Java Reference
In-Depth Information
n
! =
n
· (
n
- 1) · (
n
- 2) · … · 1 (for values of
n
greater than or equal to 1)
and
n
! = 1 (for
n
= 0)
For example, 5! = 5 · 4 · 3 · 2 · 1, which is 120.
a)
Write an application that reads a nonnegative integer and computes and prints its fac-
torial.
b)
Write an application that estimates the value of the mathematical constant
e
by using
the following formula. Allow the user to enter the number of terms to calculate.
1
1
!
1
2
!
1
3
!
…
e
=
1
++++
-----
-----
-----
Write an application that computes the value of
e
x
by using the following formula. Al-
low the user to enter the number of terms to calculate.
c)
x
2
2
!
x
3
3
!
x
1
!
e
x
…
=
1
++++
-----
-----
-----
Making a Difference
4.38
(Enforcing Privacy with Cryptography)
The explosive growth of Internet communications
and data storage on Internet-connected computers has greatly increased privacy concerns. The field
of cryptography is concerned with coding data to make it difficult (and hopefully—with the most
advanced schemes—impossible) for unauthorized users to read. In this exercise you'll investigate a
simple scheme for encrypting and decrypting data. A company that wants to send data over the In-
ternet has asked you to write a program that will encrypt it so that it may be transmitted more se-
curely. All the data is transmitted as four-digit integers. Your application should read a four-digit
integer entered by the user and encrypt it as follows: Replace each digit with the result of adding 7
to the digit and getting the remainder after dividing the new value by 10. Then swap the first digit
with the third, and swap the second digit with the fourth. Then print the encrypted integer. Write
a separate application that inputs an encrypted four-digit integer and decrypts it (by reversing the
encryption scheme) to form the original number. [
Optional reading project:
Research “public key
cryptography” in general and the PGP (Pretty Good Privacy) specific public key scheme. You may
also want to investigate the RSA scheme, which is widely used in industrial-strength applications.]
4.39
(World Population Growth)
World population has grown considerably over the centuries.
Continued growth could eventually challenge the limits of breathable air, drinkable water, arable
cropland and other limited resources. There's evidence that growth has been slowing in recent years
and that world population could peak some time this century, then start to decline.
For this exercise, research world population growth issues online.
Be sure to investigate various
viewpoints.
Get estimates for the current world population and its growth rate (the percentage by
which it's likely to increase this year). Write a program that calculates world population growth
each year for the next 75 years,
using the simplifying assumption that the current growth rate will stay
constant
. Print the results in a table. The first column should display the year from year 1 to year
75. The second column should display the anticipated world population at the end of that year.
The third column should display the numerical increase in the world population that would occur
that year. Using your results, determine the year in which the population would be double what it
is today, if this year's growth rate were to persist.
