying the values of the command-line arguments, and (iii) beginning to define the standard input stream. The string of characters that you type in the terminal window after the command line is the standard input stream. When you type characters, you are interacting with your program. The program waits for you to create the standard input stream. For example, AddInts.java takes an argument N from the command line, then reads N numbers from standard input and adds them:

  public class AddInts { public static void main(String[] args) { int N = Integer.parseInt(args[0]); int sum = 0; for (int i = 0; i < N; i++) sum += StdIn.readInt(); StdOut.println("Sum is " + sum); } }

  See the textbook for details.
• Input format. If you type abc or 12.2 or true when StdIn.readInt() is expecting an int, then it will respond with a NumberFormatException. StdIn treats strings of consecutive whitespace characters as identical to one space and allows you to delimit your numbers with such strings.
• Interactive user input. Program TwentyQuestions.java plays a simple guessing game. You type numbers, each of which is an implicit question (Is this the number?) and the program tells you whether your guess is too high or too low.
• Processing an infinite stream. Typically, input streams are finite: your program marches through the input stream, consuming values until the stream is empty. But there is no restriction of the size of the input stream. Average.java reads in a sequence of real numbers from standard input and prints their average.

Redirection and piping.

For many applications, typing input data as a standard input stream from the terminal window is untenable because doing so limits our program's processing power by the amount of data that we can type. Similarly, we often want to save the information printed on the standard output stream for later use. We can use operating system mechanisms to address both issues.

• Redirecting standard output to a file. By adding a simple directive to the command that invokes a program, we can redirect its standard output to a file, for permanent storage or for input to some other program at a later time. For example, the command

  

  specifies that the standard output stream is not to be printed in the terminal window, but instead is to be written to a text file named data.txt. Each call to StdOut.print() or StdOut.println() appends text at the end of that file. In this example, the end result is a file that contains 1,000 random values. No output appears in the terminal window: it goes directly into the file named after the > symbol. Thus, we can save away information for later retrieval.
• Redirecting standard output from a file. Similarly, we can redirect standard input so that StdIn reads data from a file instead of the terminal application. For example, the command

  

  reads a sequence of numbers from the file data.txt and computes their average value. Specifically, the < symbol is a directive to implement the standard input stream by reading from the file data.txt instead of by waiting for the user to type something into the terminal window. When the program calls StdIn.readDouble(), the operating system reads the value from the file. This facility to redirect standard input from a file enables us to process huge amounts of data from any source with our programs, limited only by the size of the files that we can store.
• Connecting two programs. The most flexible way to implement the standard input and standard output abstractions is to specify that they are implemented by our own programs! This mechanism is called piping. For example, the following command

  

  specifies that the standard output for RandomSeq and the standard input stream for Average are the same stream. That is, the result has the same effect as the following sequence of commands

  % java RandomSeq 1000 > data.txt % java Average < data.txt

  but the file data.txt is not needed.
• Filters. For many common tasks, it is convenient to think of each program as a filter that converts a standard input stream to a standard output stream in some way, with piping as the command mechanism to connect programs together. For example, MovingAverage.java takes a command-line argument N and prints on standard output a stream of numbers where each number in the output stream is the average of the N numbers starting at the corresponding position in the standard input stream.

  Your operating system also provides a number of filters. For example, the sort filter puts the lines on standard input in sorted order:

  % java RandomSeq 5 | sort 0.035813305516568916 0.14306638757584322 0.348292877655532103 0.5761644592016527 0.9795908813988247

  Another useful filter is more, which reads data from standard input and displays it in your terminal window one screenful at a time. For example, if you type

  % java RandomSeq 1000 | more

  you will see as many numbers as fit in your terminal window, but more will wait for you to hit the space bar before displaying each succeeding screenful.

Standard drawing.

Now we introduce a simple abstraction for producing drawings as output. We imagine an abstract drawing device capable of drawing lines and points on a two-dimensional canvas. The device is capable of responding to the commands that our programs issue in the form of calls to static methods in StdDraw. The primary interface consists of two kinds of methods: drawing commands that cause the device to take an action (such as drawing a line or drawing a point) and control commands that set parameters such as the pen size or the coordinate scales.

Here is the full StdDraw API.

• Basic drawing commands. We first consider the drawing commands:

  

  These methods are nearly self-documenting: StdDraw.line() draws a straight line segment connecting the point (x0, y0) with the point (x1 , y1) whose coordinates are given as arguments, StdDraw.point() draws a spot centered on the point (x, y) whose coordinates are given as arguments. The default coordinate scale is the unit square (all coordinates between 0 and 1). The standard implementation displays the canvas in a window on your computer's sceen, with black lines and points on a white background. The window includes a menu option to save your drawing to a file, in a format suitable for publishing on the Web.

  Your first drawing. The HelloWorld for graphics programming with StdDraw is to draw a triangle with a point inside. To draw the triangle, we draw three lines: one from the point (0, 0) at the lower left corner to the point (1, 0), one from that point to the third vertex at (1/2, sqrt(3)/2) and one from that point back to back to (0, 0). As a final flourish, we draw a spot in the middle of the triangle. Program Triangle.java contains the full program.

  double t = Math.sqrt(3.0)/2.0; StdDraw.line(0.0, 0.0, 1.0, 0.0); StdDraw.line(1.0, 0.0, 0.5, t); StdDraw.line(0.5, t, 0.0, 0.0); StdDraw.point(0.5, t/3.0);

• Control commands. The coordinate system that we use to communicate with the drawing device is the unit square, but we often want to draw plots at different scales. Also, we often want to draw lines of different thickness and points of different size than the standard. To accommodate these needs, StdDraw has the following methods:

  

  For example, when we issue the command StdDraw.setXscale(0, N), we are telling the drawing device that we will be using x-coordinates between 0 and N. Note that the two-call sequence

  StdDraw.setXscale(x0, x1); StdDraw.setYscale(y0, y1);

  sets the drawing coordinates to be within a bounding box whose lower left corner is at (x0, y0) and whose upper right corner is at (x1, y1).
  • Filtering data to a standard drawing. PlotFilter.java reads a sequence of points defined by (x, y) coordinates from standard input and draws a spot at each point. It adopts the convention that the first four numbers on standard input specify the bounding box, so that it can scale the plot.

    % java PlotFilter < USA.txt
    
    

  • Plotting a function graph. FunctionGraph.java plots the function y = sin(4x) + sin(20x) in the interval (0, π). There are an infinite number of points in the interval, so we have to make do with evaluating the function at a finite number of points within the interval. We sample the function by choosing a set of x values, then computing y values by evaluating the function at each x value. Plotting the function by connecting successive points with lines produces what is known as a piece-wise linear approximation.

    

• Outline and filled shapes. StdDraw also includes methods to draw circles, rectangles, and arbitrary polygons. Each shape defines an outline. When the method name is just the shape name, that outline is traced by the drawing pen. When the method name begins with filled, the named shape is instead filled solid, not traced. As usual, we summarize the available methods in an API:

  

  The arguments for circle() and define a circle of radius r; the arguments for square() define a square of side length 2r centered on the given point; and the arguments for polygon() define a sequence of points that we connect by lines, including one from the last point to the first point.

  

• Text and color. To annotate or highlight various elements in your drawings, StdDraw includes methods for drawing text, setting the font, and setting the the ink in the pen.

  

  In this code, Font and Color are abstractions that are implemented with non-primitive types that you will learn about in Section 3.1. Until then, we leave the details to StdDraw. The default ink color is black; the default font is a 16-point plain Serif font.
• Animation. The StdDraw library has two additional methods that we can use to produce the effect of motion on the screen.

  

  The HelloWorld of animation is to produce a black ball that appears to move around on the canvas. Suppose that the ball is at position (x, y) and we want to create the impression of having it move to a new position, say (x + .01, y + .02). We do so in two steps:
  • Calculate the position of the ball.
  • Clear the screen.
  • Draw the ball at its new position.
  • Pause for a short while.

  To create the illusion of movement, we would like to iterate these steps for a whole sequence of positions (that would form a straight line, in this case). Accordingly, StdDraw has a show() method that allows us to control when the result of drawing actions are actually shown on the display. You can think of it collecting all of the lines, points, shapes, and text that we tell it to draw and then immediately drawing them all when we issue the show() command. To control the apparent speed, show() takes an argument telling StdDraw to wait the given number of milliseconds after doing the drawing. By default, StdDraw issues a show() after each line(), point(), or other drawing command; we turn that option off when we call StdDraw.show(t) and turn it back on when we call StdDraw.show() with no arguments.

  BouncingBall.java implements these steps to create the illusion of a ball moving in the box of side length 2, centered on the origin. The current position of the ball is given by (rx, ry) and it the new position at each step is computed by adding vx to rx and vy to ry. Since (vx, vy) is the fixed distance that the ball moves in each time unit, it represents the velocity. To keep the ball in the drawing, we simulate the effect of the ball bouncing off the walls according to the laws of elastic collision. This effect is easy to implement: when the ball hits a vertical wall, we just change the velocity in the x-direction from vx to -vx and when the ball hits a horizontal wall, we change the velocity in the y-direction from vy to -vy. The images below, which show the track of the ball, are produced by a modified version of this code (see Exercise 1.5.34).

  

• Images. Our standard draw library supports drawing pictures as well as geometric shapes. The command StdDraw.picture(x, y, filename) plots the image in the given filename (either JPEG, GIF, or PNG format) on the canvas, centered on (x, y). DeluxeBouncingBall.java illustrates an example where the bouncing ball is replaced by an image of the earth.
• User interaction. Our standard draw library also includes methods so that the user can interact with the window using the mouse.

  double mouseX() return x coordinate of mouse double mouseY() return y coordinate of mouse boolean mousePressed() is the mouse currently being pressed?

  • A first example. MouseFollower.java is the HelloWorld of mouse interaction. It draws a blue ball, centered on the location of the mouse. When the user holds down the mouse button, the ball changes color from blue to cyan.
  • A simple attractor. OneSimpleAttractor.java simulates the motion of a blue ball that is attracted to the mouse. It also accounts for a drag force.
  • Many simple attractors. SimpleAttractors.java simulates the motion of 20 blue balls that are attracted to the mouse. It also accounts for a drag force. When the user clicks, the balls disperse randomly.
  • Springs. Springs.java implements a spring system.

Standard audio.

StdAudio is a library that you can use to play and manipulate sound files. It allows you to play .wav files, to write programs to create and manipulate arrays of double values, and to read and write them as .wav files:

We first introduce some some basic concepts behind one of the oldest and most important areas of computer science and scientific computing, which is known as digital signal processing.

• Concert A. Sound is the vibration of matter that we perceive, in particular, by the vibration of our eardrums, so oscillation is the key to understanding sound. Perhaps the simplest place to start is to consider the musical note A above middle C, which is known as concert A. This note is nothing more than a sine wave, scaled to oscillate at a frequency of 440 times per second. The function sin(t) repeats itself once every 2π units on the x axis, so if we measure t in seconds and plot the function sin(2πt × 440) we get a curve that oscillates 440 times per second. We measure frequency in hertz (cycles per second). When you double or halve the frequency, you move up or down an octave on the scale. For example 880 hertz is one octave above concert A and 110 hertz is two octaves below concert A. For reference, the frequency range of human hearing is about 20 to 20,000 hertz.The amplitude (y value) corresponds to the volume. We assume it is scaled to be between -1 and +1. The following code fragment plays concert A for 1 second.

  int SAMPLE_RATE = 44100; double[] a = new double[SAMPLE_RATE + 1]; for (int i = 0; i <= SAMPLE_RATE; i++) { a[i] = Math.sin(2 * Math.PI * i * 440 / SAMPLE_RATE); } StdAudio.play(a);

• Other notes. A simple mathematical formula characterizes the other notes on the chromatic scale. They are divided equally on a logarithmic (base 2) scale: there are twelve notes on the chromatic scale, and we get the i th note above a given note by multiplying its frequency by the (i/12)th power of 2. In other words, the frequency of each note in the chromatic scale is precisely the frequency of the previous note in the scale multiplied by the twelfth root of two. This information suffices to create music! For example, to play the tune Frere Jacques, we just need to play each of the notes A B C A by producing sine waves of the appropriate frequency for about half a second each and then repeat the pattern.

  

• Sampling. For digital sound, we represent a curve by sampling it at regular intervals, in precisely the same manner as when we plot function graphs. We sample sufficiently often that we have an accurate representation of the curve - a widely used sampling rate for digital sound is 44,100 samples per second. For concert A, that rate corresponds to plotting each cycle of the sine wave by sampling it at about 100 points. Since we sample at regular intervals, we only need to compute the y coordinates of the sample points. It is that simple: we represent sound as an array of numbers (double values that are between -1 and +1).

• Play that tune. PlayThatTune.java is an example that shows how easily we can create music with StdAudio. It takes notes from standard input, indexed on the chromatic scale from concert A, and plays them on standard audio.

Graphical user interfaces.

A graphical user interface (GUI) is.... Swing is Java's built-in library of GUI widgets. It includes primitives for creating buttons, menus, scrollbars, and many other common graphical components that everyday applications (browser, email client, word processor) use. The text editor JEdit that you have been using to write your programs is written in Java. We will defer interactive graphics until later, but just to give you an idea of what is possible, GUI.java is a bare-bones Java program that contains a clickable button. Each operating system displays the program using its own look-and-feel to blend in with native applications. Below is the same program under Windows XP and Mac OS X.

Standard draw 3D.

The library StdDraw3D supports 3D graphics.

Standard Libraries

Standard libraries.

Below is a table of the input and output libraries that we use throughout the textbook and beyond. The API documentation of the Stdlib is here.

§	PROGRAM	DESCRIPTION / JAVADOC
1.5	StdIn.java	read numbers and text from standard input
1.5	StdOut.java	write numbers and text to standard output
1.5	StdDraw.java	draw geometric shapes in a window
1.5	StdAudio.java	create, play, and manipulate sound
2.2	StdRandom.java	generate random numbers
2.2	StdStats.java	compute statistics
2.2	StdArrayIO.java	read and write 1D and 2D arrays
3.1	In.java	read numbers and text from files and URLs
3.1	Out.java	write numbers and text to files
3.1	Draw.java	draw geometric shapes
3.1	Picture.java	process digital images
3.2	Stopwatch.java	measure running time
–	BinaryStdIn.java	read bits from standard input
–	BinaryStdOut.java	write bits to standard output
–	BinaryIn.java	read bits from files and URLs
–	BinaryOut.java	write bits to files
–	StdDraw3D.java	3D graphics

 

 

Using the standard libraries.

The file stdlib.jar bundles together all of our standard libraries into one file. There are a number of ways to access the libraries:

• Current directory. The easiest (but not the sanest) way to use the standard libraries to download stdlib.jar and unjar it in your current working directory.

  % jar xf stdlib.jar

  Alternatively, you can download the individual .java files you need (such as StdIn.java) and put them in the same directory as the program you are writing. Then, compile and execute as usual.

  % javac MyProgram.java % java  MyProgram

  This approach has the drawback that you need a copy of each .java file you need in each directory where you need it.

• Classpath. Put stdlib.jar in the same directory as the program you are writing (but do not unjar it). Then, compile and execute as follows:

  Windows ------------ % javac -cp .;stdlib.jar MyProgram.java % java  -cp .;stdlib.jar MyProgram OS X / Linux ------------ % javac -cp .:stdlib.jar MyProgram.java % java  -cp .:stdlib.jar MyProgram

  The -cp flag sets the classpath. The . tells Java to look in the current directory for .java and .class files (such as MyProgram.java and MyProgram.class). The stdlib.jar tells Java to also look in the .jar file. On OS X, the : separates directories in the classpath; on Windows the ; separates directories.

• Configure your IDE. You can configure your IDE to automatically include stdlib.jar in the classpath. In DrJava, it is Preferences -> Extra Classpath -> Add.

Standard input and standard output.

StdIn.java and StdOut.java are libraries for reading in numbers and text from standard input and printing out numbers and text to standard output. Our versions have a simpler interface than the corresponding Java ones (and provide a few tecnical improvements). Average.java reads in a sequence of real numbers from standard input and prints their average on standard output.

% java Average 10.0 5.0 6.0 3.0 7.0 32.0 3.14 6.67 17.71 <Ctrl-d> Average is 10.05777777777778

In.java and Out.java are object-oriented versions that support multiple input and output streams, including reading from a file or URL and writing to a file. Wget.java reads in data from the URL specified on the command line and save it in a file with the same name.

% java Wget http://www.cs.princeton.edu/IntroProgramming/datafiles/codes.csv % more codes.csv United States,USA,00 Alabama,AL,01 Alaska,AK,02 ...

 

Binary standard input and standard output.

BinaryStdIn.java and BinaryStdOut.java are the analogs for binary data. Copy.java reads a binary file from standard input and writes it to standard output.

% java Copy < mandrill.jpg > copy.jpg % diff mandrill.jpg copy.jpg

 

Standard drawing.

StdDraw.java is an easy-to-use library for drawing geometric shapes, such as points, lines, and circles. RightTriangle.java draws a right triangle and a circumscribing circle.

  % java RightTriangle

BouncingBall.java illustrates how to produce an animation using standard drawing.

Draw.java is an object-oriented versions that support drawing in multiple windows.

Standard audio.

StdAudio.java is an easy-to-use library for synthesizing sound. Tone.java reads in a frequency and duration from the command line, and it sonifies a sine wave of the given frequency for the given duration.

% java Tone 440.0 3.0

Image processing.

Picture.java is an easy-to-use library for image processing. Scale.java takes the name of a picture file and two integers (width w and height h) as command-line arguments and scales the image to w-by-h.

% java Scale mandrill.jpg 298 298

% java Scale mandrill.jpg 200 200

% java Scale mandrill.jpg 200 400

Q + A

Q. How can I create an animated GIF?

A. Currently our graphics library does not support saving animated file formats like MPEG, animated GIF, or AVI. However, with an external utility (e.g., ImageMagick) the process is not difficult, and we have used it to create some of the animations on this booksite. The idea is to use StdDraw.save() to save a sequence of PNG files named frame100.png, frame101.png, frame102.png, and so on. Assuming ImageMagick is installed (Unix, Linux, OS X, and Windows are all supported) you can use the command

convert -delay 10 -loop 5 T*.png duke.gif

The convert program stitches together the frames (in lexicographic order), displays them every 10 milliseconds (ten per second), and repeats the loop 5 times.

Q. If I use a named package to structure my code, the compiler can no longer access the libraries in stdlib.jar. Why not?

A. The libraries in stdlib.jar are in the "default" package. In Java, you can't access classes in the default package from a named package. If you need to use our standard libraries with a named package, you must put our libraries in a package, as in this solution.

Exercises

1. Write a program MaxMin.java that reads in integers (as many as the user enters) from standard input and prints out the maximum and minimum alues.
2. Modify your program from the previous exercise to insist that the integers must be positive (by prompting the user to enter positive integers whenever the value entered is not positive).
3. Write a program Stats.java that takes an integer N from the command line, reads N double values from standard input, and prints their mean (average value) and standard deviation (square root of the sum of the squares of their differences from the average, divided by N - 1).
4. Extend your program from the previous exercise to create a filter that prints all the values that are further than 1.5 standard deviations from the mean.
5. Write a program LongestRun.java that reads in a sequence of integers and prints out both the integer that appears in a longest consecutive run and the length of the run. For example, if the input is 1 2 2 1 5 1 1 7 7 7 7 1 1, then your program should print Longest run: 4 consecutive 7s.
6. Write a filter that reads in a sequence of integers and prints out the integers, removing repeated values that appear consecutively. For example, if the input is 1 2 2 1 5 1 1 7 7 7 7 1 1 1 1 1 1 1 1 1, your program should print out 1 2 1 5 1 7 1.
7. Write a program that takes a command-line argument N, reads in N-1 distinct integers between 1 and N, and determines the missing value.
8. Write a program GeometricMean.java that reads in positive real numbers from standard input and prints out their geometric mean. The geometric mean of N positive numbers x₁, x₂, ..., x_N is (x₁ * x₂ * ... * x_N)^1/N. Write a program HarmonicMean.java that reads in positive real numbers from standard input and prints out their harmonic mean. The harmonic mean of N positive numbers x₁, x₂, ..., x_N is (1/x₁ + 1/x₂ + ... + 1/x_N) / (1 / N).

   Hint: for the geometric mean, consider taking logs to avoid overflow.

9. Suppose that the file input.txt contains the two strings F and F. What does the following command do? Here is the Java program Dragon.java.

   java Dragon < input.txt | java Dragon | java Dragon

10. Write a filter TenPerLine.java that takes a sequence of integers between 0 and 99 and prints 10 integers per line, with columns aligned. Then write a program RandomIntSeq that takes two command-line arguments M and N and outputs N random integers between 0 and M-1. Test your programs with the command java RandomIntSeq 200 100 | java TenPerLine.
11. Write a program WordCount.java that reads in text from standard input and prints out the number of words in the text. For the purpose of this exercise, a word is a sequence of non-whitespace characters that is surrounded by whitespace.
12. Write a program that reads in lines from standard input with each line containing a name and two integers and then uses printf() to print a table with a column of the names, the integers, and the result of dividing the first by the second, accurate to three decimal places. You could use a program like this to tabulate batting averages for baseball players or grades for students.
13. Which of the following require saving all the values from standard input (in an array, say), and which could be implemented as a filter using only a fixed number of variables? For each, the input comes from standard input and consists of N real numbers between 0 and 1.
    • Print the maximum and minimum numbers.
    • Print the kth smallest value.
    • Print the sum of the squares of the numbers.
    • Print the average of the N numbers.
    • Print the percentage of numbers greater than the average.
    • Print the N numbers in increasing order.
    • Print the N numbers in random order.
14. Write a program that prints a table of the monthly payments, remaining principal, and interest paid for a loan, taking three numbers as command-line arguments: the number of years, the principal, and the interest rate (see Exercise 1.2.24).
15. Write a program Closest.java that takes three command-line arguments x, y, z, reads from standard input a sequence of point coordinates (x_i, y_i, z_i), and prints the coordinates of the point closest to (x, y, z). Recall that the square of the distance between (x, y, z) and (x_i, y_i, z_i) is (x - x_i)² + (y - y_i)² + (z - z_i)². For efficiency, do not use Math.sqrt() or Math.pow().
16. Given the positions and masses of a sequence of objects, write a progrm to compute their center-of-mass or centroid. The centroid is the average position of the N objects, weighted by msass. If the positions and masses are given by (x_i, y_i, m_i), then the centroid (x, y, m) is given by:

    m = m1 + m2 + ... + mN x = (m1x1 + ... + mnxN) / m y = (m1y1 + ... + mnyN) / m

    Write a program Centroid.java that reads in a sequence of positions and masses (x_i, y_i, m_i) from standard input and prints out their center of mass (x, y, m). Hint: model your program after Average.java.

17. Write a program SignalAnalyzer.java that reads in a sequence of real numbers between -1 and 1 and prints out their average magnitude, average power, and the number of zero crossings. The average magnitude is the average of the absolute values of the data values. The average power is the average of the squares of the data values. The number of zero crossings is the number of times a data value transitions from a strictly negative number to a strictly positive number, or vice versa. These three statistics are widely used to analyze digital signals.
18. Write a program CheckerBoard.java that takes a command-line argument N and plots an N-by-N checkerboard with red and black squares. Color the lower left square red.

19. Write a program that takes as command-line arguments an integer N and a double value p (between 0 and 1), plots N equally spaced points of size on the circumference of a circle, and then, with probability p for each pair of points, draws a gray line connecting them.

20. Write code to draw hearts, spades, clubs, and diamonds. To draw a heart, draw a diamond, then attach two semicircles to the upper left and upper right sides.
21. Write a program Rose.java that takes a command-line argument N and plots a rose with N petals (if N is odd) or 2N petals (if N is even) by plotting the polar coordinates (r, θ) of the function r = sin(N × θ) for θ ranging from 0 to 2π radians. Below is the desired output for N = 4, 7, and 8.

22. Write a program Banner.java that takes a string s from the command line and display it in banner style on the screen, moving from left to right and wrapping back to the beginning of the string as the end is reached. Add a second command-line argument to control the speed.
23. Modify PlayThatTune.java to take additional command-line arguments that control the volume (multiply each sample value by the volume) and the tempo (multiply each notes duration by the tempo).
24. Write a program that takes the name of a .wav file and a playback rate r as command-line arguments and plays the file at the given rate. First, use StdAudio.read() to read the file into an array a[]. If r = 1, just play a[]; otherwise create a new array b[] of approximate size r times a.length. If r < 1, populate b[] by sampling from the original; if r > 1, populate b[] by interpolating from the original. Then play b[].
25. Write programs that uses StdDraw to create each of the following designs.

    

26. Write a program Circles.java that draws filled circles of random size at random positions in the unit square, producing images like those below. Your program should take four command-line arguments: the number of circles, the probability that each circle is black, the minimum radius, and the maximum radius.
27. Visualizing audio. Modify PlayThatTune.java to send the values played to standard drawing, so that you can watch the sound waves as they are played. You will have to experiment with plotting multiple curves in the drawing canvas to synchronize the sound and the picture.
28. Statistical polling. When collecting statistical data for certain political polls, it is very important to obtain an unbiased sample of registered voters. Assume that you have a file with N registered voters, one per line. Write a filter that prints out a random sample of size M.
29. Terrain analysis. Suppose that a terrain is represented by a two-dimensional grid of elevation values (in meters). A peak is a grid point whose four neighboring cells (left, right, up, and down) have strictly lower elevation values. Write a program Peaks.java that reads a terrain from standard input and then computes and prints the number of peaks in the terrain.
30. Histogram. Suppose that the standard input stream is a sequence of double values. Write a program that takes an integer N and two double values l and r from the command line and uses StdDraw to plot a histogram of the count of the numbers in the standard input stream that fall in each of the N intervals defined by dividing (l , r) into N equal-sized intervals.
31. Spirographs. Write a program Spirograph.java that takes three command-line arguments R, r, and a and draws the resulting spirograph. A spirograph (technically, an epicycloid) is a curve formed by rolling a circle of radius r around a larger fixed circle or radius R. If the pen offset from the center of the rolling circle is (r+a), then the equation of the resulting curve at time t is given by

    x(t) = (R+r)*cos(t) - (r+a)*cos(((R+r)/r)*t) y(t) = (R+r)*sin(t) - (r+a)*sin(((R+r)/r)*t)

    Such curves were popularized by a best-selling toy that contains discs with gear teeth on the edges and small holes that you could put a pen in to trace spirographs.

    For a dramatic 3d effect, draw a circular image, e.g., earth.gif instead of a dot, and show it rotating over time. Here's a picture of the resulting spirograph when R = 180, r = 40, and a = 15.

32. Clock. Write a program Clock.java that displays an animation of the second, minute, and hour hands of an analog clock. Use the method StdDraw.show(1000) to update the display roughly once per second.

    Hint: this may be one of the rare times when you want to use the % operator with a double - it works the way you would expect.

33. Oscilloscope. Write a program Oscilloscope.java to simulate the output of an oscilloscope and produce Lissajous patterns. These patterns are named after the French physicist, Jules A. Lissajous, who studied the patterns that arise when two mutually perpendicular periodic disturbances occur simultaneously. Assume that the inputs are sinusoidal, so tha the following parametric equations describe the curve:

    x = Ax sin (wxt + θx) y = Ay sin (wyt + θy) Ax, Ay = amplitudes wx, wy = angular velocity θx, θy = phase factors

    Take the six parameters A_x, w_x, θ_x, θ_y, w_y, and θ_y from the command line.

    For example, the first image below has Ax = Ay = 1, w_x = 2, w_y = 3, θ_x = 20 degrees, θ_y = 45 degrees. The other has parameters (1, 1, 5, 3, 30, 45)

34. Bouncing ball with tracks. Modify BouncingBall.java to produce images like the ones shown in the text, which show the track of the ball on a gray background.
35. Bouncing ball with gravity. Modify BouncingBall.java to incorporate gravity in the vertical direction. Add calls to StdAudio.play() to add one sound effect when the ball hits a wall and a different one when it hits the floor.
36. Random tunes. Write a program that uses StdAudio to play random tunes. Experiment with keeping in key, assigning high probabilities to whole steps, repetition, and other rules to produce reasonable melodies.
37. Tile patterns. Write a program TilePattern that takes a command-line argument N and draws an N-by-N pattern, using the tile of your choice. Add a second command-line argument that adds a checkerboard option. Add a third command-line argument for color selection. Using the patterns below as a starting point, design a tile floor. Be creative!

    

    Note: These are all designs from antiquity that you can find in many ancient (and modern) buildings such as from from San Giovanni in Laterno (Basilica of St. John Latern) in Rome [ 1 2 3 4 5 6 ] or from the Tile Museum in Lisbon [ 1 2 3 4 5 6 7 8 9 10 ]

38. Word and line count. Modify WordCount.java so that reads in text from standard input and prints out the number of characters, words, and lines in the text.
39. Rainfall problem. Write a program Rainfall.java that reads in nonnegative integers (representing rainfall) one at a time until 999999 is entered, and then prints out the average of value (not including 999999).
40. Remove duplicates. Write a program Duplicates.java that reads in a sequence of integers and prints back out the integers, except that it removes repeated values if they appear consecutively. For example, if the input is 1 2 2 1 5 1 1 7 7 7 7 1 1, your program should print out 1 2 1 5 1 7 1.
41. Run length encoding. Write a program RunLengthEncoder.java that encodes a binary input using run length encoding. Write a program RunLengthDecoder.java that decodes a run length encoded message.
42. Head and tail. Write programs Head.java and Tail.java that take an integer command line input N and print out the first or last N lines of the given file. (Print the whole file if it consists of <= N lines of text.)
43. Print a random word. Read a list of N words from standard input, where N is unknown ahead of time, and print out one of the N words uniformly at random. Do not store the word list. Instead, use Knuth's method: when reading in the ith word, select it with probability 1/i to be the selected word, replacing the previous champion. Print out the word that survives after reading in all of the data.
44. Caesar cipher. Julius Caesar sent secret messages to Cicero using a scheme that is now known as a Caesar cipher. Each letter is replaced by the letter k positions ahead of it in the alphabet (and you wrap around if needed). The table below gives the Caesar cipher when k = 3.

    Original: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Caesar: D E F G H I J K L M N O P Q R S T U V W X Y Z A B C

    For example the message "VENI, VIDI, VICI" is converted to "YHQL, YLGL, YLFL". Write a program Caesar.java that takes a command-line argument k and applies a Caesar cipher with shift = k to a sequence of letters read from standard input. If a letter is not an uppercase letter, simply print it back out.

45. Caesar cipher decoding. How would you decode a message encrypted using a Caesar cipher? Hint: you should not need to write any more code.
46. Parity check. A Boolean matrix has the parity property when each row and each column has an even sum. This is a simple type of error-correcting code because if one bit is corrupted in transmission (bit is flipped from 0 to 1 or from 1 to 0) it can be detected and repaired. Here's a 4 x 4 input file which has the parity property:

    1 0 1 0 0 0 0 0 1 1 1 1 0 1 0 1

    Write a program ParityCheck.java that takes an integer N as a command line input and reads in an N-by-N Boolean matrix from standard input, and outputs if (i) the matrix has the parity property, or (ii) indicates which single corrupted bit (i, j) can be flipped to restore the parity property, or (iii) indicates that the matrix was corrupted (more than two bits would need to be changed to restore the parity property). Use as little internal storage as possible. Hint: you do not even have to store the matrix!

47. Takagi's function. Plot Takagi's function: everywhere continuous, nowhere differentiable.
48. Hitchhiker problem. You are interviewing N candidates for the sole position of American Idol. Every minute you get to see a new candidate, and you have one minute to decide whether or not to declare that person the American Idol. You may not change your mind once you finish interviewing the candidate. Suppose that you can immediately rate each candidate with a single real number between 0 and 1, but of course, you don't know the rating of the candidates not yet seen. Devise a strategy and write a program AmericanIdol that has at least a 25% chance of picking the best candidate (assuming the candidates arrive in random order), reading the 500 data values from standard input.

    Solution: interview for N/2 minutes and record the rating of the best candidate seen so far. In the next N/2 minutes, pick the first candidate that has a higher rating than the recorded one. This yields at least a 25% chance since you will get the best candidate if the second best candidate arrives in the first N/2 minutes, and the best candidate arrives in the final N/2 minutes. This can be improved slightly to 1/e = 0.36788 by using essentially the same strategy, but switching over at time N/e.

49. Nested diamonds. Write a program Diamonds.java that takes a command line input N and plots N nested squares and diamonds. Below is the desired output for N = 3, 4, and 5.

50. Regular polygons. Create a function to plot an N-gon, centered on (x, y) of size length s. Use the function to draws nested polygons like the picture below.

    

51. Bulging squares. Write a program BulgingSquares.java that draws the following optical illusion from Akiyoshi Kitaoka The center appears to bulge outwards even though all squares are the same size.

    

52. Spiraling mice. Suppose that N mice that start on the vertices of a regular polygon with N sides, and they each head toward the nearest other mouse (in counterclockwise direction) until they all meet. Write a program to draw the logarithmic spiral paths that they trace out by drawing nested N-gons, rotated and shrunk as in this animation.
53. Spiral. Write a program to draw a spiral like the one below.

54. Globe. Write a program Globe.java that takes a real command-line argument α and plots a globe-like pattern with parameter α. Plot the polar coordinates (r, θ) of the function f(θ) = cos(α × θ) for θ ranging from 0 to 7200 degrees. Below is the desired output for α = 0.8, 0.9, and 0.95.

55. Drawing strings. Write a program RandomText.java that takes a string s and an integer N as command line inputs, and writes the string N times at a random location, and in a random color.

    
    

56. 2D random walk. Write a program RandomWalk.java to simulate a 2D random walk and animate the results. Start at the center of a 2N-by-2N grid. The current location is displayed in blue; the trail in white.

57. Rotating table. You are seated at a rotating square table (like a lazy Susan), and there are four coins placed in the four corners of the table. Your goal is to flip the coins so that they are either all heads or all tails, at which point a bell rings to notify you that you are done. You may select any two of them, determine their orientation, and (optionally) flip either or both of them over. To make things challenging, you are blindfolded, and the table is spun after each time you select two coins. Write a program RotatingTable.java that initializes the coins to random orientations. Then, it prompts the user to select two positions (1-4), and identifies the orientation of each coin. Next, the user can specify which, if any of the two coins to flip. The process repeats until the user solves the puzzle.
58. Rotating table solver. Write another program RotatingTableSolver.java to solve the rotating table puzzle. One effective strategy is to choose two coins at random and flip them to heads. However, if you get really unlucky, this could take an arbitrary number of steps. Goal: devise a strategy that always solves the puzzle in at most 5 steps.

59. Hex. Hex is a two-player board game popularized by John Nash while a graduate student at Princeton University, and later commercialized by Parker Brothers. It is played on a hexagonal grid in the shape of an 11-by-11 diamond. Write a program Hex.java that draws the board.
60. Projectile motion with drag. Write a program BallisticMotion.java that plots the trajectory of a ball that is shot with velocity v at an angle theta. Account for gravitational and drag forces. Assume that the drag force is proportional to the square of the velocity. Using Newton's equations of motions and the Euler-Cromer method, update the position, velocity, and acceleration according to the following equations:

    v = sqrt(vx*vx + vy*vy) ax = - C * v * vx ay = -G - C * v * vy vx = vx + ax * dt vy = vy + ay * dt x = x + vx * dt y = y + vy * dt

    Use G = 9.8, C = 0.002, and set the initial velocity to 180 and the angle to 60 degrees.

61. Heart. Write a program Heart.java to draw a pink heart: Draw a diamond, then draw two circles to the upper left and upper right sides.

    

62. Changing square. Write a program that draws a square and changes its color each second.
63. Simple harmonic motion. Repeat the previous exercise, but animate the Lissajous patterns as in this applet. Ex: A = B = w_x = w_y = 1, but at each time t draw 100 (or so) points with φ_x ranging from 0 to 720 degrees, and φ_x ranging from 0 to 1080 degrees.
64. Bresenham's line drawing algorithm. To plot a line segment from (x1, y1) to (x2, y2) on a monitor, say 1024-by-1024, you need to make a discrete approximation to the continuous line and determine exactly which pixels to turn on. Bresenham's line drawing algorithm is a clever solution that works when the slope is between 0 and 1 and x1 < x2.

    int dx = x2 - x1; int dy = y2 - y1; int y = y1; int eps = 0; for (int x = x1; x <= x2; x++) { StdDraw.point(x, y); eps += dy; if (2*eps >= dx) { y++; eps -= dx; } }

65. Modify Bresenham's algorithm to handle arbitrary line segments.
66. Miller's madness. Write a program Madness.java to plot the parametric equation:

    x = sin(0.99 t) - 0.7 cos( 3.01 t) y = cos(1.01 t) + 0.1 sin(15.03 t)

    where the parameter t is in radians. You should get the following complex picture. Experiment by changing the parameters and produce original pictures.
67. Fay's butterfly. Write a program Butterfly.java to plot the polar equation:

    r = e^(cos t) - 2 cos(4t) + (sin(t/12)^5)

    where the parameter t is in radians. You should get an image like the following butterfly-like figure. Experiment by changing the parameters and produce original pictures.

    

68. Student database. The file students.txt contains a list of students enrolled in an introductory computer science class at Princeton. The first line contains an integer N that specifies the number of students in the database. Each of the next N lines consists of four pieces of information, separated by whitespace: first name, last name, email address, and section number. The program Students.java reads in the integer N and then N lines of data of standard input, stores the data in four parallel arrays (an integer array for the section number and string arrays for the other fields). Then, the program prints out a list of students in section 4 and 5.
69. Shuffling. In the October 7, 2003 California state runoff election for governor, there were 135 official candidates. To avoid the natural prejudice against candidates whose names appear at the end of the alphabet (Jon W. Zellhoefer), California election officials sought to order the candidates in random order. Write a program program Shuffle.java that takes a command-line argument N, reads in N strings from standard input, and prints them back out in shuffled order. (California decided to randomize the alphabet instead of shuffling the candidates. Using this strategy, not all N! possible outcomes are equally likely or even possible! For example, two candidates with very similar last names will always end up next to each other.)
70. Reverse. Write a program Reverse.java that reads in an arbitrary number of real values from standard input and prints them in reverse order. Sometimes we need to store a large quantity of values in an array, but we don't know how many ahead of time. The problem is that once we allocate memory for an array, its size is fixed as long as the array continues to exist.

    It is not possible to grow or shrink the size of an array. Instead, initialize the array to have size = 1. If the array is not big enough to hold the next element, allocate a new array of double the size and copy the old elements into the new array. This repeated doubling strategy is a tradeoff between the work involved in copying the old elements and the space wasted from leaving the array half empty.

71. Time series analysis. This problem investigates two methods for forecasting in time series analysis. Moving average or exponential smoothing.
72. Polar plots. Create any of these polar plots.
73. Java games. Use StdDraw.java to implement one of the games at javaunlimited.net.
74. Consider the following program.

    public class Mystery { public static void main(String[] args) { int N = Integer.parseInt(args[0]); int[] a = new int[M]; while(!StdIn.isEmpty()) { int num = StdIn.readInt(); a[num]++; } for (int i = 0; i < M; i++) for (int j = 0; j < a[i]; j++) System.out.print(i + " "); System.out.println(); } }

    Suppose the file input.txt contains the following integers:

    8 8 3 5 1 7 0 9 2 6 9 7 4 0 5 3 9 3 7 6

    What is the contents of the array a after running the following command

    java Mystery 10 < input.txt

75. High-low. Shuffle a deck of cards, and deal one to the player. Prompt the player to guess whether the next card is higher or lower than the current card. Repeat until player guesses it wrong. Game show: ???? used this.
76. Elastic collisions. Write a program CollidingBalls.java that takes a command line input N and plots the trajectories of N bouncing balls that bounce of the walls and each other according to the laws of elastic collisions. Assume all the balls have the same mass.
77. Elastic collisions with obstacles. Each ball should have its own mass. Put a large ball in the center with zero initial velocity. Brownian motion.
78. Statistical outliers. Modify Average.java to print out all the values that are larger than 1.5 standard deviations from the mean. You will need an array to store the values.
79. Optical illusions. Create a Kofka ring or one of the other optical illusions collected by Edward Adelson.
80. Computer animation. In 1995 James Gosling presented a demonstration of Java to Sun executives, illustrating its potential to deliver dynamic and interactive Web content. At the time, web pages were fixed and non-interactive. To demonstrate what the Web could be, Gosling presented applets to rotate 3D molecules, visualize sorting routines, and Duke cart-wheeling across the screen. Java was officially introduced in May 1995 and widely adopted in the technology sector. The Internet would never be the same.

    

    Program Duke.java reads in the 17 images T1.gif through T17.gif and produces the animation. To execute on your computer, download the 17 GIF files and put in the same directory as Duke.java. (Alternatively, download and unzip the file duke.jar to extract all 17 GIFs.)
81. Cart-wheeling Duke. Modify Duke.java so that it cartwheels 5 times across the screen, from right to left, wrapping around when it hits the window boundary. Repeat this cart-wheeling cycle 100 times. Hint: after displaying a sequence of 17 frames, move 57 pixels to the left and repeat. Name your program MoreDuke.java.
82. Tac (cat backwards). Write a program Tac.java that reads lines of text from standard input and prints the lines out in reverse order.
83. Game. Implement the game dodge using StdDraw: move a blue disc within the unit square to touch a randomly placed green disc, while avoiding the moving red discs. After each touch, add a new moving red disc.
84. Simple harmonic motion. Create an animation like the one below from Wikipedia of simple harmonic motion.

    

85. Yin yang. Draw a yin yang using StdDraw.arc().
86. Twenty questions. Write a program QuestionsTwenty.java that plays 20 questions from the opposite point of view: the user thinks of a number between 1 and a million and the computer makes the guesses. Use binary search to ensure that the computer needs at most 20 guesses.
87. Write a program DeleteX.java that reads in text from standard input and deletes all occurrences of the letter X. To filter a file and remove all X's, run your program with the following command:

    % java DeleteX < input.txt > output.txt

88. Write a program ThreeLargest.java that reads integers from standard input and prints out the three largest inputs.
89. Write a program Pnorm.java that takes a command-line argument p, reads in real numbers from standard input, and prints out their p-norm. The p-norm norm of a vector (x₁, ..., x_N) is defined to be the pth root of (|x₁|^p + |x₂|^p + ... + |x_N|^p).
90. Consider the following Java program.

    public class Mystery { public static void main(String[] args) { int i = StdIn.readInt(); int j = StdIn.readInt(); System.out.println((i-1)); System.out.println((j*i)); } }

    Suppose that the file input.txt contains

    5 1

    What does the following command do?

    java Mystery < input.txt

91. Repeat the previous exercise but use the following command instead

    java Mystery < input.txt | java Mystery | java Mystery | java Mystery

92. Consider the following Java program.

    public class Mystery { public static void main(String[] args) { int i = StdIn.readInt(); int j = StdIn.readInt(); int k = i + j; System.out.println(j); System.out.println(k); } }

    Suppose that the file input.txt contains the integers 1 and 1. What does the following command do?

    java Mystery < input.txt | java Mystery | java Mystery | java Mystery

93. Consider the Java program Ruler.java.

    public class Ruler { public static void main(String[] args) { int n = StdIn.readInt(); String s = StdIn.readString(); System.out.println((n+1) + " " + s + (n+1) + s); } }

    Suppose that the file input.txt contains the integers 1 and 1. What does the following command do?

    java Ruler < input.txt | java Ruler | java Ruler | java Ruler

94. Modify Add.java so that it re-asks the user to enter two positive integers if the user types in a non-positive integer.
95. Modify TwentyQuestions.java so that it re-asks the user to enter a response if the user types in something other than true or false. Hint: add a do-while loop within the main loop.
96. Nonagram. Write a program to plot a nonagram.
97. Star polygons. Write a program StarPolygon.java that takes two command line inputs p and q, and plots the {p/q}-star polygon.
98. Complete graph. Write a program to plot that takes an integer N, plots an N-gon, where each vertex lies on a circle of radius 256. Then draw a gray line connecting each pair of vertices.
99. Necker cube. Write a program NeckerCube.java to plot a Necker cube.
100. What happens if you move the StdDraw.clear(Color.BLACK) command to before the beginning of the while loop in BouncingBall.java? Answer: try it and observe a nice woven 3d pattern with the given starting velocity and position.
101. What happens if you change the parameter of StdDraw.show() to 0 or 1000 in BouncingBall.java?
102. Write a program to plot a circular ring of width 10 like the one below using two calls to StdDraw.filledCircle().
103. Write a program to plot a circular ring of width 10 like the one below using a nested for loop and many calls to StdDraw.point().
104. Write a program to plot the Olympic rings.
     
105. Write a program DeluxeBouncingBall.java that embellishes BouncingBall.java by playing a sound effect upon collision with the wall using StdAudio and the sound files laser.wav and pop.wav.