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문제

현대 분자 생물학에서 유전자 정보는 모두 DNA로 인코딩해서 나타낸다. 컴퓨터 과학에서는 DNA를 {A, G, T, C}로만 이루어진 길이가 아주 긴 문자열로 표현한다.

다른 것보다 많이 등장하는 DNA(부분문자열) 패턴을 찾는 일은 유전병 연구에서 매우 중요하다. 이 문제에서는 합성적으로 같은(compositionally equivalent) 부분문자열을 찾으려고 한다. 두 문자열 P, Q에서 등장하는 네 문자 {A, G, T, C}의 개수가 모두 동일할 때, P와 Q는 합성적으로 같은 문자열이라고 한다. 예를 들어, P="ATTATGC"와 Q="GTATCTA"는 P에서 등장하는 'A', G', 'C', 'T'의 개수가 Q와 같기 때문에, 두 문자열은 합성적으로 같다고 한다. "TTGCA"는 "TGCCA"와 합성적으로 같지 않다.

k-Major Composition Substring, 줄여서 k-MCS는 길이가 k인 부분 문자열중에서 가장 많이 등장하는 합성적으로 같은 부분문자열이다. 한 DNA의 k-MCS는 유일하지 않을 수도 있다. k-부분문자열은 길이가 k인 부분문자열을 나타낸다.

예를 들어, 길이가 14인 DNA 문자열 W="GCAGGAGCGCCAGG"에서 합성적으로 다른 3-부분문자열은 GCA, CAG, GGa, GAG, ..., CAG, AGG가 있다. "AGG"는 총 4번 (AGG, GGA, GAG, AGG) 등장하기 때문에, 이 문자열의 3-MCS가 된다. W에서 4번 보다 많이 등장하는 3-부분문자열은 없다.

DNA 문자열과 k이 주어졌을 때, k-MCS가 몇 번 등장하는지 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스는 한 줄로 이루어져 있다. 첫 번째 숫자는 k(1 ≤ k ≤ 600)이고, 그 다음에 DNA 문자열 W가 주어진다. (10 ≤ |W| ≤ 60000)

출력

각 테스트 케이스 마다, 입력으로 주어진 W에서 k-MCS가 몇 번 등장하는지 출력한다.

예제 입력 1

3
3 GCAGGAGCGCCAGG
4 AGTCCTTAGAG
5 GGGAGGGGGGGTGGGGGGGGT

예제 출력 1

4
2
7

힌트

[{"problem_id":"8933","problem_lang":"0","title":"MCS","description":"<p>\ud604\ub300 \ubd84\uc790 \uc0dd\ubb3c\ud559\uc5d0\uc11c \uc720\uc804\uc790 \uc815\ubcf4\ub294 \ubaa8\ub450 DNA\ub85c \uc778\ucf54\ub529\ud574\uc11c \ub098\ud0c0\ub0b8\ub2e4. \ucef4\ud4e8\ud130 \uacfc\ud559\uc5d0\uc11c\ub294 DNA\ub97c {A, G, T, C}\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \uae38\uc774\uac00 \uc544\uc8fc \uae34 \ubb38\uc790\uc5f4\ub85c \ud45c\ud604\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub2e4\ub978 \uac83\ubcf4\ub2e4 \ub9ce\uc774 \ub4f1\uc7a5\ud558\ub294 DNA(\ubd80\ubd84\ubb38\uc790\uc5f4) \ud328\ud134\uc744 \ucc3e\ub294 \uc77c\uc740 \uc720\uc804\ubcd1 \uc5f0\uad6c\uc5d0\uc11c \ub9e4\uc6b0 \uc911\uc694\ud558\ub2e4. \uc774 \ubb38\uc81c\uc5d0\uc11c\ub294 \ud569\uc131\uc801\uc73c\ub85c \uac19\uc740(compositionally equivalent) \ubd80\ubd84\ubb38\uc790\uc5f4\uc744 \ucc3e\uc73c\ub824\uace0 \ud55c\ub2e4. \ub450 \ubb38\uc790\uc5f4 P, Q\uc5d0\uc11c \ub4f1\uc7a5\ud558\ub294 \ub124 \ubb38\uc790 {A, G, T, C}\uc758 \uac1c\uc218\uac00 \ubaa8\ub450 \ub3d9\uc77c\ud560 \ub54c, P\uc640 Q\ub294 \ud569\uc131\uc801\uc73c\ub85c \uac19\uc740 \ubb38\uc790\uc5f4\uc774\ub77c\uace0 \ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, P=&quot;ATTATGC&quot;\uc640 Q=&quot;GTATCTA&quot;\ub294 P\uc5d0\uc11c \ub4f1\uc7a5\ud558\ub294 &#39;A&#39;, G&#39;, &#39;C&#39;, &#39;T&#39;\uc758 \uac1c\uc218\uac00 Q\uc640 \uac19\uae30 \ub54c\ubb38\uc5d0, \ub450 \ubb38\uc790\uc5f4\uc740 \ud569\uc131\uc801\uc73c\ub85c \uac19\ub2e4\uace0 \ud55c\ub2e4. &quot;TTGCA&quot;\ub294 &quot;TGCCA&quot;\uc640 \ud569\uc131\uc801\uc73c\ub85c \uac19\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>k-Major Composition Substring, \uc904\uc5ec\uc11c k-MCS\ub294 \uae38\uc774\uac00 k\uc778 \ubd80\ubd84 \ubb38\uc790\uc5f4\uc911\uc5d0\uc11c \uac00\uc7a5 \ub9ce\uc774 \ub4f1\uc7a5\ud558\ub294 \ud569\uc131\uc801\uc73c\ub85c \uac19\uc740 \ubd80\ubd84\ubb38\uc790\uc5f4\uc774\ub2e4. \ud55c DNA\uc758 k-MCS\ub294 \uc720\uc77c\ud558\uc9c0 \uc54a\uc744 \uc218\ub3c4 \uc788\ub2e4. k-\ubd80\ubd84\ubb38\uc790\uc5f4\uc740 \uae38\uc774\uac00 k\uc778 \ubd80\ubd84\ubb38\uc790\uc5f4\uc744 \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\uc608\ub97c \ub4e4\uc5b4, \uae38\uc774\uac00 14\uc778 DNA \ubb38\uc790\uc5f4 W=&quot;GCAGGAGCGCCAGG&quot;\uc5d0\uc11c \ud569\uc131\uc801\uc73c\ub85c \ub2e4\ub978 3-\ubd80\ubd84\ubb38\uc790\uc5f4\uc740 GCA, CAG, GGa, GAG, ..., CAG, AGG\uac00 \uc788\ub2e4. &quot;AGG&quot;\ub294 \ucd1d 4\ubc88 (AGG, GGA, GAG, AGG) \ub4f1\uc7a5\ud558\uae30 \ub54c\ubb38\uc5d0, \uc774 \ubb38\uc790\uc5f4\uc758 3-MCS\uac00 \ub41c\ub2e4. W\uc5d0\uc11c 4\ubc88 \ubcf4\ub2e4 \ub9ce\uc774 \ub4f1\uc7a5\ud558\ub294 3-\ubd80\ubd84\ubb38\uc790\uc5f4\uc740 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>DNA \ubb38\uc790\uc5f4\uacfc k\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, k-MCS\uac00 \uba87 \ubc88 \ub4f1\uc7a5\ud558\ub294\uc9c0 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub294 \ud55c \uc904\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uccab \ubc88\uc9f8 \uc22b\uc790\ub294 k(1 &le; k &le; 600)\uc774\uace0, \uadf8 \ub2e4\uc74c\uc5d0 DNA \ubb38\uc790\uc5f4 W\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (10 &le; |W| &le; 60000)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 W\uc5d0\uc11c k-MCS\uac00 \uba87 \ubc88 \ub4f1\uc7a5\ud558\ub294\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8933","problem_lang":"1","title":"MCS","description":"<p>In modern molecular biology the genome of an organism is its hereditary information encoded in DNA. The genome includes both the genes and the non-coding sequences of the DNA. In the view of computer science, the genome can be regarded as a very long string consisting of only four letters {A,G,T,C}.&nbsp;<br \/>\r\n&nbsp;<br \/>\r\nIn order to study specific genetic diseases, it is very important to examine if there are DNA (substring) patterns which appear more frequently than others in a whole genome. Especially we are intended in finding &ldquo;compositionally equivalent&rdquo; substrings. A string P is said to be compositionally equivalent to a string Q if the number of 4 letters {A,G,T,C} appearing in P and Q is exactly the same. For example, P=&ldquo;ATTATGC&rdquo; is compositionally equivalent to Q=&ldquo;GTATCTA&rdquo; since the number of &lsquo;A&rsquo; , &lsquo;G&rsquo; , &lsquo;C&rsquo; and &lsquo;T&rsquo; in P is exactly same to that in Q, respectively. In the other hand, &ldquo;TTGCA&rdquo; is not compositionally equivalent to &ldquo;TGCCA&rdquo;.&nbsp;<\/p>\r\n\r\n<p>In this problem we want to find the k-Major Composition Substring (k-MCS for short). For a genome string given, k-MCS is defined as the most frequently appearing substring of length k up to compositionally equivalence. Since the k-MCS for a given input genome is not necessarily unique, two or more different k-MCS could be possible. In the following, k-substring means a substring of length k.&nbsp;<\/p>\r\n\r\n<p>Let us show one example. We have a genome string W=&ldquo;GCAGGAGCGCCAGG&rdquo; with length 14. There are many different compositionally equivalent 3-substrings such as GCA, CAG, GGA, GAG,&hellip; CAG and AGG. In W it is easy to find that &ldquo;AGG&rdquo;is a 3-MCS which appears four times as AGG, GGA, GAG and AGG, since there is no other 3-substring (up to compositionally equivalence) which appears more than 4 times in W.&nbsp;<\/p>\r\n","input":"<p>Your program is to read the input from standard input. 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 (input genome) starts with the value k for k-MCS and the genome string W, where 1 &le; k &le; 600. The length of the input genome string, |W|, is bounded by 10 &le; |W| &le; 60000.<\/p>\r\n","output":"<p>Your program is to write the number of occurrence of a k-MCS appearing in each genome string.&nbsp;<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Seoul 2008 B번