### Exercises on Flow Controls

#### Exercises on Conditional (Decision)

Exercise CheckPassFail (if-else): Write a program called

which prints "**CheckPassFail**`PASS`

" if the `int`

variable "`mark`

" is more than or equal to `50`

; or prints "`FAIL`

" otherwise.

Hints:

public classCheckPassFail{ // saved as "CheckPassFail.java" public static void main(String[] args) { int mark = 49; // set the value of mark here! System.out.println("The mark is " + mark); if ( ...... ) { System.out.println( ...... ); } else { System.out.println( ...... ); } } }

Exercise CheckOddEven (if-else): Write a program called

which prints "**CheckOddEven**`Odd Number`

" if the `int`

variable “`number`

” is odd, or “`Even Number`

” otherwise.

Hints: `n`

is an even number if `(n % 2)`

is `0`

.

public classCheckOddEven{ // saved as "CheckOddEven.java" public static void main(String[] args) { int number = 49; // set the value of number here! System.out.println("The number is " + number); if ( ...... ) { System.out.println( ...... ); } else { System.out.println( ...... ); } } }

Exercise PrintNumberInWord (nested-if, switch-case): Write a program called

which prints "ONE", "TWO",... , "NINE", "OTHER" if the **PrintNumberInWord**`int`

variable "`number`

" is 1, 2,... , 9, or other, respectively. Use (a) a "nested-if" statement; (b) a "switch-case" statement.

Hints:

public classPrintNumberInWord{ // saved as "PrintNumberInWord.java" public static void main(String[] args) { int number = 5; // Using nested-if if (number == 1) { System.out.println("ONE"); } else if (......) { ...... } else if (......) { ...... ...... } else { ...... } // Using switch-case switch(number) { case 1: System.out.println("ONE"); break; case 2: ...... ...... ...... default: System.out.println("OTHER"); } } }

Similarly, write a program called ** PrintDayInWord**, which prints “Sunday”, “Monday”, ... “Saturday” if the

`int`

variable "`day`

" is 0, 1, ..., 6, respectively. Otherwise, it shall print “Not a valid day”.#### Exercises on Loop (Iteration)

Exercise SumAndAverage (Loop): Write a program called

to produce the sum of 1, 2, 3, ..., to an upperbound (e.g., 100). Also compute and display the average. The output shall look like:**SumAndAverage**

The sum is 5050 The average is 50.5

Hints:

public classSumAndAverage{ // saved as "SumAndAverage.java" public static void main (String[] args) { int sum = 0; // store the accumulated sum, init to 0 double average; // average in double int lowerbound = 1; // the lower bound to sum int upperbound = 100; // the upper bound to sum for (int number = lowerbound; number <= upperbound; ++number) { // for loop sum += number; // same as "sum = sum + number" } // Compute average in double. Beware that int/int produces int. ...... // Print sum and average. ...... } }

TRY:

- Modify the program to use a "while-do" loop instead of "for" loop.
int number = lowerbound; int sum = 0; while (number <= upperbound) { sum += number; ++number; }

- Modify the program to use a "do-while" loop.
int number = lowerbound; int sum = 0; do { sum += number; ++number; } while (number <= upperbound);

- What is the difference between "for" and "while-do" loops? What is the difference between "while-do" and "do-while" loops?
- Modify the program to sum from 111 to 8899, and compute the average. Introduce an
`int`

variable called`count`

to count the numbers in the specified range.`int count = 0; // count the number within the range, init to 0 for (...; ...; ...) { ...... ++count; }`

- Modify the program to sum only the
*odd*numbers from 1 to 100, and compute the average. (Hint:`n`

is an odd number if`n % 2`

is not`0`

.) - Modify the program to sum those numbers from 1 to 100 that is divisible by 7, and compute the average.
- Modify the program to find the "sum of the squares" of all the numbers from 1 to 100, i.e. 1*1 + 2*2 + 3*3 + ... + 100*100.

Exercise Product1ToN (Loop): Write a program called

to compute the product of integers 1 to 10 (i.e., 1×2×3×...×10). Try computing the product from 1 to 11, 1 to 12, 1 to 13 and 1 to 14. Write down the product obtained and explain the results.**Product1ToN**

Hints: Declares an `int`

variable called `product`

(to accumulate the product) and initialize to 1.

Exercise HarmonicSum (Loop): Write a program called

to compute the sum of a harmonic series, as shown below, where **HarmonicSum**

=50000. The program shall compute the sum from *n**left-to-right* as well as from the *right-to-left*. Obtain the difference between these two sums and explain the difference. Which sum is more accurate?

Hints:

public classHarmonicSum{ // saved as "HarmonicSum.java" public static void main (String[] args) { int maxDenominator = 50000; double sumL2R = 0.0; // sum from left-to-right double sumR2L = 0.0; // sum from right-to-left // for-loop for summing from left-to-right for (int denominator = 1; denominator <= maxDenominator; ++denominator) { ...... // Beware that int/int gives int. } // for-loop for summing from right-to-left ...... // Find the difference and display ...... } }

Exercise ComputePI (Loop & Condition): Write a program called

to compute the value of π, using the following series expansion. You have to decide on the termination criterion used in the computation (such as the number of terms used or the magnitude of an additional term). Is this series suitable for computing π?**ComputePI**

JDK maintains the value of π in a `double`

constant called `Math.PI`

. Compare the values obtained and the `Math.PI`

, in percents of `Math.PI`

.

Hint: Add to sum if the denominator modulus 4 is 1, and subtract from sum if it is 3.

double sum = 0; int maxDenom = 10000000; for (int denom = 1; ..... ; denom = denom + 2) { if (denom % 4 == 1) { sum += ......; } else if (denom % 4 == 3) { sum -= ......; } else { System.out.println("The computer has gone crazy?!"); } }

Exercise CozaLozaWoza (Loop & Condition): Write a program called

which prints the numbers 1 to 110, 11 numbers per line. The program shall print "Coza" in place of the numbers which are multiples of 3, "Loza" for multiples of 5, "Woza" for multiples of 7, "CozaLoza" for multiples of 3 and 5, and so on. The output shall look like:**CozaLozaWoza**

1 2 Coza 4 Loza Coza Woza 8 Coza Loza 11 Coza 13 Woza CozaLoza 16 17 Coza 19 Loza CozaWoza 22 23 Coza Loza 26 Coza Woza 29 CozaLoza 31 32 Coza ......

Hints:

public classCozaLozaWoza{ // saved as "CozaLozaWoza.java" public static void main(String[] args) { int lowerbound = 1; int upperbound = 110; for (int number = lowerbound; number <= upperbound; ++number) { // Print "Coza" if number is divisible by 3 if (......) { System.out.print("Coza"); } // Print "Loza" if number is divisible by 5 if (......) { System.out.print(.....); } // Print "Woza" if number is divisible by 7 ...... // Print the number if it is not divisible by 3, 5 and 7 if (......) { ...... } // Print a newline if number is divisible by 11; else print a space if (......) { System.out.println(); } } } }

TRY: Modify the program to use nested-if (`if ... else if ... else if ... else`

) instead.

Exercise Fibonacci (Loop): Write a program called

to display the first 20 Fibonacci numbers **Fibonacci**`F(n)`

, where `F(n)=F(n–1)+F(n–2)`

and `F(1)=F(2)=1`

. Also compute their average. The output shall look like:

The first 20 Fibonacci numbers are: 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 6765 The average is 885.5

Hints:

public classFibonacci{ public static void main (String args[]) { int n = 3; // the index n for F(n), starting from n=3 int fn; // F(n) to be computed int fnMinus1 = 1; // F(n-1), init to F(2) int fnMinus2 = 1; // F(n-2), init to F(1) int nMax = 20; // maximum n, inclusive int sum = fnMinus1 + fnMinus2; double average; System.out.println("The first " + nMax + " Fibonacci numbers are:"); ...... while (n <= nMax) { // Compute F(n), print it and add to sum ...... // Adjust the index n and shift the numbers ...... } // Compute and display the average (=sum/nMax) ...... } }

*Tribonacci numbers* are a sequence of numbers `T(n)`

similar to *Fibonacci numbers*, except that a number is formed by adding the three previous numbers, i.e., `T(n)=T(n-1)+T(n-2)+T(n-3)`

, `T(1)=T(2)=1`

, and `T(3)=2`

. Write a program called ** Tribonacci** to produce the first twenty Tribonacci numbers.

Extracting Digits: Write a program to extract each digit from an `int`

, in the reverse order. For example, if the `int`

is 1542, the output shall be "2,4,5,1", with a comma separating the digits.

Hints: Use `n % 10`

to extract a digit; and `n = n / 10`

to discard the last digit.

int n = ....; while (n > 0) { int digit = n % 10; // Extract the last digit ...... ..... n = n / 10; // Drop last digit and repeat the loop }

#### Exercises on Nested-Loop

Exercise SquareBoard (nested-loop): Write a program called

that displays the following **SquareBoard**

(*n*×*n*

) pattern using two nested for-loops.*n*=5

# # # # # # # # # # # # # # # # # # # # # # # # #

Your program should use only two output statements, one EACH of the followings:

System.out.print("# "); // print # and a space, without newline System.out.println(); // print a newline

Hints:

public classSquareBoard{ // saved as "SquareBoard.java" public static void main (String[] args) { int size = 5; // size of the board for (int row = 1; ......; ......) { for (int col = 1; ......; ......) { ...... } ...... } } }

Exercise CheckerBoard (nested-loop): Write a program called

that displays the following **CheckerBoard**

(*n*×*n*

) checkerboard pattern using two nested for-loops.*n*=7

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # #

Your program should use only three output statements, one EACH of the followings:

System.out.print("# "); // print # and a space, without newline System.out.print(" "); // print a space, without newline System.out.println(); // print a newline

Hints:

public classCheckerBoard{ // saved as "CheckerBoard.java" public static void main (String[] args) { int size = 7; // size of the board for (int row = 1; ......; ......) { // Use modulus 2 to find alternate lines if ((row % 2) == 0) { // row 2, 4, 6, 8 ...... } for (int col = 1; ......; ......) { ...... } ...... } } }

Exercise TimeTable (nested-loop): Write a program called `TimeTable`

to produce the multiplication table of 1 to 9 as shown using two nested for-loops:

* | 1 2 3 4 5 6 7 8 9 ------------------------------- 1 | 1 2 3 4 5 6 7 8 9 2 | 2 4 6 8 10 12 14 16 18 3 | 3 6 9 12 15 18 21 24 27 4 | 4 8 12 16 20 24 28 32 36 5 | 5 10 15 20 25 30 35 40 45 6 | 6 12 18 24 30 36 42 48 54 7 | 7 14 21 28 35 42 49 56 63 8 | 8 16 24 32 40 48 56 64 72 9 | 9 18 27 36 45 54 63 72 81

Modify the program to print the multiplication table of 1 to 12.

### Exercises on Keyboard and File Input

Exercise KeyboardScanner (Keyboard Input): Write a program called `KeyboardScanner`

to prompt user for an `int`

, a `double`

, and a `String`

. The output shall look like (the inputs are shown in bold):

Enter an integer:12Enter a floating point number:33.44Enter your name:PeterHi! Peter, the sum of 12 and 33.44 is 45.44

Hints:

import java.util.Scanner; // needed to use Scanner for input public classKeyboardScanner{ public static void main(String[] args) { int num1; double num2; String name; double sum; // Setup a Scanner called in to scan the keyboard (System.in) Scanner in = new Scanner(System.in); System.out.print("Enter an integer: "); num1 = in.nextInt(); // use nextInt() to read int System.out.print("Enter a floating point number: "); num2 = in.nextDouble(); // use nextDouble() to read double System.out.print("Enter your name: "); name = in.next(); // use next() to read String // Display ...... // Close the input stream in.close(); } }

Exercise FileScanner (File Input): Write a program called

to read an **FileScanner**`int`

, a `double`

, and a `String`

form a text file called "`in.txt`

", and produce the following output:

The integer read is 12 The floating point number read is 33.44 The String read is "Peter" Hi! Peter, the sum of 12 and 33.44 is 45.44

You need to create a text file called "`in.txt`

" (in Eclipse, right-click on the "project" ⇒ "New" ⇒ "File") with the following contents:

12 33.44 Peter

import java.util.Scanner; // Needed to use Scanner for input import java.io.File; // Needed to use File import java.io.FileNotFoundException; // Needed for file operation public classFileScanner{ public static void main(String[] args) throws FileNotFoundException { // Needed for file operation int num1; double num2; String name; double sum; // Setup a Scanner to read from a text file Scanner in = new Scanner(new File("in.txt")); num1 = in.nextInt(); // use nextInt() to read int num2 = in.nextDouble(); // use nextDouble() to read double name = in.next(); // use next() to read String // Display ...... in.close(); } }

Exercise CircleComputation (User Input): Write a program called ** CircleComputation**, which prompts user for a

`radius`

(of `double`

) and compute the `area`

and `perimeter`

of a circle. The output shall look like:Enter the radius:1.2The area is 4.5239 The perimeter is 7.5398223686155035

Hints: π is kept in a constant called `Math.PI`

.

### Exercises on User Input and String Operations

Exercise ReverseString: Write a program called `ReverseString`

, which prompts user for a `String`

, and prints the *reverse* of the `String`

. The output shall look like:

Enter a String:abcdefThe reverse of String "abcdef" is "fedcba".

Hints:

import java.util.Scanner; public classReverseString{ public static void main(String[] args) { String inStr; // input String int inStrLen; // length of the input String Scanner in = new Scanner(System.in); System.out.print("Enter a String: "); inStr = in.next(); // use next() to read String inStrLen = inStr.length(); // Use inStr.charAt(index) to extract character at 'index' from inStr ...... } }

For a `String`

called `inStr`

, you can use `inStr.length()`

to get the *length* of the `String`

; and `inStr.charAt(index)`

to retrieve the `char`

at the `index`

position, where `index`

begins with 0.

Exercise PhoneKeyPad: On your phone keypad, the alphabets are mapped to digits as follows: `ABC(2)`

, `DEF(3)`

, `GHI(4)`

, `JKL(5)`

, `MNO(6)`

, `PQRS(7)`

, `TUV(8)`

, `WXYZ(9)`

.

Write a program called `PhoneKeyPad`

, which prompts user for a `String`

(case insensitive), and converts to a sequence of Keypad digits. Use a nested-if (or switch-case) in this exercise. Modify your program to use an *array* for table look-up later.

Hints: You can use `in.next().toLowerCase()`

to read a string and convert it to lowercase to reduce your cases.

Exercise TestPalindromicWord: A word that reads the same backward as forward is called a *palindrome*, e.g., "mom", "dad", "racecar", "madam", and "Radar" (case-insensitive). Write a program called `TestPalindromicWord`

, that prompts user for a word and prints "`"xxx" is|is not a palindrome`

".

Hints: Read in a word and convert to lowercase via `in.next().toLowercase()`

.

A phrase that reads the same backward as forward is also called a palindrome, e.g., "Madam, I'm Adam", "A man, a plan, a canal - Panama!" (ignoring punctuation and capitalization). Modify your program (called `TestPalindromicPhrase`

) to test palindromic phrase.

Hints: Read in the lowercase phrase via `in.nextLine().toLowercase()`

. Maintain two indexes, `forwardIndex`

and `backwardIndex`

, used to scan the phrase forward and backward.

Exercise Bin2Dec: Write a program called `Bin2Dec`

to convert an input binary string into its equivalent decimal number. Your output shall look like:

Enter a Binary string:1011The equivalent decimal number for binary "1011" is 11 Enter a Binary string:1234Error: Invalid Binary String "1234"

Hints: For a `n`

-bit binary number `b`

, the equivalent decimal number is _{n-1}b_{n-2}...b_{1}b_{0}, b_{i}∈{0,1}`b`

._{n-1}×2^{n-1}+b_{n-2}×2^{n-2}+ ...+b_{1}×2^{1}+b_{0}×2^{0}

import java.util.Scanner; public classBin2Dec{ public static void main(String[] args) { String binStr; // input binary string int binStrLen; // length of the input string int dec = 0; // equivalent decimal number char binChar; // each individual char in the binary string Scanner in = new Scanner(System.in); // Read input binary string ...... // Convert binary string into Decimal ...... } }

binStr : 1 0 1 1 1 0 0 1 charAt(idx) : 0 1 2 3 4 5 6 7 Math.pow(2, order) : 7 6 5 4 3 2 1 0 binStr.length() = 8 idx + order = binStr.length() - 1

You can use JDK method `Math.pow(x, y)`

to compute the `x`

raises to the power of `y`

. This method takes two `double`

s as argument and returns a `double`

. You may have to cast the result back to `int`

.

To convert a `char`

(of digit `'0'`

to `'9'`

) to `int`

(`0`

to `9`

), simply subtract by `char`

`'0'`

, e.g., `'5'-'0'`

gives `int`

`5`

.

Exercise Hex2Dec: Write a program called `Hex2Dec`

to convert an input hexadecimal string into its equivalent decimal number. Your output shall look like:

Enter a Hexadecimal string:1aThe equivalent decimal number for hexadecimal "1a" is 26 Enter a Hexadecimal string:1y3Error: Invalid Hexadecimal String "1y3"

Hints:

For a `n`

-digit hexadecimal number `h`

, the equivalent decimal number is _{n-1}h_{n-2}...h_{1}h_{0}, h_{i}∈{0,…,9,A,…,F}`h`

._{n-1}×16^{n-1}+h_{n-2}×16^{n-2}+ ...+h_{1}×16^{1}+h_{0}×16^{0}

You do not need a big nested-if statement of 16 cases (or 22 considering the upper and lower letters). Extract the individual character from the hexadecimal string, says `c`

. If char `c`

is between `'0'`

to `'9'`

, you can get the integer offset via `c-'0'`

. If `c`

is between `'a'`

to `'f'`

or `'A'`

to `'F'`

, the integer offset is `c-'a'+10`

or `c-'A'+10`

.

String hexStr; char hexChar; ...... hexChar = hexStr.charAt(i); ...... if (hexChar >= '0' && hexChar <= '9') { ... (hexChar-'0') ... ... } else if (hexChar >= 'a' && hexChar <= 'f') { // lowercase ... (hexChar-'a'+10) ... ... } else if (hexChar >= 'A' && hexChar <= 'F') { // uppercase ... (hexChar-'A'+10) ... ... } else { System.out.println("Error: Invalid hexadecimal string"); System.exit(1); // quit the program }

### Exercises on Array

Exercise GradesAverage (Array): Write a program called `GradesAverage`

, which prompts user for the number of students, reads it from the keyboard, and saves it in an `int`

variable called `numStudents`

. It then prompts user for the grades of each of the students and saves them in an `int`

array called `grades`

. Your program shall check that the `grade`

is between `0`

and `100`

. A sample session is as follow:

Enter the number of students:3Enter the grade for student 1:55Enter the grade for student 2:108Invalid grade, try again... Enter the grade for student 2:56Enter the grade for student 3:57The average is 56.0

Exercise Hex2Bin (Array and Table Lookup): Write a program called `Hex2Bin`

to convert a hexadecimal string into its equivalent binary string. The output shall look like:

Enter a Hexadecimal string:1abcThe equivalent binary for hexadecimal "1abc" is 0001 1010 1011 1100

Hints: Use an array of 16 binary `String`

s corresponding to hexadecimal number `'0'`

to `'F'`

(or `'f'`

), as follows:

String[] hexBits = {"0000", "0001", "0010", "0011", "0100", "0101", "0110", "0111", "1000", "1001", "1010", "1011", "1100", "1101", "1110", "1111"};

### Exercises on Command-line Arguments

Exercise Arithmetic (Command-line arguments): Write a program called

that takes three command-line arguments: two integers followed by an arithmetic operator (**Arithmetic**`+`

, `-`

, `*`

or `/`

). The program shall perform the corresponding operation on the two integers and print the result. For example:

> java Arithmetic3 2 +3+2=5 > java Arithmetic3 2 -3-2=1 > java Arithmetic3 2 /3/2=1

Hints:

The method `main(String[] args)`

takes an argument: "an array of `String`

", which is often (but not necessary) named `args`

. This parameter captures the command-line arguments supplied by the user when the program is invoked. For example, if a user invokes:

> java Arithmetic12345 4567 +

The three command-line arguments `"12345"`

, `"4567"`

and `"+"`

will be captured in a `String`

array `{"12345", "4567", "+"}`

and passed into the `main()`

method as the argument `args`

. That is,

args is {"12345", "4567", "+"}; // args is a String array args.length is 3; // length of the array args[0] is "12345"; // 1st element of the String array args[1] is "4567"; // 2nd element of the String array args[2] is "+"; // 3rd element of the String array args[0].length() is 5; // length of 1st String element args[1].length() is 4; // length of the 2nd String element args[2].length() is 1; // length of the 3rd String element

public classArithmetic{ public static void main (String[] args) { int operand1, operand2; char theOperator; // Check if there are 3 command-line arguments in the // String array args[] by using length variable of array. if (args.length != 3) { System.err.println("Usage: java Arithmetic int1 int2 op"); return; } // Convert the 3 Strings args[0], args[1], args[2] to int and char. // Use the Integer.parseInt(aStr) to convert a String to an int. operand1 = Integer.parseInt(args[0]); operand2 = ...... // Get the operator, assumed to be the first character of // the 3rd string. Use method charAt() of String. theOperator = args[2].charAt(0); System.out.print(args[0] + args[2] + args[1] + "="); switch(theOperator) { case ('-'): System.out.println(operand1 - operand2); break; case ('+'): ...... case ('*'): ...... case ('/'): ...... default: System.err.println("Error: invalid operator!"); } } }

Notes:

- To provide command-line arguments, use the "cmd" shell to run your program in the form "
`java`

".*ClassName**arg1**arg2*.... - To provide command-line arguments in Eclipse, right click the source code ⇒ "Run As" ⇒ "Run Configurations..." ⇒ Select "Main" and choose the proper main class ⇒ Select "Arguments" ⇒ Enter the command-line arguments, e.g., "3 2 +" in "Program Arguments".
- To provide command-line arguments in NetBeans, right click the "Project" name ⇒ "Set Configuration" ⇒ "Customize..." ⇒ Select categories "Run" ⇒ Enter the command-line arguments, e.g., "3 2 +" in the "Arguments" box (but make sure you select the proper Main class).

Question: Try "`java Arithmetic 2 4 *`

" (in CMD shell and Eclipse/NetBeans) and explain the result obtained. How to resolve this problem?

In Windows' CMD shell, `*`

is known as a wildcard character, that expands to give the list of file in the directory (called Shell Expansion). For example, "`dir *.java`

" lists all the file with extension of "`.java`

". You could double-quote the * to prevent shell expansion. Eclipse has a bug in handling this, even * is double-quoted. NetBeans??

Exercise SumDigits (Command-line arguments): Write a program called `SumDigits`

to sum up the individual digits of a positive integer, given in the command line. The output shall look like:

>java SumDigits 12345The sum of digits = 1 + 2 + 3 + 4 + 5 = 15

### Exercises on Method

Exercise GradesStatistics (Method): Write a program called

, which reads in **GradesStatistics**

grades (of *n*`int`

between `0`

and `100`

, inclusive) and displays the *average*, *minimum*, *maximum*, and *standard deviation*. Your program shall check for valid input. You should keep the grades in an `int[]`

and use a method for each of the computations. Your output shall look like:

Enter the number of students:4Enter the grade for student 1:50Enter the grade for student 2:51Enter the grade for student 3:56Enter the grade for student 4:53The average is 52.5 The minimum is 50 The maximum is 56 The standard deviation is 2.29128784747792

Hints: The formula for calculating standard deviation is:

public classGradesStatistics{ public static int[] grades; // Declare an int[], to be allocated later // main() method public static void main(String[] args) { readGrades(); System.out.println("The average is " + average()); System.out.println("The minimum is " + min()); System.out.println("The maximum is " + max()); System.out.println("The standard deviation is " + stdDev()); } // Prompt user for the number of students and allocate the "grades" array. // Then, prompt user for grade, check for valid grade, and store in "grades". public static void readGrades() { ....... } // Return the average value of int[] grades public static double average() { ...... } // Return the maximum value of int[] grades public static int max() { ...... } // Return the minimum value of int[] grades public static int min() { ....... } // Return the standard deviation of the int[] grades public static double stdDev() { ....... } }

Exercise GradesHistogram (Method): Write a program called

, which reads in **GradesHistogram**

grades (of *n*`int`

between `0`

and `100`

, inclusive) from a text file called "`grades.in`

" and displays the histogram horizontally and vertically. The file has the following format:

numStduents:int grade1:int grade2:int .... gradeN:int

For example:

15 49 50 51 59 0 5 9 10 15 19 50 55 89 99 100

The output shall consist of a horizontal histogram and a vertical histogram as follows:

0 - 9: *** 10 - 19: *** 20 - 29: 30 - 39: 40 - 49: * 50 - 59: ***** 60 - 69: 70 - 79: 80 - 89: * 90 -100: ** * * * * * * * * * * * * * * * 0-9 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-100

Hints:

public classGradesHistogram{ public static int[] grades; // Declare an int array of grades, to be allocated later public static int[] bins = new int[10]; // Declare and allocate an int array for histogram bins. // 10 bins for 0-9, 10-19,...., 90-100 public static void main(String[] args) { readGrades("grades.in"); computeHistogram(); printHistogramHorizontal(); printHistogramVertical(); } // Read the grades from "filename", store in "grades" array. // Assume that the inputs are valid. public static void readGrades(String filename) { ...... } // Based on "grades" array, populate the "bins" array. public static void computeHistogram() { ....... } // Print histogram based on the "bins" array. public static void printHistogramHorizontal() { ...... } // Print histogram based on the "bins" array. public static void printHistogramVertical() { ...... } }

Exercise ReverseArrayTest (Method): Write a method called `reverseArray()`

with the following signature:

public static void reverseArray(int[] intArray)

The method accepts an `int`

array, and reverses its orders. For example, if the input array is `{12, 56, 34, 79, 26}`

, the reversal is `{26, 79, 34, 56, 12}`

. You MUST NOT use another array in your method (but you need a temporary variable to do the swap). Also write a test class called `ReverseArrayTest`

to test this method.

Take note that the array passed into the method can be modified by the method (this is called "*pass by reference*"). On the other hand, primitives passed into a method cannot be modified. This is because a clone is created and passed into the method instead of the original copy (this is called "*pass by value*").

### More (Difficult) Exercises

Exercise (JDK Source Code): Extract the source code of the class `Math`

from the JDK source code ("`$JAVA_HOME`

" ⇒ "`src.zip`

" ⇒ "`Math.java`

" under folder "`java.lang`

"). Study how constants such as `E`

and `PI`

are defined. Also study how methods such as `abs()`

, `max()`

, `min()`

, `toDegree()`

, etc, are written.

Exercise Matrix: Similar to `Math`

class, write a `Matrix`

library that supports matrix operations (such as addition, subtraction, multiplication) via 2D arrays. The operations shall support both `double`

s and `int`

s. Also write a test class to exercise all the operations programmed.

Hints:

public classMatrix{ public static void printMatrix(int[][] m) { ...... } public static void printMatrix(double[][] m) { ...... } public static boolean haveSameDimension(int[][] m1, int[][] m2) { ...... } public static boolean haveSameDimension(double[][] m1, double[][] m2) { ...... } public static int[][] add(int[][] m1, int[][] m2) { ...... } public static double[][] add(double[][] m1, double[][] m2) { ...... } ...... }

Exercise PrintAnimalPattern (Special Characters and Escape Sequences): Write a program called ** PrintAnimalPattern**, which uses

`println()`

to produce this pattern:'__' (©©) /========\/ / || %% || * ||----|| ¥¥ ¥¥ "" ""

Hints:

- Use escape sequence
`\uhhhh`

where`hhhh`

are four hex digits to display Unicode characters such as ¥ and ©. ¥ is`165`

(`00A5H`

) and © is`169`

(`00A9H`

) in both ISO-8859-1 (Latin-1) and Unicode character sets. - Double-quote (
`"`

) and black-slash (`\`

) require escape sign inside a String. Single quote (`'`

) does not require escape sign.

TRY: Print the same pattern using `printf()`

. (Hints: Need to use `%%`

to print a `%`

in `printf()`

because `%`

is the suffix for format specifier.)

Exercise PrintPatterns: Write a method to print each of the followings patterns using nested loops in a class called

. The signatures of the methods are:**PrintPatterns**

`public static void printPatternX(int size) // 'X' from 'A' to ..., size is a positive integer.`

# # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # (a) (b) (c) (d) Hints: On the diagonal, row = col. On the opposite diagonal, row + col = size + 1. # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # (e) (f) (g) (h) (i) # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # # (j) (k) # # # # # # # # # # # # # # # # # # # # # # # # # (l) 1 1 2 3 4 5 6 7 8 1 8 7 6 5 4 3 2 1 1 2 1 2 3 4 5 6 7 2 1 7 6 5 4 3 2 1 1 2 3 1 2 3 4 5 6 3 2 1 6 5 4 3 2 1 1 2 3 4 1 2 3 4 5 4 3 2 1 5 4 3 2 1 1 2 3 4 5 1 2 3 4 5 4 3 2 1 4 3 2 1 1 2 3 4 5 6 1 2 3 6 5 4 3 2 1 3 2 1 1 2 3 4 5 6 7 1 2 7 6 5 4 3 2 1 2 1 1 2 3 4 5 6 7 8 1 8 7 6 5 4 3 2 1 1 (m) (n) (o) (p) 1 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 1 2 1 1 2 3 4 5 6 7 6 5 4 3 2 1 1 2 3 2 1 1 2 3 4 5 6 5 4 3 2 1 1 2 3 4 3 2 1 1 2 3 4 5 4 3 2 1 1 2 3 4 5 4 3 2 1 1 2 3 4 3 2 1 1 2 3 4 5 6 5 4 3 2 1 1 2 3 2 1 1 2 3 4 5 6 7 6 5 4 3 2 1 1 2 1 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 1 (q) (r) 1 1 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 1 2 2 1 1 2 3 4 5 6 7 7 6 5 4 3 2 1 1 2 3 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 5 5 4 3 2 1 1 2 3 4 4 3 2 1 1 2 3 4 5 6 6 5 4 3 2 1 1 2 3 3 2 1 1 2 3 4 5 6 7 7 6 5 4 3 2 1 1 2 2 1 1 2 3 4 5 6 7 8 7 6 5 4 3 2 1 1 1 (s) (t) 1 2 3 2 3 4 5 4 3 4 5 6 7 6 5 4 5 6 7 8 9 8 7 6 5 6 7 8 9 0 1 0 9 8 7 6 7 8 9 0 1 2 3 2 1 0 9 8 7 8 9 0 1 2 3 4 5 4 3 2 1 0 9 8 (u)

Exercise PrintTriangles: Write a method to print each of the following patterns using nested-loops in a class called ** PrintTriangles**. The signatures of the methods are:

`public static void printXxxTriangle(int numRows) // Xxx is the pattern's name`

Write the `main()`

which prompts the user for the `numRows`

and prints all the patterns.

1 1 2 1 1 2 4 2 1 1 2 4 8 4 2 1 1 2 4 8 16 8 4 2 1 1 2 4 8 16 32 16 8 4 2 1 1 2 4 8 16 32 64 32 16 8 4 2 1 1 2 4 8 16 32 64 128 64 32 16 8 4 2 1 (a) PowerOf2Triangle 1 1 1 1 1 1 1 2 1 1 2 1 1 3 3 1 1 3 3 1 1 4 6 4 1 1 4 6 4 1 1 5 10 10 5 1 1 5 10 10 5 1 1 6 15 20 15 6 1 1 6 15 20 15 6 1 (b) PascalTriangle1 (c) PascalTriangle2

Exercise TrigonometricSeries: Write a method to compute `sin(x)`

and `cos(x)`

using the following series expansion, in a class called ** TrigonometricSeries**. The headers of the methods are:

```
public static double sin(double x, int numTerms) // x in radians
public static double cos(double x, int numTerms)
```

Compare the values computed using the series with the JDK methods `Math.sin()`

, `Math.cos()`

at `x=0`

, `π/6`

, `π/4`

, `π/3`

, `π/2`

using various numbers of terms.

Hints: Avoid generating large numerator and denominator (which may cause arithmetic overflow, e.g., `13!`

is out of `int`

range). Compute the terms as:

Exercise SpecialSeries: Write a method to compute the sum of the series in a class called `SpecialSeries`

. The signature of the method is:

public static double sumOfSeries(double x, int numTerms)

Exercise FibonacciInt (Overflow) : Write a program called

to list all the Fibonacci numbers, which can be expressed as an **FibonacciInt**`int`

(i.e., 32-bit signed integer in the range of `[-2147483648, 2147483647]`

). The output shall look like:

F(0) = 1 F(1) = 1 F(2) = 2 ... F(45) = 1836311903 F(46) is out of the range of int

Hints: The maximum and minimum values of a 32-bit int are kept in constants `Integer.MAX_VALUE`

and `Integer.MIN_VALUE`

, respectively. Try these statements:

System.out.println(Integer.MAX_VALUE); System.out.println(Integer.MIN_VALUE); System.out.println(Integer.MAX_VALUE + 1);

Take note that in the third statement, Java Runtime does not flag out an overflow error, but silently wraps the number around. Hence, you cannot use `F(n-1) + F(n-2) > Integer.MAX_VALUE`

to check for overflow. Instead, overflow occurs for `F(n)`

if `(Integer.MAX_VALUE – F(n-1)) < F(n-2)`

(i.e., no room for the next Fibonacci number).

Write a similar program for Tribonacci numbers.

Exercise FactorialInt (Overflow): Write a program called

, to compute the factorial of **Factorial1to10**`n`

, for `1≤n≤10`

. Your output shall look like:

The factorial of 1 is 1 The factorial of 2 is 2 ... The factorial of 10 is 3628800

Modify your program (called ** FactorialInt**), to list all the factorials, that can be expressed as an

`int`

(i.e., 32-bit signed integer). Your output shall look like:The factorial of 1 is 1 The factorial of 2 is 2 ... The factorial of 12 is 479001600 The factorial of 13 is out of range

Hints: Overflow occurs for `Factorial(n+1)`

if `(Integer.MAX_VALUE / Factorial(n)) < (n+1)`

.

Modify your program again (called ** FactorialLong**) to list all the factorial that can be expressed as a

`long`

(64-bit signed integer). The maximum value for `long`

is kept in a constant called `Long.MAX_VALUE`

.

Exercise NumberConversion: Write a method call `toRadix()`

which converts a positive integer from one radix into another. The method has the following header:

`public static String toRadix(String in, int inRadix, int outRadix) // The input and output are treated as String.`

Write a program called `NumberConversion`

, which prompts the user for an input number, an input radix, and an output radix, and display the converted number. The output shall look like:

Enter a number and radix: A1B2 Enter the input radix: 16 Enter the output radix: 2 "A1B2" in radix 16 is "1010000110110010" in radix 2.

Exercise NumberGuess: Write a program called ** NumberGuess** to play the number guessing game. The program shall generate a random number between

`0`

and `99`

. The player inputs his/her guess, and the program shall response with "Try higher", "Try lower" or "You got it in n trials" accordingly. For example:>java NumberGuessKey in your guess:50Try higher70Try lower65Try lower " You got it in 4 trials!

Hints: Use `Math.random()`

to produce a random number in `double`

between `0.0`

and (less than) `1.0`

. To produce an int between `0`

and `99`

, use:

int secretNumber = (int)(Math.random()*100);

Exercise WordGuess: Write a program called `WordGuess`

to guess a word by trying to guess the individual characters. The word to be guessed shall be provided using the command-line argument. Your program shall look like:

>java WordGuess testingKey in one character or your guess word:tTrail 1: t__t___ Key in one character or your guess word:gTrail 2: t__t__g Key in one character or your guess word:eTrail 3: te_t__g Key in one character or your guess word:testingTrail 4: Congratulation! You got in 4 trials

Hints:

- Set up a
`boolean`

array to indicate the positions of the word that have been guessed correctly. - Check the length of the input
`String`

to determine whether the player enters a single character or a guessed word. If the player enters a single character, check it against the word to be guessed, and update the`boolean`

array that keeping the result so far. - Try retrieving the word to be guessed from a text file (or a dictionary) randomly.

Exercise DateUtil: Complete the following methods in a class called `DateUtil`

:

`boolean isLeapYear(int year)`

: returns`true`

if the given`year`

is a leap year. A year is a leap year if it is divisible by 4 but not by 100, or it is divisible by 400.`boolean isValidDate(int year, int month, int day)`

: returns`true`

if the given`year`

,`month`

and`day`

constitute a given date. Assume that year is between 1 and 9999, month is between 1 (Jan) to 12 (Dec) and day shall be between 1 and 28|29|30|31 depending on the month and whether it is a leap year.`int getDayOfWeek(int year, int month, int day)`

: returns the day of the week, where 0 for SUN, 1 for MON, ..., 6 for SAT, for the given date. Assume that the date is valid.`String toString(int year, int month, int day)`

: prints the given date in the format "`xxxday d mmm yyyy`

", e.g., "Tuesday 14 Feb 2012". Assume that the given date is valid.

To find the day of the week (Reference: Wiki "Determination of the day of the week"):

- Based on the first two digit of the year, get the number from the following "century" table.
1700- 1800- 1900- 2000- 2100- 2200- 2300- 2400- 4 2 0 6 4 2 0 6 - Add to the last two digit of the year.
- Add to "the last two digit of the year divide by 4, truncate the fractional part".
- Add to the number obtained from the following month table:
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Non-Leap Year 0 3 3 6 1 4 6 2 5 0 3 5 Leap Year 6 2 same as above - Add to the day.
- The sum modulus 7 gives the day of the week, where 0 for SUN, 1 for MON, ..., 6 for SAT.

For example: 2012, Feb, 17

(6 + 12 + 12/4 + 2 + 17) % 7 = 5 (Fri)

/* Utilities for Date Manipulation */ public classDateUtil{ // Month's name – for printing public static String strMonths[] = {"Jan", "Feb", "Mar", "Apr", "May", "Jun", "Jul", "Aug", "Sep", "Oct", "Nov", "Dec"}; // Number of days in each month (for non-leap years) public static int daysInMonths[] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; // Returns true if the given year is a leap year public static boolean isLeapYear(int year) { ...... } // Return true if the given year, month, day is a valid date // year: 1-9999 // month: 1(Jan)-12(Dec) // day: 1-28|29|30|31. The last day depends on year and month public static boolean isValidDate(int year, int month, int day) { ...... } // Return the day of the week, 0:Sun, 1:Mon, ..., 6:Sat public static int getDayOfWeek(int year, int month, int day) { ...... } // Return String "xxxday d mmm yyyy" (e.g., Wednesday 29 Feb 2012) public static String printDate(int year, int month, int day) { ...... } public static void main(String[] args) { System.out.println(isLeapYear(1900)); // false System.out.println(isLeapYear(2000)); // true System.out.println(isLeapYear(2011)); // false System.out.println(isLeapYear(2012)); // true System.out.println(isValidDate(2012, 2, 29)); // true System.out.println(isValidDate(2011, 2, 29)); // false System.out.println(isValidDate(2099, 12, 31)); // true System.out.println(isValidDate(2099, 12, 32)); // true System.out.println(getDayOfWeek(1982, 4, 24)); // 6:Sat System.out.println(getDayOfWeek(2000, 1, 1)); // 6:Sat System.out.println(getDayOfWeek(2054, 6, 19)); // 5:Fri System.out.println(getDayOfWeek(2012, 2, 17)); // 5:Fri System.out.println(toString(2012, 2, 14)); // Tuesday 14 Feb 2012 } }

You can compare the day obtained with the Java's `Calendar`

class as follows:

// Construct a Calendar instance with the given year, month and day Calendar cal = new GregorianCalendar(year, month - 1, day); // month is 0-based // Get the day of the week number: 1 (Sunday) to 7 (Saturday) int dayNumber = cal.get(Calendar.DAY_OF_WEEK); String[] calendarDays = { "Sunday", "Monday", "Tuesday", "Wednesday", "Thursday", "Friday", "Saturday" }; // Print result System.out.println("It is " + calendarDays[dayNumber - 1]);

The calendar we used today is known as *Gregorian calendar*, which came into effect in October 15, 1582 in some countries and later in other countries. It replaces the *Julian calendar*. 10 days were removed from the calendar, i.e., October 4, 1582 (Julian) was followed by October 15, 1582 (Gregorian). The only difference between the Gregorian and the Julian calendar is the "leap-year rule". In Julian calendar, every four years is a leap year. In Gregorian calendar, a leap year is a year that is divisible by 4 but not divisible by 100, or it is divisible by 400, i.e., the Gregorian calendar omits century years which are not divisible by 400. Furthermore, Julian calendar considers the first day of the year as march 25th, instead of January 1st.

This above algorithm work for Gregorian dates only. It is difficult to modify the above algorithm to handle pre-Gregorian dates. A better algorithm is to find the number of days from a known date.

### Exercises on Number Theory

Exercise (Perfect and Deficient Numbers): A positive integer is called a *perfect number* if the sum of all its factors (excluding the number itself, i.e., proper divisor) is equal to its value. For example, the number `6`

is perfect because its proper divisors are `1`

, `2`

, and `3`

, and `6=1+2+3`

; but the number `10`

is not perfect because its proper divisors are `1`

, `2`

, and `5`

, and `10≠1+2+5`

.

A positive integer is called a *deficient number* if the sum of all its proper divisors is less than its value. For example, `10`

is a deficient number because `1+2+5<10`

; while `12`

is not because `1+2+3+4+6>12`

.

Write a method called `isPerfect(int posInt)`

that takes a positive integer, and return true if the number is perfect. Similarly, write a method called `isDeficient(int posInt)`

to check for deficient numbers.

Using the methods, write a program called `PerfectNumberList`

that prompts user for an upper bound (a positive integer), and lists all the perfect numbers less than or equal to this upper bound. It shall also list all the numbers that are neither deficient nor perfect. The output shall look like:

Enter the upper bound:1000These numbers are perfect: 6 28 496 [3 perfect numbers found (0.30%)] These numbers are neither deficient nor perfect: 12 18 20 24 30 36 40 42 48 54 56 60 66 70 72 78 80 ...... [246 numbers found (24.60%)]

Exercise (Primes): A positive integer is a *prime* if it is divisible by `1`

and itself only. Write a method called `isPrime(int posInt)`

that takes a positive integer and returns `true`

if the number is a prime. Write a program called `PrimeList`

that prompts the user for an upper bound (a positive integer), and lists all the primes less than or equal to it. Also display the percentage of prime (up to 2 decimal places). The output shall look like:

Please enter the upper bound:100001 2 3 ...... ...... 9967 9973 [1230 primes found (12.30%)]

Hints: To check if a number n is a prime, the simplest way is try dividing `n`

by `2`

to `√n`

.

Exercise (Prime Factors): Write a method `isProductOfPrimeFactors(int posInt)`

that takes a positive integer, and return `true`

if the product of all its prime factors (excluding 1 and the number itself) is equal to its value. For example, the method returns true for `30`

(`30=2×3×5`

) and false for `20`

(`20≠2×5`

). You may need to use the `isPrime()`

method in the previous exercise.

Write a program called `PerfectPrimeFactorList`

that prompts user for an upper bound. The program shall display all the numbers (less than or equal to the upper bound) that meets the above criteria. The output shall look like:

Enter the upper bound:100These numbers are equal to the product of prime factors: 1 6 10 14 15 21 22 26 30 33 34 35 38 39 42 46 51 55 57 58 62 65 66 69 70 74 77 78 82 85 86 87 91 93 94 95 [36 numbers found (36.00%)]

Exercise (Greatest Common Divisor): One of the earlier known algorithms is the Euclid algorithm to find the GCD of two integers (developed by the Greek Mathematician Euclid around 300BC). By definition, `GCD(a, b)`

is the greatest factor that divides both `a`

and `b`

. Assume that `a`

and `b`

are positive integers, and `a≥b`

, the Euclid algorithm is based on these two properties:

GCD(a, 0) = a GCD(a, b) = GCD(b, a mod b), where (a mod b) denotes the remainder of a divides by b.

For example,

GCD(15, 5) = GCD(5, 0) = 5 GCD(99,88) = GCD(88,11) = GCD(11,0) = 11 GCD(3456,1233) = GCD(1233,990) = GCD(990,243) = GCD(243,18) = GCD(18,9) = GCD(9,0) = 9

The pseudocode for the Euclid algorithm is as follows:

GCD(a, b) // assume that a ≥ b while (b != 0) { // Change the value of a and b: a ← b, b ← a mod b, and repeat until b is 0 temp ← b b ← a mod b a ← temp } // after the loop completes, i.e., b is 0, we have GCD(a, 0) GCD is a

Write a method called `gcd()`

with the following signature:

public static int gcd(int a, int b)

Your methods shall handle arbitrary values of `a`

and `b`

, and check for validity.

TRY: Write a *recursive* version called `gcdRecursive()`

to find the GCD.