Why is the len ( ) function useful when using a loop to iterate through a stack?
the len ( ) function will print the elements of the stack.
the len ( ) function will run with each iteration, printing the element number each time.
the len ( ) function will tell the program the number of elements in the stack.
the len ( ) function will remove the duplicate elements in the stack.

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 e↵ective 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 di↵erence of the larger and smaller integer. this continues until the two values are equal. that is then the gcd.

Assume that there is a 4% rate of disk drive failure in a year. a. if all your computer data is stored on a hard disk drive with a copy stored on a second hard disk drive, what is the probability that during a year, you can avoid catastrophe with at least one working drive? b. if copies of all your computer data are stored on three independent hard disk drives, what is the probability that during a year, you can avoid catastrophe with at least one working drive?

When you type the pwd command, you notice that your current location on the linux filesystem is the /usr/local directory. answer the following questions, assuming that your current directory is /usr/local for each question. a. which command could you use to change to the /usr directory using an absolute pathname? b. which command could you use to change to the /usr directory using a relative pathname? c. which command could you use to change to the /usr/local/share/info directory using an absolute pathname? d. which command could you use to change to the /usr/local/share/info directory using a relative pathname? e. which command could you use to change to the /etc directory using an absolute pathname? f. which command could you use to change to the /etc directory using a relative pathname?