시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

숫자가 적혀져 있고, 순서가 있는 루트 있는 트리(Labeled and ordered rooted tree) 2개 T와 T'가 주어진다. 이때, T와 T'사이의 거리를 구하는 프로그램을 작성하시오. 거리란 T를 T'와 동등하게 만드는 최소 연산의 횟수이다.

연산은 총 세가지로 이루어져 있다.

  1. T의 한 노드에 적혀있는 숫자를 바꾼다.
  2. T에서 루트가 아닌 노드를 하나 삭제한다.
  3. T의 루트 아래 어딘가에 노드를 하나 삽입한다.

T와 T'는 순서가 있는 트리이다. 따라서, 리프가 아닌 노드가 자식을 c개 가지고 있는 경우에 1부터 c까지 순서가 존재하며, 1번째 자식, 2번째 자식, ..., c번째 자식이 존재한다.

X와 Y가 동등한 트리가 되려면 X와 Y의 루트에 같은 숫자가 적혀있어야 하고, 같은 개수의 자식을 가져야 한다. 자식의 수를 c라고 했을 때, i번째 자식을 루트로하는 서브트리가 동등해야 한다. (i = 1, 2, ..., c)

T의 루트가 아닌 노드를 삽입하고 삭제하는 방법은 다음과 같다. 먼저, 루트가 아닌 노드 w가 자식을 d개 가지고 있고, w의 부모가 u이고, w가 u의 i번째 자식인 경우를 생각해보자. w를 삭제하게 되면, w의 첫 번째 자식은 u의 i번째 자식이 되고, 두 번째 자식은 u의 (i+1)번째 자식이 된다. j<i인 u의 j번째 자식의 순서는 그대로 유지되지만, j>i인 j번째 자식은 모두 u의 (j+d-1)번째 자식이 된다. w의 자식이 u의 자식으로 삽입되어서 오른쪽으로 밀려난다고 생각하면 된다.

루트가 아닌 노드 w를 삽입하려면, 먼저 w의 부모가 될 노드 u를 선택해야 한다. 그 다음, u의 자식 중에서 연속된 부분 수열을 골라서 w의 자식으로 만들어주고, 그 자리에 w를 삽입한다. 삽입과 동시에 w에는 적절한 숫자를 적을 수 있다.

T의 루트를 삭제하거나, 루트의 위에 새 노드를 삽입하는 것은 불가능하다. 루트에 적혀있는 숫자는 바꿀 수 있다.

w를 삭제하는 경우와 u의 2번째 자식부터 4번째 자식을 w의 자식으로 만들고 u 아래에 삽입하는 경우.

입력

첫째 줄에 T와 T'의 크기 n, m이 주어진다. (1 ≤ n, m ≤ 60) 다음 n개 줄에는 T의 정보가 주어진다. i번째 줄에는 i번째 노드의 정보가 주어진다. 노드에 적혀있는 숫자, 자식의 수가 주어지며, 그 다음에는 자식이 순서대로 주어진다. 다음 m개 줄에는 T'의 정보가 주어진다. 숫자는 항상 음이 아닌 정수이며, 각 트리의 루트 노드는 다른 노드의 자식으로 포함되지 않는 노드이다.

출력

T를 T'와 동등하게 만들기 위해 필요한 연산의 최소 횟수를 출력한다.

예제 입력 1

3 2
6 0
1 2 0 2
4 0
2 1 1
4 0

예제 출력 1

2
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(i = 1, 2, ..., c)<\/p>\r\n\r\n<p>T\uc758 \ub8e8\ud2b8\uac00 \uc544\ub2cc \ub178\ub4dc\ub97c \uc0bd\uc785\ud558\uace0 \uc0ad\uc81c\ud558\ub294 \ubc29\ubc95\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4. \uba3c\uc800, \ub8e8\ud2b8\uac00 \uc544\ub2cc \ub178\ub4dc w\uac00 \uc790\uc2dd\uc744 d\uac1c \uac00\uc9c0\uace0 \uc788\uace0, w\uc758 \ubd80\ubaa8\uac00 u\uc774\uace0, w\uac00 u\uc758 i\ubc88\uc9f8 \uc790\uc2dd\uc778 \uacbd\uc6b0\ub97c \uc0dd\uac01\ud574\ubcf4\uc790. w\ub97c \uc0ad\uc81c\ud558\uac8c \ub418\uba74, w\uc758 \uccab \ubc88\uc9f8 \uc790\uc2dd\uc740 u\uc758 i\ubc88\uc9f8 \uc790\uc2dd\uc774 \ub418\uace0, \ub450 \ubc88\uc9f8 \uc790\uc2dd\uc740 u\uc758 (i+1)\ubc88\uc9f8 \uc790\uc2dd\uc774 \ub41c\ub2e4. j&lt;i\uc778 u\uc758 j\ubc88\uc9f8 \uc790\uc2dd\uc758 \uc21c\uc11c\ub294 \uadf8\ub300\ub85c \uc720\uc9c0\ub418\uc9c0\ub9cc, j&gt;i\uc778 j\ubc88\uc9f8 \uc790\uc2dd\uc740 \ubaa8\ub450 u\uc758 (j+d-1)\ubc88\uc9f8 \uc790\uc2dd\uc774 \ub41c\ub2e4. w\uc758 \uc790\uc2dd\uc774 u\uc758 \uc790\uc2dd\uc73c\ub85c \uc0bd\uc785\ub418\uc5b4\uc11c \uc624\ub978\ucabd\uc73c\ub85c \ubc00\ub824\ub09c\ub2e4\uace0 \uc0dd\uac01\ud558\uba74 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub8e8\ud2b8\uac00 \uc544\ub2cc \ub178\ub4dc w\ub97c \uc0bd\uc785\ud558\ub824\uba74, \uba3c\uc800 w\uc758 \ubd80\ubaa8\uac00 \ub420 \ub178\ub4dc u\ub97c \uc120\ud0dd\ud574\uc57c \ud55c\ub2e4. \uadf8 \ub2e4\uc74c, u\uc758 \uc790\uc2dd \uc911\uc5d0\uc11c \uc5f0\uc18d\ub41c \ubd80\ubd84 \uc218\uc5f4\uc744 \uace8\ub77c\uc11c w\uc758 \uc790\uc2dd\uc73c\ub85c \ub9cc\ub4e4\uc5b4\uc8fc\uace0, \uadf8 \uc790\ub9ac\uc5d0 w\ub97c \uc0bd\uc785\ud55c\ub2e4. \uc0bd\uc785\uacfc \ub3d9\uc2dc\uc5d0 w\uc5d0\ub294 \uc801\uc808\ud55c \uc22b\uc790\ub97c \uc801\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p>T\uc758 \ub8e8\ud2b8\ub97c \uc0ad\uc81c\ud558\uac70\ub098, \ub8e8\ud2b8\uc758 \uc704\uc5d0 \uc0c8 \ub178\ub4dc\ub97c \uc0bd\uc785\ud558\ub294 \uac83\uc740&nbsp;\ubd88\uac00\ub2a5\ud558\ub2e4. \ub8e8\ud2b8\uc5d0 \uc801\ud600\uc788\ub294 \uc22b\uc790\ub294 \ubc14\uafc0 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/treesim.png\" style=\"height:228px; width:543px\" \/><\/p>\r\n\r\n<p>w\ub97c \uc0ad\uc81c\ud558\ub294 \uacbd\uc6b0\uc640 u\uc758 2\ubc88\uc9f8 \uc790\uc2dd\ubd80\ud130 4\ubc88\uc9f8 \uc790\uc2dd\uc744 w\uc758 \uc790\uc2dd\uc73c\ub85c \ub9cc\ub4e4\uace0 u \uc544\ub798\uc5d0 \uc0bd\uc785\ud558\ub294 \uacbd\uc6b0.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 T\uc640 T&#39;\uc758 \ud06c\uae30 n, m\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; n, m &le; 60) \ub2e4\uc74c n\uac1c \uc904\uc5d0\ub294 T\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. i\ubc88\uc9f8 \uc904\uc5d0\ub294 i\ubc88\uc9f8 \ub178\ub4dc\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub178\ub4dc\uc5d0 \uc801\ud600\uc788\ub294 \uc22b\uc790, \uc790\uc2dd\uc758 \uc218\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uadf8 \ub2e4\uc74c\uc5d0\ub294 \uc790\uc2dd\uc774 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c m\uac1c \uc904\uc5d0\ub294 T&#39;\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uc22b\uc790\ub294 \ud56d\uc0c1 \uc74c\uc774 \uc544\ub2cc \uc815\uc218\uc774\uba70, \uac01 \ud2b8\ub9ac\uc758 \ub8e8\ud2b8 \ub178\ub4dc\ub294 \ub2e4\ub978 \ub178\ub4dc\uc758 \uc790\uc2dd\uc73c\ub85c \ud3ec\ud568\ub418\uc9c0 \uc54a\ub294 \ub178\ub4dc\uc774\ub2e4.<\/p>\r\n","output":"<p>T\ub97c T&#39;\uc640 \ub3d9\ub4f1\ud558\uac8c \ub9cc\ub4e4\uae30 \uc704\ud574 \ud544\uc694\ud55c \uc5f0\uc0b0\uc758 \ucd5c\uc18c \ud69f\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"7618","problem_lang":"1","title":"Tree Similarity","description":"<p>You are given two labeled and ordered rooted trees T and T&#39; and would like to calculate the distance from T to T&#39;, which is the minimum number of operations you can perform on T to make it equivalent to T&#39;. For each operation you can choose to do one of three things: (1) change the label of one node in T, (2) delete a non-root node in T, or (3) insert a new node in T at a position somewhere below its root. Recall the trees T and T&#39; are ordered, which means that if a non-leaf node has c children, its children are ordered from 1 to c. That is, there is a 1st child, a 2nd child, etc., all the way up to a cth child. When we say a tree X is equivalent to a tree Y , we mean the root of X should have the same label as the root of Y , their roots should have the same number of children (call it c), and the subtree rooted at the ith child of the root of X should be equivalent to the subtree rooted at the ith child of the root of Y for i = 1, 2, . . . , c.<\/p>\r\n\r\n<p>We now describe what we mean by deletion and insertion of non-root nodes in T. When deleting a non-root node w with d children, let u be its parent and suppose w is u&rsquo;s ith child. Then the \ufb01rst child of w becomes u&rsquo;s ith child, the second child of w becomes u&rsquo;s (i + 1)st child, etc. For j &lt; i, the jth child of u remains the same, but for all j &gt; i, the child which was formerly the jth child of u now becomes its (j+d&minus;1)st child (they get &ldquo;shifted over&rdquo; due to the insertion of w&rsquo;s children into u&rsquo;s child list). To insert a non-root node w into the tree, we can choose any node u to be its parent, and we can choose any contiguous subsequence (possibly empty) of u&rsquo;s children to become w&rsquo;s children, putting w in their place. When inserting a node, we can give it any label we want at the time of insertion. The root of T can never be deleted, and you can never insert a new node above the root to become the old root&rsquo;s parent. You can, however, change the label of the root.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/treesim.png\" style=\"height:228px; width:543px\" \/><\/p>\r\n","input":"<p>The \ufb01rst line contains n and m separated by a space, the sizes of the trees T and T&#39;, respectively (1 &le; n, m &le; 60). The next n lines describe T. On the ith line is a description of the ith node in the tree: its label, the number of children it has, then a list of its children in order from \ufb01rst to last, all space-separated. The next m lines similarly describe T&#39;. Labels are always nonnegative integers. The root of each tree is the node which is not the child of any other node in the tree.<\/p>\r\n","output":"<p>On a single line output the minimum number of operations that can be performed on T to make it equivalent to T&#39;, followed by a newline.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

University > The MIT Programming Contest > 2008-09 > MIT Programming Contest Individual Round 2008 6번