DNA Sorting
Time Limit:
1000MS |
|
Memory Limit:
10000K |
Total Submissions:
47618 |
|
Accepted:
18598 |
Description
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 contains two integers: a positive integer n (0 < n <=
50) giving the length of the strings; and a positive integer m (0 < m
<= 100) giving the number of strings. These are followed by m lines,
each containing a string of length n.
Output
Output
the list of input strings, arranged from ``most sorted'' to ``least
sorted''. Since two strings can be equally sorted, then output them
according to the orginal order.
Sample Input
10 6
AACATGAAGG
TTTTGGCCAA
TTTGGCCAAA
GATCAGATTT
CCCGGGGGGA
ATCGATGCAT
Sample Output
CCCGGGGGGA
AACATGAAGG
GATCAGATTT
ATCGATGCAT
TTTTGGCCAA
TTTGGCCAAA
Source
code: