Human Gene Functions
Time Limit: 2 Seconds
Memory Limit: 65536 KB
It is well known that a human gene can be considered as a sequence, consisting
of four nucleotides, which are simply denoted by four letters, A, C, G, and T.
Biologists have been interested in identifying human genes and determining their
functions, because these can be used to diagnose human diseases and to design new
drugs for them.
A human gene can be identified through a series of time-consuming biological
experiments, often with the help of computer programs. Once a sequence of a gene is
obtained, the next job is to determine its function. One of the methods for biologists
to use in determining the function of a new gene sequence that they have just identified
is to search a database with the new gene as a query. The database to be searched stores
many gene sequences and their functions �C many researchers have been submitting their genes
and functions to the database and the database is freely accessible through the Internet.
A database search will return a list of gene sequences from the database that
are similar to the query gene. Biologists assume that sequence similarity often implies
functional similarity. So, the function of the new gene might be one of the functions that
the genes from the list have. To exactly determine which one is the right one another series
of biological experiments will be needed.
Your job is to make a program that compares two genes and determines their similarity
as explained below. Your program may be used as a part of the database search if you can provide
an efficient one.
Given two genes AGTGATG and GTTAG, how similar are they? One of the methods
to measure the similarity of two genes is called alignment. In an alignment, spaces are inserted,
if necessary, in appropriate positions of the genes to make them equally long and score the
resulting genes according to a scoring matrix.
For example, one space is inserted into AGTGATG to result in AGTGAT-G, and three spaces
are inserted into GTTAG to result in �CGT--TAG. A space is denoted by a minus sign (-).
The two genes are now of equal length. These two strings are aligned:
In this alignment, there are four matches, namely, G in the second position, T in the third,
T in the sixth, and G in the eighth. Each pair of aligned characters is assigned a score
according to the following scoring matrix.
* denotes that a space-space match is not allowed. The score of the alignment
above is (-3)+5+5+(-2)+(-3)+5+(-3)+5=9.
Of course, many other alignments are possible. One is shown below (a different
number of spaces are inserted into different positions):
This alignment gives a score of (-3)+5+5+(-2)+5+(-1) +5=14. So, this one is
better than the previous one. As a matter of fact, this one is optimal since no other
alignment can have a higher score. So, it is said that the similarity of the two genes is 14.
The input consists of T test cases. The number of test cases ) (T is given in
the first line of the input. Each test case consists of two lines: each line
contains an integer, the length of a gene, followed by a gene sequence.
The length of each gene sequence is at least one and does not exceed 100.
The output should print the similarity of each test case, one per line.
Output for the Sample Input
Source: Asia 2001, Taejon (South Korea)