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                           BRONZE PROBLEMS
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                  Three problems numbered 11 through 13
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Problem 11: DNA strings [Woburn contest, 2005]

Farmer John has performed DNA sequencing on his prize milk-producing
cow, Bessie.  DNA sequences are ordered lists (strings) containing
one or more of the letters 'A', 'C', 'G', and 'T'.

As is usual for DNA sequencing, the results are a set of strings
that are sequenced fragments of DNA. A pair of strings like 'GATTA'
and 'TACA' most probably represent the string 'GATTACA' as the
overlapping characters are merged, since they were probably duplicated
in the sequencing process. Generally, merging a pair of strings
involves removing the greatest overlap between the two as they are
concatenated.  Note that overlaps are between the end of one string
and beginning of another string, not in the middle of a string. The
string 'GATTACA' overlaps 'TTACA' completely, though the strings
'GATTACA' and 'TTA' have no overlap at all.

Given a set of N (2 <= N <= 100) DNA sequences all of whose lengths
are in the range 1..50, find and print the length of the greatest
overlap between any pair of strings.

PROBLEM NAME: dna

INPUT FORMAT:

* Line 1: A single integer N

* Lines 2..N+1: Each line contains a single DNA subsequence

SAMPLE INPUT (file dna.in):

4
CGCCAC
TGTCGC
GAATGA
GAGGCGA

INPUT DETAILS:

Four strings; six and seven characters each

OUTPUT FORMAT:

* Line 1: A single line that contains the integer length of the
        greatest overlap between any pair of strings (in either order)

SAMPLE OUTPUT (file dna.out):

3

OUTPUT DETAILS:

CGC begins the first string and ends the second:
   CGCCAC
TGTCGC
so the greatest overlap is 3

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Problem 12: Palindromes [Traditional, 2004]

A palindrome is a series of digits (or letters, if you wish) that
reads the same forwards and backwards.  The number 12344321 is a
palindrome, as is both 12321 and 3.  The number 2468 is not a
palindrome.

Read a number as long as 75 digits from the input file and find the
longest palindrome that occurs in the number. The palindrome will
be anywhere from two digits in length all the way up to the entire
number and is guaranteed to be unique.

PROBLEM NAME: pal

INPUT FORMAT:

* Line 1: A single number up to 75 digits long

SAMPLE INPUT (file pal.in):

82910341234565432158735

OUTPUT FORMAT:

* Line 1: The longest palindrome anywhere in the number

SAMPLE OUTPUT (file pal.out):

12345654321

OUTPUT DETAILS:

8291034-->12345654321<--58735

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Problem 13: Negative Powers of Two [Traditional , 2005]

Given an integer N (1 <= N <= 250), print the exact reciprocal of 2 to the
Nth power.  Print it in the form "0.x..." with no trailing zeroes.

PROBLEM NAME: nptwo

INPUT FORMAT:

* Line 1: A single integer N.

SAMPLE INPUT (file nptwo.in):

67

OUTPUT FORMAT:

* Line 1: The decimal representation of 1 / (2^N).

SAMPLE OUTPUT (file nptwo.out):

0.0000000000000000000067762635780344027125465800054371356964111328125

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