시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

그래프 G는 정점의 집합 V와 간선의 집합 E로 이루어져 있고, G = (V, E)로 나타낸다. 대부분의 경우에 V와 E는 명시되어 있다. 일부 그래프의 경우에는 집합이 명시되어 있지 않다. 예를 들어, 순열 그래프는 간선의 집합이 명시되어 있지 않다.

{1, 2, 3, 4, 5}로 이루어진 두 순열 (2, 5, 4, 1, 3)과 (1, 5, 3, 2, 4)가 있다. 평행선을 그리고, 그 위에 순열에 적힌 숫자 순서대로 정점을 그린다. 그 다음 같은 숫자끼리 선분을 연결한다. 아래 그림과 같이 교차하는 선분의 쌍은 총 여섯 개라는 것을 알 수 있다.

교차하는 쌍은 순열 그래프의 간선이 된다. 순열 그래프의 정점은 숫자가 되고, 간선은 교차하는 쌍이 된다. 위의 예를 이용해 순열 그래프를 만들면 V = {1, 2, 3, 4, 5}, E = {(1,2), (1,4), (1,5), (2,3), (2,5), (3,4)}. 위의 두 순열을 이용해 순열 그래프를 그리면 아래 그림과 같이 된다.

{1, 2, ..., n}으로 이루어진 두 순열이 주어졌을 때, 두 순열을 이용해 만든 순열 그래프의 간선의 개수를 구하는 프로그램을 작성하시오. 예를 들어, (2, 5, 4, 1, 3)과 (1, 5, 3, 2, 4)로 만든 순열 그래프의 간선의 개수는 6개이다.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 n이 주어진다. 둘째 줄과 셋째 줄에는 두 순열이 주어진다. 순열은 {1, 2, ..., n}으로 이루어져 있고, 공백으로 구분되어져 있다. (1 ≤ n ≤ 100,000)

출력

각 테스트 케이스 마다, 입력으로 주어진 두 순열로 만든 순열 그래프의 간선의 개수를 출력한다.

예제 입력 1

3
5
2 5 4 1 3
1 5 3 2 4
7
5 6 7 1 2 3 4
5 6 7 1 2 3 4
7
1 5 3 4 2 7 6
7 1 5 3 4 2 6

예제 출력 1

6
0
5

힌트

[{"problem_id":"9463","problem_lang":"0","title":"\uc21c\uc5f4 \uadf8\ub798\ud504","description":"<p>\uadf8\ub798\ud504 G\ub294 \uc815\uc810\uc758 \uc9d1\ud569 V\uc640 \uac04\uc120\uc758 \uc9d1\ud569 E\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, G = (V, E)\ub85c \ub098\ud0c0\ub0b8\ub2e4. \ub300\ubd80\ubd84\uc758 \uacbd\uc6b0\uc5d0 V\uc640 E\ub294 \uba85\uc2dc\ub418\uc5b4 \uc788\ub2e4. \uc77c\ubd80 \uadf8\ub798\ud504\uc758 \uacbd\uc6b0\uc5d0\ub294 \uc9d1\ud569\uc774 \uba85\uc2dc\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc21c\uc5f4 \uadf8\ub798\ud504\ub294 \uac04\uc120\uc758 \uc9d1\ud569\uc774 \uba85\uc2dc\ub418\uc5b4 \uc788\uc9c0 \uc54a\ub2e4.<\/p>\r\n\r\n<p>{1, 2, 3, 4, 5}\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ub450 \uc21c\uc5f4 (2, 5, 4, 1, 3)\uacfc (1, 5, 3, 2, 4)\uac00 \uc788\ub2e4. \ud3c9\ud589\uc120\uc744 \uadf8\ub9ac\uace0, \uadf8 \uc704\uc5d0 \uc21c\uc5f4\uc5d0 \uc801\ud78c \uc22b\uc790 \uc21c\uc11c\ub300\ub85c \uc815\uc810\uc744 \uadf8\ub9b0\ub2e4. \uadf8 \ub2e4\uc74c \uac19\uc740 \uc22b\uc790\ub07c\ub9ac \uc120\ubd84\uc744 \uc5f0\uacb0\ud55c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc774 \uad50\ucc28\ud558\ub294 \uc120\ubd84\uc758 \uc30d\uc740 \ucd1d \uc5ec\uc12f \uac1c\ub77c\ub294 \uac83\uc744 \uc54c \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/perm1.png\" \/><\/p>\r\n\r\n<p>\uad50\ucc28\ud558\ub294 \uc30d\uc740 \uc21c\uc5f4 \uadf8\ub798\ud504\uc758 \uac04\uc120\uc774 \ub41c\ub2e4. \uc21c\uc5f4 \uadf8\ub798\ud504\uc758 \uc815\uc810\uc740 \uc22b\uc790\uac00 \ub418\uace0, \uac04\uc120\uc740 \uad50\ucc28\ud558\ub294 \uc30d\uc774 \ub41c\ub2e4. \uc704\uc758 \uc608\ub97c \uc774\uc6a9\ud574 \uc21c\uc5f4 \uadf8\ub798\ud504\ub97c \ub9cc\ub4e4\uba74 V = {1, 2, 3, 4, 5}, E = {(1,2), (1,4), (1,5), (2,3), (2,5), (3,4)}. \uc704\uc758 \ub450 \uc21c\uc5f4\uc744 \uc774\uc6a9\ud574 \uc21c\uc5f4 \uadf8\ub798\ud504\ub97c \uadf8\ub9ac\uba74 \uc544\ub798 \uadf8\ub9bc\uacfc \uac19\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/perm2.png\" style=\"height:150px; width:232px\" \/><\/p>\r\n\r\n<p>{1, 2, ..., n}\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \ub450 \uc21c\uc5f4\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub450 \uc21c\uc5f4\uc744 \uc774\uc6a9\ud574 \ub9cc\ub4e0 \uc21c\uc5f4 \uadf8\ub798\ud504\uc758 \uac04\uc120\uc758 \uac1c\uc218\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc608\ub97c \ub4e4\uc5b4, (2, 5, 4, 1, 3)\uacfc (1, 5, 3, 2, 4)\ub85c \ub9cc\ub4e0 \uc21c\uc5f4 \uadf8\ub798\ud504\uc758 \uac04\uc120\uc758 \uac1c\uc218\ub294 6\uac1c\uc774\ub2e4.<\/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\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 n\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uacfc \uc14b\uc9f8 \uc904\uc5d0\ub294 \ub450 \uc21c\uc5f4\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uc21c\uc5f4\uc740 {1, 2, ..., n}\uc73c\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\uace0, \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4\uc838 \uc788\ub2e4. (1 &le; n &le; 100,000)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ub450 \uc21c\uc5f4\ub85c \ub9cc\ub4e0 \uc21c\uc5f4 \uadf8\ub798\ud504\uc758 \uac04\uc120\uc758 \uac1c\uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9463","problem_lang":"1","title":"Permutation Graphs","description":"<p>A graph G is defined as a tuple of the set of vertices V and the set of edges E, i.e. G = (V, E). The two sets, V and E, are usually given explicitly. For some graphs, however, these sets are given implicitly. A permuation graph is such a graph, where the set of edges is given implicitly.&nbsp;<br \/>\r\n&nbsp;<br \/>\r\nFor instance, consider two permutations (2, 5, 4, 1, 3) and (1, 5, 3, 2, 4) of the numbers {1, 2, 3, 4, 5}. If we draw line segments connecting the corresponding numbers between two parallel lines, containing the vertices in the two permutation orders, we can find six intersecting pairs of line segments as shown in Figure 1.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/perm1.png\" style=\"opacity:0.9\" \/><\/p>\r\n\r\n<p>Figure 1: Six intersecting pairs of line segments given two permutations&nbsp;<\/p>\r\n\r\n<p>The intersecting pairs define a permutation graph. Its vertices are the numbers and its edges are the intersecting pairs. In this example, V = {1, 2, 3, 4, 5} and E = {(1, 2), (1, 4), (1, 5), (2, 3), (2, 5), (3, 4)}. This kind of graphs is called a permutation graph. The two permutations above define the permutation graph as shown in Figure 2.&nbsp;<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/perm2.png\" style=\"height:150px; width:232px\" \/><\/p>\r\n\r\n<p>Figure 2: The permutation graph defined by two permutations (2, 5, 4, 1, 3) and (1, 5, 3, 2, 4)<\/p>\r\n\r\n<p>The problem is to find the number of edges of the permutation graph given two permutations of the same set of numbers {1, 2, &hellip;, n} for some n. For instance, if the two permutations (2, 5, 4, 1, 3) and (1, 5, 3, 2, 4) are given as input, your program should print 6.&nbsp;<\/p>\r\n","input":"<p>Your program is to read 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. From the second line, each test case is given. A test case consists of three lines. The first line of a test case contains n, the upper bound of the elements of the set {1, 2, &hellip;, n} for which the permutations are to be defined. The second and the third lines of the test case contain two permutations. The permutations are given as a sequence of natural numbers in {1, 2, &hellip;, n} separated by one space. The largest possible number n of a permutation is less than or equal to 100,000 (1 &le; n &le; 100,000).&nbsp;<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain the number of edges for the permutation graph corresponding to each test case.&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 - Daejeon 2013 I번