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문제

'인간 유전자 서열(Human Gene Function)'이란 인간의 유전 정보를 담고 있는 서열입니다. 이 유전자 서열은 DNA라는 분자에 표현되어 있는데, 아시다시피 DNA를 구성하는 염기는 아데닌, 구아닌, 티민, 사이토신의 네 개밖에 없기 때문에 인간 유전자 서열은 'A', 'G', 'T', 'C' 의 네 개의 문자로만 구성됩니다.

어떤 두 인간 유전자 서열이 주어질 때, 이 두 서열 간 유사도(비슷한 정도, similarity)를 측정하고 싶습니다. 이는 다음과 같은 대응표를 참조하여 아래와 같이 정의됩니다.

table.png

  • 각 서열의 곳곳에 적당히 공백('*')을 삽입하여 같은 길이의 문자열로 만든다. 그리고 위 표에 의해, 같은 위치에 있는 두 문자들의 매칭값에 해당하는 값들을 모두 더하면 어떤 값을 얻을 수 있다. (단, 공백 끼리 매칭하는 것은 불가능하기에 표의 값이 주어져있지 않다)
  • 공백을 여러 가지 방법으로 삽입할 수 있는데, 가능한 모든 방법 중 매칭값의 합이 가장 최대가 될 때, 그 값을 유사도라고 한다.

예를 들어, 두 서열이 각각 AGTGATG와 GTTAG 라고 합시다.

만약 공백을 아래와 같이 넣는다면 매칭값의 합은 다음과 같이 9가 됩니다.

AGTGAT*G
*GT**TAG
→  (-3)+5+5+(-2)+(-3)+5+(-3)+5=9.

하지만, 만약 공백을 다음과 같이 넣는다면 매칭값은 14가 되고, 이것이 모든 가능한 방법 중 가장 큰 매칭값을 나타냅니다. 따라서 최종적으로 두 서열 간의 유사도는 14가 됩니다.

AGTGATG
*GTTA*G
→ (-3)+5+5+(-2)+5+(-1) +5=14

두 서열이 주어질 때, 유사도를 구하는 프로그램을 작성하세요.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어집니다.

T개의 테스트 케이스마다 두 개의 줄로 구성된 입력이 주어집니다.

각 줄은 서열의 길이와, 인간 유전자 서열을 담고 있습니다.

(모든 인간 유전자 서열의 길이는 100을 넘지 않는다고 합니다)

출력

각 테스트 케이스 별로, 주어진 두 인간 유전자 서열의 유사도를 출력합니다.

예제 입력 1

2
7 AGTGATG
5 GTTAG
7 AGCTATT
9 AGCTTTAAA

예제 출력 1

14
21
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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.<\/p>\r\n\r\n<p>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 &ndash; many researchers have been submitting their genes and functions to the database and the database is freely accessible through the Internet.<\/p>\r\n\r\n<p>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.<\/p>\r\n\r\n<p>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.<\/p>\r\n\r\n<p>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.<\/p>\r\n\r\n<p>For example, one space is inserted into AGTGATG to result in AGTGAT-G, and three spaces are inserted into GTTAG to result in &ndash;GT--TAG. A space is denoted by a minus sign (-). The two genes are now of equal length. These two strings are aligned:<\/p>\r\n\r\n<pre>\r\nAGTGAT-G\r\n-GT--TAG\r\n<\/pre>\r\n\r\n<p>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.<\/p>\r\n\r\n<table class=\"table table-bordered\" style=\"width:20%\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td>&nbsp;<\/td>\r\n\t\t\t<th>A<\/th>\r\n\t\t\t<th>C<\/th>\r\n\t\t\t<th>G<\/th>\r\n\t\t\t<th>T<\/th>\r\n\t\t\t<th>-<\/th>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>A<\/th>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>-1<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-1<\/td>\r\n\t\t\t<td>-3<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>C<\/th>\r\n\t\t\t<td>-1<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>-3<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-4<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>G<\/th>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-3<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>T<\/th>\r\n\t\t\t<td>-1<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>5<\/td>\r\n\t\t\t<td>-1<\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<th>-<\/th>\r\n\t\t\t<td>-3<\/td>\r\n\t\t\t<td>-4<\/td>\r\n\t\t\t<td>-2<\/td>\r\n\t\t\t<td>-1<\/td>\r\n\t\t\t<td>*<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>* 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.<\/p>\r\n\r\n<p>Of course, many other alignments are possible. One is shown below (a different number of spaces are inserted into different positions):<\/p>\r\n\r\n<pre>\r\nAGTGATG\r\n&ndash;GTTA-G<\/pre>\r\n\r\n<p>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.<\/p>\r\n","input":"<p>The input consists of T test cases. The number of test cases (T) is given in the first line of the input file. 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.<\/p>\r\n","output":"<p>The output should print the similarity of each test case, one per line.<\/p>\r\n\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

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ICPC > Regionals > Asia Pacific > Korea > Asia Regional - Taejon 2001 D번

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