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문제

연결된, 무향 그래프 G=(V, E)가 주어졌을 때, V가 정점의 집합을 나타내고, E가 간선의 집합을 나타낸다고 하자. V의 부분집합 S를 G에서 제거했을 때, 그래프가 두 개의 연결 요소로 나눠지면 S를 분리자라고 한다. 그래프에서 정점을 제거하면 제거한 정점에 연결된 간선도 함께 제거된다. 이와 같은 상황을 [S, W, B] 라는 기호로 나타내기로 하자. 이는 그래프가 분리자 S에 의해서 W와 B라는 두 개의 연결 요소로 나뉘어 진다는 의미이다.

우리는 격자 모양의 그래프에서의 분리자를 살펴보려 한다. 이 그래프에서 각각의 격자점이 정점을 이루며, 각각의 정점은 이웃한 8개의 정점들과 연결되어 있다. 아래에 6×6 격자 에 대한 예제 그림이 있다. 흰색은 W, 회색은 S, 검은색은 B를 나타낸다.

문제를 단순화하기 위해, 다음의 조건을 만족하는 분리자만 다루기로 하자.

  1. 분리자의 부분집합은 분리자를 이루지 않는다.
  2. 분리자는 그래프에서 맨 윗줄의 한 점과 맨 아랫줄의 한 점을 포함한다. 단, 0, 5, 30, 35는 제외한다.
  3. 분리자를 따라서 그래프를 위에서 아래로 이동할 때, 내려오다가 다시 올라가는 경우는 없다.

이제 다음의 두 단계를 수행하여 분리자의 크기를 줄이려고 한다.

  1. B에서 몇 개의 정점을 택해서 S에 포함시킨다. 이때 택한 정점들은 반드시 왼쪽 정점으로 S에 포함된 정점을 가지고 있어야 한다.
  2. S에서 몇 개의 정점을 제거하여 W에 포함시킨다. 단, 이전 단계에서 포함시킨 정점들은 제거할 수 없다.

이와 같은 개선 방법을 이용하여 S가 여전히 분리자이도록 하고, 이때 S의 크기를 최소로 하라. 위의 예제는 다음과 같이 하면 S의 크기가 7로 최소가 된다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다.

첫째 줄에 격자의 크기를 나타내는 두 정수 N, M(3≤N,M≤200)이 주어진다. 이는 격자의 크기가 N×M이라는 의미이다. 다음 N개의 줄에는 M개의 문자가 주어지는데, 각각은 S, W, B 중의 하나이다. 이는 해당 정점이 S, W, B 중 어느 집합에 속해있는지를 나타낸다. W는 반드시 S의 왼쪽에 존재한다. 잘못된 입력이 주어지지는 않는다고 가정해도 좋다. 모든 문자는 붙어서 입력된다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

첫째 줄에 S의 최소 크기를 출력한다.

예제 입력 1

6 6
WWSBBB
WSSBBB
WSBBBB
WSBBBB
WSSSBB
WWWSBB
0 0

예제 출력 1

7
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V\uc758 \ubd80\ubd84\uc9d1\ud569 S\ub97c G\uc5d0\uc11c \uc81c\uac70\ud588\uc744 \ub54c, \uadf8\ub798\ud504\uac00 \ub450 \uac1c\uc758 \uc5f0\uacb0 \uc694\uc18c\ub85c \ub098\ub220\uc9c0\uba74 S\ub97c \ubd84\ub9ac\uc790\ub77c\uace0 \ud55c\ub2e4. \uadf8\ub798\ud504\uc5d0\uc11c \uc815\uc810\uc744 \uc81c\uac70\ud558\uba74 \uc81c\uac70\ud55c \uc815\uc810\uc5d0 \uc5f0\uacb0\ub41c \uac04\uc120\ub3c4 \ud568\uaed8 \uc81c\uac70\ub41c\ub2e4. \uc774\uc640 \uac19\uc740 \uc0c1\ud669\uc744 [S, W, B] \ub77c\ub294 \uae30\ud638\ub85c \ub098\ud0c0\ub0b4\uae30\ub85c \ud558\uc790. \uc774\ub294 \uadf8\ub798\ud504\uac00 \ubd84\ub9ac\uc790 S\uc5d0 \uc758\ud574\uc11c W\uc640 B\ub77c\ub294 \ub450 \uac1c\uc758 \uc5f0\uacb0 \uc694\uc18c\ub85c \ub098\ub258\uc5b4 \uc9c4\ub2e4\ub294 \uc758\ubbf8\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc6b0\ub9ac\ub294 \uaca9\uc790 \ubaa8\uc591\uc758 \uadf8\ub798\ud504\uc5d0\uc11c\uc758 \ubd84\ub9ac\uc790\ub97c \uc0b4\ud3b4\ubcf4\ub824 \ud55c\ub2e4. \uc774 \uadf8\ub798\ud504\uc5d0\uc11c \uac01\uac01\uc758 \uaca9\uc790\uc810\uc774 \uc815\uc810\uc744 \uc774\ub8e8\uba70, \uac01\uac01\uc758 \uc815\uc810\uc740 \uc774\uc6c3\ud55c 8\uac1c\uc758 \uc815\uc810\ub4e4\uacfc \uc5f0\uacb0\ub418\uc5b4 \uc788\ub2e4. \uc544\ub798\uc5d0 6&times;6 \uaca9\uc790 \uc5d0 \ub300\ud55c \uc608\uc81c \uadf8\ub9bc\uc774 \uc788\ub2e4. \ud770\uc0c9\uc740 W, \ud68c\uc0c9\uc740 S, \uac80\uc740\uc0c9\uc740 B\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201009\/1.PNG\" style=\"height:352px; width:349px\" \/><\/p>\r\n\r\n<p>\ubb38\uc81c\ub97c \ub2e8\uc21c\ud654\ud558\uae30 \uc704\ud574, \ub2e4\uc74c\uc758 \uc870\uac74\uc744 \ub9cc\uc871\ud558\ub294 \ubd84\ub9ac\uc790\ub9cc \ub2e4\ub8e8\uae30\ub85c \ud558\uc790.<\/p>\r\n\r\n<ol>\r\n\t<li>\ubd84\ub9ac\uc790\uc758 \ubd80\ubd84\uc9d1\ud569\uc740 \ubd84\ub9ac\uc790\ub97c \uc774\ub8e8\uc9c0 \uc54a\ub294\ub2e4.<\/li>\r\n\t<li>\ubd84\ub9ac\uc790\ub294 \uadf8\ub798\ud504\uc5d0\uc11c \ub9e8 \uc717\uc904\uc758 \ud55c \uc810\uacfc \ub9e8 \uc544\ub7ab\uc904\uc758 \ud55c \uc810\uc744 \ud3ec\ud568\ud55c\ub2e4. \ub2e8, 0, 5, 30, 35\ub294 \uc81c\uc678\ud55c\ub2e4.<\/li>\r\n\t<li>\ubd84\ub9ac\uc790\ub97c \ub530\ub77c\uc11c \uadf8\ub798\ud504\ub97c \uc704\uc5d0\uc11c \uc544\ub798\ub85c \uc774\ub3d9\ud560 \ub54c, \ub0b4\ub824\uc624\ub2e4\uac00 \ub2e4\uc2dc \uc62c\ub77c\uac00\ub294 \uacbd\uc6b0\ub294 \uc5c6\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc774\uc81c \ub2e4\uc74c\uc758 \ub450 \ub2e8\uacc4\ub97c \uc218\ud589\ud558\uc5ec \ubd84\ub9ac\uc790\uc758 \ud06c\uae30\ub97c \uc904\uc774\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<ol>\r\n\t<li>B\uc5d0\uc11c \uba87 \uac1c\uc758 \uc815\uc810\uc744 \ud0dd\ud574\uc11c S\uc5d0 \ud3ec\ud568\uc2dc\ud0a8\ub2e4. \uc774\ub54c \ud0dd\ud55c \uc815\uc810\ub4e4\uc740 \ubc18\ub4dc\uc2dc \uc67c\ucabd \uc815\uc810\uc73c\ub85c S\uc5d0 \ud3ec\ud568\ub41c \uc815\uc810\uc744 \uac00\uc9c0\uace0 \uc788\uc5b4\uc57c \ud55c\ub2e4.<\/li>\r\n\t<li>S\uc5d0\uc11c \uba87 \uac1c\uc758 \uc815\uc810\uc744 \uc81c\uac70\ud558\uc5ec W\uc5d0 \ud3ec\ud568\uc2dc\ud0a8\ub2e4. \ub2e8, \uc774\uc804 \ub2e8\uacc4\uc5d0\uc11c \ud3ec\ud568\uc2dc\ud0a8 \uc815\uc810\ub4e4\uc740 \uc81c\uac70\ud560 \uc218 \uc5c6\ub2e4.<\/li>\r\n<\/ol>\r\n\r\n<p>\uc774\uc640 \uac19\uc740 \uac1c\uc120 \ubc29\ubc95\uc744 \uc774\uc6a9\ud558\uc5ec S\uac00 \uc5ec\uc804\ud788 \ubd84\ub9ac\uc790\uc774\ub3c4\ub85d \ud558\uace0, \uc774\ub54c S\uc758 \ud06c\uae30\ub97c \ucd5c\uc18c\ub85c \ud558\ub77c. \uc704\uc758 \uc608\uc81c\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \ud558\uba74 S\uc758 \ud06c\uae30\uac00 7\ub85c \ucd5c\uc18c\uac00 \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/JudgeOnline\/upload\/201009\/2.PNG\" style=\"height:352px; width:349px\" \/><\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uccab\uc9f8 \uc904\uc5d0 \uaca9\uc790\uc758 \ud06c\uae30\ub97c \ub098\ud0c0\ub0b4\ub294 \ub450 \uc815\uc218 N, M(3&le;N,M&le;200)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \uaca9\uc790\uc758 \ud06c\uae30\uac00 N&times;M\uc774\ub77c\ub294 \uc758\ubbf8\uc774\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 M\uac1c\uc758 \ubb38\uc790\uac00 \uc8fc\uc5b4\uc9c0\ub294\ub370, \uac01\uac01\uc740 S, W, B \uc911\uc758 \ud558\ub098\uc774\ub2e4. \uc774\ub294 \ud574\ub2f9 \uc815\uc810\uc774 S, W, B \uc911 \uc5b4\ub290 \uc9d1\ud569\uc5d0 \uc18d\ud574\uc788\ub294\uc9c0\ub97c \ub098\ud0c0\ub0b8\ub2e4. W\ub294 \ubc18\ub4dc\uc2dc S\uc758 \uc67c\ucabd\uc5d0 \uc874\uc7ac\ud55c\ub2e4. \uc798\ubabb\ub41c \uc785\ub825\uc774 \uc8fc\uc5b4\uc9c0\uc9c0\ub294 \uc54a\ub294\ub2e4\uace0 \uac00\uc815\ud574\ub3c4 \uc88b\ub2e4. \ubaa8\ub4e0 \ubb38\uc790\ub294 \ubd99\uc5b4\uc11c \uc785\ub825\ub41c\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 S\uc758 \ucd5c\uc18c \ud06c\uae30\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2288","problem_lang":"1","title":"The Separator in Grid","description":"<p>Given a connected, undirected graph G = (V, E), where V is the vertex set consisting a collection of nodes, and E is the set of edges, each of which connects two nodes from V. A vertex subset S is a separator if the subgraph induced by the vertices in V, but not in S, has two connected components. We shall use the notation [S, W, B] to represent the partition, where the removal of the separator S will give two connected components W and B.&nbsp;<\/p>\r\n\r\n\r\n\r\n<table class=\"table\" style=\"width:100%\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td style=\"width:50%\"><img alt=\"\" src=\"\/JudgeOnline\/upload\/201009\/1.PNG\" style=\"height:352px; opacity:0.9; width:349px\" \/><\/td>\r\n\t\t\t<td style=\"width:50%\"><img alt=\"\" src=\"\/JudgeOnline\/upload\/201009\/2.PNG\" style=\"height:352px; opacity:0.9; width:349px\" \/><\/td>\r\n\t\t<\/tr>\r\n\t\t<tr>\r\n\t\t\t<td>Figure-1. Partition (S,W,B)<\/td>\r\n\t\t\t<td>Figure-2. New Partition<\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n<\/table>\r\n\r\n<p>In this problem, we consider the separators in grids. Each node in a grid is connected to its eight neighbors (if they exist). In Figure-1, we illustrate a partition of a 6*6 grid with a 9-point separator (gray nodes in the figure). The nodes on the left of the separator are in set W (white nodes), and the nodes on the right of the separator are in set B (black nodes).&nbsp;<\/p>\r\n\r\n<p>To simplify the problem, you can assume that all the separators referred in this problem satisfy the following restrictions:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>It&rsquo;s a minimal separator. A separator is minimal if no subset of it forms a separator.&nbsp;<\/li>\r\n\t<li>It begins from a node on the top line of the grid, except the corner (i.e. 30 and 35 in the figures), and ends with a node on the bottom line of the grid, also except the corner (i.e. 0 and 5 in the figures).<\/li>\r\n\t<li>On its way from top to bottom, it can go left, right or down, but never go up.&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>Now we describe a method to improve a given partition on a grid, through which we can reduce the number of nodes in the separator. This method contains two steps:&nbsp;<\/p>\r\n\r\n<ol>\r\n\t<li>Select several nodes from B and add them into S. Any of the selected nodes must have a left neighbor which is in S.&nbsp;<\/li>\r\n\t<li>Remove several nodes from S (excluding the nodes added in the former step), and add them into W.&nbsp;<\/li>\r\n<\/ol>\r\n\r\n<p>After the improvement, we should ensure S is still a separator, and make the number of nodes in S as small as possible. As for Figure-1, we should add 14 and 20 into S, and remove 7, 13, 19 and 25 from S. After that, we obtain a new partition with a 7-point separator shown in Figure-2.&nbsp;<\/p>\r\n\r\n<p>Your task is, given a partition on a grid, to determine the least number of nodes in the separator after the improvement.&nbsp;<\/p>\r\n","input":"<p>There are several test cases. Each case begins with a line containing two integers, N and M (3 &le; M, N &le;&nbsp;200). In each of the following N lines, there are M characters, describing the initial partition of the M*N grid. Every character is &#39;S&#39;, &#39;W&#39; or &#39;B&#39;. It is confirmed that each of these three characters appears at least once in each line, and &#39;W&#39;s are always on the left of &#39;S&#39;s.&nbsp;<\/p>\r\n\r\n<p>A test case of N = 0 and M = 0 indicates the end of input, and should not be processed.&nbsp;<\/p>\r\n","output":"<p>For each test case, you should output one line containing one integer, which is the least number of nodes in the separator after the improvement.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]