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## Programming Exercises for Chapter 4

This page contains several exercises for Chapter 4 in Introduction to Programming Using Java. For each exercise, a link to a possible solution is provided. Each solution includes a discussion of how a programmer might approach the problem and interesting points raised by the problem or its solution, as well as complete source code of the solution.

### Exercise 4.1:

To "capitalize" a string means to change the first letter of each word in the string to upper case (if it is not already upper case). For example, a capitalized version of "Now is the time to act!" is "Now Is The Time To Act!". Write a subroutine named printCapitalized that will print a capitalized version of a string to standard output. The string to be printed should be a parameter to the subroutine. Test your subroutine with a main() routine that gets a line of input from the user and applies the subroutine to it.

Note that a letter is the first letter of a word if it is not immediately preceded in the string by another letter. Recall that there is a standard boolean-valued function Character.isLetter(char) that can be used to test whether its parameter is a letter. There is another standard char-valued function, Character.toUpperCase(char), that returns a capitalized version of the single character passed to it as a parameter. That is, if the parameter is a letter, it returns the upper-case version. If the parameter is not a letter, it just returns a copy of the parameter.

### Exercise 4.2:

The hexadecimal digits are the ordinary, base-10 digits '0' through '9' plus the letters 'A' through 'F'. In the hexadecimal system, these digits represent the values 0 through 15, respectively. Write a function named hexValue that uses a switch statement to find the hexadecimal value of a given character. The character is a parameter to the function, and its hexadecimal value is the return value of the function. You should count lower case letters 'a' through 'f' as having the same value as the corresponding upper case letters. If the parameter is not one of the legal hexadecimal digits, return -1 as the value of the function.

A hexadecimal integer is a sequence of hexadecimal digits, such as 34A7, FF8, 174204, or FADE. If str is a string containing a hexadecimal integer, then the corresponding base-10 integer can be computed as follows:

```value = 0;
for ( i = 0; i < str.length();  i++ )
value = value*16 + hexValue( str.charAt(i) );```

Of course, this is not valid if str contains any characters that are not hexadecimal digits. Write a program that reads a string from the user. If all the characters in the string are hexadecimal digits, print out the corresponding base-10 value. If not, print out an error message.

### Exercise 4.3:

Write a function that simulates rolling a pair of dice until the total on the dice comes up to be a given number. The number that you are rolling for is a parameter to the function. The number of times you have to roll the dice is the return value of the function. The parameter should be one of the possible totals: 2, 3, ..., 12. The function should throw an IllegalArgumentException if this is not the case. Use your function in a program that computes and prints the number of rolls it takes to get snake eyes. (Snake eyes means that the total showing on the dice is 2.)

### Exercise 4.4:

This exercise builds on Exercise 4.3. Every time you roll the dice repeatedly, trying to get a given total, the number of rolls it takes can be different. The question naturally arises, what's the average number of rolls to get a given total? Write a function that performs the experiment of rolling to get a given total 10000 times. The desired total is a parameter to the subroutine. The average number of rolls is the return value. Each individual experiment should be done by calling the function you wrote for Exercise 4.3. Now, write a main program that will call your function once for each of the possible totals (2, 3, ..., 12). It should make a table of the results, something like:

```Total On Dice     Average Number of Rolls
-------------     -----------------------
2               35.8382
3               18.0607
.                .
.                .```

### Exercise 4.5:

The sample program RandomMosaicWalk.java from Section 4.6 shows a "disturbance" that wanders around a grid of colored squares. When the disturbance visits a square, the color of that square is changed. The applet at the bottom of Section 4.7 shows a variation on this idea. In this applet, all the squares start out with the default color, black. Every time the disturbance visits a square, a small amount is added to the red component of the color of that square. Write a subroutine that will add 25 to the red component of one of the squares in the mosaic. The row and column numbers of the square should be passed as parameters to the subroutine. Recall that you can discover the current red component of the square in row r and column c with the function call Mosaic.getRed(r,c). Use your subroutine as a substitute for the changeToRandomColor() subroutine in the program RandomMosaicWalk2.java. (This is the improved version of the program from Section 4.7 that uses named constants for the number of rows, number of columns, and square size.) Set the number of rows and the number of columns to 80. Set the square size to 5.

### Exercise 4.6:

For this exercise, you will write another program based on the non-standard Mosaic class that was presented in Section 4.6. While the program does not do anything particularly interesting, it's interesting as a programming problem. The program will do the same thing as the following applet:

The program will show a rectangle that grows from the center of the applet to the edges, getting brighter as it grows. The rectangle is made up of the little squares of the mosaic. You should first write a subroutine that draws a rectangle on a Mosaic window. More specifically, write a subroutine named rectangle such that the subroutine call statement

`rectangle(top,left,height,width,r,g,b);`

will call Mosaic.setColor(row,col,r,g,b) for each little square that lies on the outline of a rectangle. The topmost row of the rectangle is specified by top. The number of rows in the rectangle is specified by height (so the bottommost row is top+height-1). The leftmost column of the rectangle is specified by left. The number of columns in the rectangle is specified by width (so the rightmost column is left+width-1.)

The animation loops through the same sequence of steps over and over. In each step, a rectangle is drawn in gray (that is, with all three color components having the same value). There is a pause of 200 milliseconds so the user can see the rectangle. Then the very same rectangle is drawn in black, effectively erasing the gray rectangle. Finally, the variables giving the top row, left column, size, and color level of the rectangle are adjusted to get ready for the next step. In the applet, the color level starts at 50 and increases by 10 after each step. When the rectangle gets to the outer edge of the applet, the loop ends. The animation then starts again at the beginning of the loop. You might want to make a subroutine that does one loop through all the steps of the animation.

The main() routine simply opens a Mosaic window and then does the animation loop over and over until the user closes the window. There is a 1000 millisecond delay between one animation loop and the next. Use a Mosaic window that has 41 rows and 41 columns. (I advise you not to used named constants for the numbers of rows and columns, since the problem is complicated enough already.)

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