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We then repeat the process with the second prime number in the list, which is 3,
and then iterate through the remainder of the list, removing any number that is a
multiple of 3 (in this case 9), leaving
2 3 5 7
We then repeat starting with each successive prime number, but no elements are
removed because there are no multiples of 5 or 7 (a more efficient implementation
of the algorithm would stop without examining 5 or 7). The numbers that remain
in the list are all prime numbers.
Implement this algorithm using an
ArrayList
of integers that is initialized to the
values from 2 to 100. Your program can iterate numerically through the
ArrayList
from index 0 to index
size()-1
to get the current prime number, but should use
an
Iterator
to scan through the remainder of the list to eliminate the multiples.
You can use the
listIterator
method to retrieve the iterator starting at a specified
index into the
ArrayList
. Output all remaining prime numbers to the console.
3. The birthday paradox is that there is a surprisingly high probability that two or
more people in the same room happen to share the same birthday. By birthday,
we mean the same day of the year (ignoring leap years), but not the exact birthday
that includes the birth year or time of day. Write a program that approximates the
probability that 2 or more people in the same room have the same birthday, for
2 to 50 people in the room.
The program should use simulation to approximate the answer. Over many trials
(say, 5,000), randomly assign birthdays (i.e., a number from 1-365) to everyone
in the room. Use a
HashSet
to store the birthdays. As the birthdays are randomly
generated, use the
contains
method of a
HashSet
to see if someone with the same
birthday is already in the room. If so, increment a counter that tracks how many
times at least two people have the same birthday and then move on to the next trial.
After the trials are over, divide the counter by the number of trials to get an estimated
probability that two or more people share the same birthday for a given room size.
Your output should look something like the following. It will not be exactly the
same due to the random numbers:
For 2 people, the probability of two birthdays is about 0.002
For 3 people, the probability of two birthdays is about 0.0082
For 4 people, the probability of two birthdays is about 0.0163
...
For 49 people, the probability of two birthdays is about 0.9654
For 50 people, the probability of two birthdays is about 0.969
4. The text files
boynames.txt
and
girlnames.txt
, which are included in the source
code for this topic, contain lists of the 1,000 most popular boy and girl names in the
United States for the year 2005, as compiled by the Social Security Administration.
VideoNote
Solution to
Programming
Project 16.3
These are blank-delimited files where the most popular name is listed first, the
second most popular name is listed second, and so on to the 1,000th most popular
name, which is listed last. Each line consists of the first name followed by a blank
