Problemset

Problem C: Vito's
family

Background

The world-known gangster Vito Deadstone is moving to New York. He has a very big family
there, all of them living in Lamafia Avenue. Since he will visit all his relatives very often, he is
trying to find a house close to them.

Problem

Vito wants to minimize the total distance to all of them and has blackmailed you to write a
program that solves his problem.

Input

The input consists of several test cases. The first line contains the number of test cases.

For each test case you will be given the integer number of relatives r ( 0 < r < 500) and the

street numbers (also integers) where they live ( 0 < si < 30000 ). Note that

several relatives could live in the same street number.

Output

For each test case your program must write the minimal sum of distances from the optimal
Vito's house to each one of his relatives. The distance between two street numbers si and sj is
dij= |si-sj|.

Sample Input

2
224
3246

Sample Output

2
4

DNA
Sorting

One measure of ``unsortedness'' in a sequence is the number of pairs of entries that are out of
order with respect to each other. For instance, in the letter sequence ``DAABEC'', this measure
is 5, since D is greater than four letters to its right and E is greater than one letter to its right.
This measure is called the number of inversions in the sequence. The sequence ``AACEDGG''
has only one inversion (E and D)--it is nearly sorted--while the sequence ``ZWQM'' has 6
inversions (it is as unsorted as can be--exactly the reverse of sorted).

You are responsible for cataloguing a sequence of DNA strings (sequences containing only the
four letters A, C, G, and T). However, you want to catalog them, not in alphabetical order, but
rather in order of ``sortedness'', from ``most sorted'' to ``least sorted''. All the strings are of the
same length.

Input

The first line of the input is an integer M, then a blank line followed by M datasets. There is a
blank line between datasets.

The first line of each dataset contains two integers: a positive integer n ( ) giving

the length of the strings; and a positive integer m ( ) giving the number of strings.

These are followed by m lines, each containing a string of length n.

Output

For each dataset, output the list of input strings, arranged from ``most sorted'' to ``least
sorted''. If two or more strings are equally sorted, list them in the same order they are in the
input file.

Sample Input

1

10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT

Sample Output

CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA

Searching
Quickly

Background

Searching and sorting are part of the theory and practice of computer science. For example,
binary search provides a good example of an easy-to-understand algorithm with sub-linear

complexity. Quicksort is an efficient [average case] comparison based sort.

KWIC-indexing is an indexing method that permits efficient ``human search'' of, for example, a
list of titles.

The Problem

Given a list of titles and a list of ``words to ignore'', you are to write a program that generates a
KWIC (Key Word In Context) index of the titles. In a KWIC-index, a title is listed once for each
keyword that occurs in the title. The KWIC-index is alphabetized by keyword.

Any word that is not one of the ``words to ignore'' is a potential keyword.

For example, if words to ignore are ``the, of, and, as, a'' and the list of titles is:

Descent of Man
The Ascent of Man
The Old Man and The Sea
A Portrait of The Artist As a Young Man

A KWIC-index of these titles might be given by:

a portrait of the ARTIST as a young man
the ASCENT of man
DESCENT of man
descent of MAN
the ascent of MAN
the old MAN and the sea

a portrait of the artist as a young MAN
the OLD man and the sea
a PORTRAIT of the artist as a young man
the old man and the SEA
a portrait of the artist as a YOUNG man

The Input

The input is a sequence of lines, the string :: is used to separate the list of words to ignore
from the list of titles. Each of the words to ignore appears in lower-case letters on a line by
itself and is no more than 10 characters in length. Each title appears on a line by itself and may
consist of mixed-case (upper and lower) letters. Words in a title are separated by whitespace.
No title contains more than 15 words.

There will be no more than 50 words to ignore, no more than than 200 titles, and no more than
10,000 characters in the titles and words to ignore combined. No characters other than 'a'-'z',
'A'-'Z', and white space will appear in the input.

The Output

The output should be a KWIC-index of the titles, with each title appearing once for each
keyword in the title, and with the KWIC-index alphabetized by keyword. If a word appears more
than once in a title, each instance is a potential keyword.

The keyword should appear in all upper-case letters. All other words in a title should be in
lower-case letters. Titles in the KWIC-index with the same keyword should appear in the same
order as they appeared in the input file. In the case where multiple instances of a word are
keywords in the same title, the keywords should be capitalized in left-to-right order.

Case (upper or lower) is irrelevant when determining if a word is to be ignored.

The titles in the KWIC-index need NOT be justified or aligned by keyword, all titles may be
listed left-justified.

Sample Input

is
the
of
and
as
a
but

::
Descent of Man
The Ascent of Man
The Old Man and The Sea
A Portrait of The Artist As a Young Man
A Man is a Man but Bubblesort IS A DOG

Sample Output

a portrait of the ARTIST as a young man
the ASCENT of man
a man is a man but BUBBLESORT is a dog
DESCENT of man
a man is a man but bubblesort is a DOG
descent of MAN
the ascent of MAN
the old MAN and the sea
a portrait of the artist as a young MAN
a MAN is a man but bubblesort is a dog
a man is a MAN but bubblesort is a dog
the OLD man and the sea
a PORTRAIT of the artist as a young man
the old man and the SEA
a portrait of the artist as a YOUNG man

Satellites

The Problem

The radius of earth is 6440 Kilometer. There are many Satellites and Asteroids moving around
the earth. If two Satellites create an angle with the center of earth, can you find out the
distance between them? By distance we mean both the arc and chord distances. Both
satellites are on the same orbit. (However, please consider that they are revolving on a circular
path rather than an elliptical path.)

The Input

The input file will contain one or more test cases.

Each test case consists of one line containing two-integer s and a and a string "min" or
"deg". Here s is the distance of the satellite from the surface of the earth and a is the angle
that the satellites make with the center of earth. It may be in minutes ( ‘ ) or in degrees ( 0 ).
Remember that the same line will never contain minute and degree at a time.

The Output

For each test case, print one line containing the required distances i.e. both arc distance
and chord distance respectively between two satellites in Kilometer. The distance will be a
floating-point value with six digits after decimal point.

Sample Input

500 30 deg
700 60 min
200 45 deg

Sample Output

3633.775503 3592.408346
124.616509 124.614927
5215.043805 5082.035982

Polygon Inside A
Circle

The Problem

Consider a polygon of equal sides inside a circle as shown in the figure below.

Figure: The regular polygon inside a circle

Given the radius of the circle and number of sides. You have to find the area of the polygon.

The Input

In each line there will be two numbers indicating the radius `r' (0<r<20000) and the number of
sides of the polygon `n' (2<n<20000) respectively. Input is terminated by `EOF'.

The Output

Output the area in each line. The number must be rounded to the third digit after the decimal
point.

Sample Input

2 2000
10 3000

Sample Output

Problemset

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