AUTHOR: your name

FILENAME: title of the source file

SPECIFICATION: description of the program

FOR: CSE 110: homework #- days and time of your class

TIME SPENT: how long it took you to complete the assignment

Part #1: Written Exercises
1. (4 pts) What do the following loops print?
a) for (int i = 10; i > 1; i--)
System.out.print(i + " ");
b) int j = 1;
while (j < 20) {
if (j % 5 == 0)
System.out.print(j + " ");
j += 2;
}
1
2.Given the following code segment that reads in a String str:

String str = in.nextLine();

Write a loop that will print out the value entered into str in reverse. That is if the user entered "Harry", the loop should print "yrraH". This does not have to be a complete program, but you should test your loop inside a complete program. Section 4.7.2 in the book and the Examples for Loops lecture video show some String loop examples with a for loop.

Part #2 - Programming (10 pts)

Write a program called Assignment3 (saved in a file Assignment3.java) that computes the greatest common divisor of two given integers. One of the oldest numerical algorithms was described by the Greek mathematician, Euclid, in 300 B.C. It is a simple but very effective algorithm that computes the greatest common divisor of two given integers. For instance, given integers 24 and 18, the greatest common divisor is 6, because 6 is the largest integer that divides evenly into both 24 and 18. We will denote the greatest common divisor of x and y as gcd(x, y).

The algorithm is based on the clever idea that the gcd(x, y) = gcd(x - y, y) if x >= y and gcd(x, y) = gcd(x, y - x) if x < y. The algorithm consists of a series of steps (loop iterations) where the "larger" integer is replaced by the difference of the larger and smaller integer. This continues until the two values are equal. That is then the gcd. You are required to do the following:

• Prompt the user to enter two integers and read them from the keyboard.
• Create a loop, and inside of it replace the larger integer with the difference between the larger integer and the smaller integer (if the integers are equal you may choose either one as the "larger") during each iteration. You will need to use an if/else statement to determine the larger value.
• Continue looping until the two integers are equal.
• Print out the remaining value as the gcd. See the sample output below.

Sample Outputs
Sample 1:
Enter the first integer: 72
Enter the second integer: 54
The gcd of 72 and 54 is 18
Sample 2:
Enter the first integer: 18
Enter the second integer: 24
The gcd of 18 and 24 is 6