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문제

지질학에서 하천계는 유향그래프로 나타낼 수 있다. 강은 간선으로 나타내며, 물이 흐르는 방향이 간선의 방향이 된다. 노드는 호수나 샘처럼 강이 시작하는 곳, 강이 합쳐지거나 나누어지는 곳, 바다와 만나는 곳이다.

네모 안의 숫자는 순서를 나타내고, 동그라미 안의 숫자는 노드 번호를 나타낸다.

하천계의 Strahler 순서는 다음과 같이 구할 수 있다.

  • 강의 근원인 노드의 순서는 1이다.
  • 나머지 노드는 그 노드로 들어오는 강의 순서 중 가장 큰 값을 i라고 했을 때, 들어오는 모든 강 중에서 Strahler 순서가 i인 강이 1개이면 순서는 i, 2개 이상이면 순서는 i+1이다.

하천계의 순서는 바다와 만나는 노드의 순서와 같다. 바다와 만나는 노드는 항상 1개이며, 위의 그림의 Strahler 순서는 3이다.

하천계의 정보가 주어졌을 때, Strahler 순서를 구하는 프로그램을 작성하시오.

실제 강 중에서 Strahler 순서가 가장 큰 강은 아마존 강(12)이며, 미국에서 가장 큰 값을 갖는 강은 미시시피 강(10)이다.

노드 M은 항상 바다와 만나는 노드이다.

입력

첫째 줄에 테스트 케이스의 수 T (1 ≤ T ≤ 1000)가 주어진다.

각 테스트 케이스의 첫째 줄에는 K, M, P가 주어진다. K는 테스트 케이스 번호, M은 노드의 수, P는 간선의 수이다. (2 ≤ M ≤ 1000) 다음 P개 줄에는 간선의 정보를 나타내는 A, B가 주어지며, A에서 B로 물이 흐른다는 뜻이다. (1 ≤ A, B ≤ M) M은 항상 바다와 만나는 노드이며, 밖으로 향하는 간선은 존재하지 않는다.

출력

각 테스트 케이스마다 테스트 케이스 번호와 입력으로 주어진 하천계의 Strahler 순서를 출력한다.

예제 입력 1

1
1 7 8
1 3
2 3
6 4
3 4
3 5
6 7
5 7
4 7

예제 출력 1

1 3
[{"problem_id":"9470","problem_lang":"0","title":"Strahler \uc21c\uc11c","description":"<p>\uc9c0\uc9c8\ud559\uc5d0\uc11c \ud558\ucc9c\uacc4\ub294 \uc720\ud5a5\uadf8\ub798\ud504\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uac15\uc740 \uac04\uc120\uc73c\ub85c \ub098\ud0c0\ub0b4\uba70, \ubb3c\uc774 \ud750\ub974\ub294 \ubc29\ud5a5\uc774 \uac04\uc120\uc758 \ubc29\ud5a5\uc774 \ub41c\ub2e4. \ub178\ub4dc\ub294 \ud638\uc218\ub098 \uc0d8\ucc98\ub7fc \uac15\uc774 \uc2dc\uc791\ud558\ub294 \uacf3, \uac15\uc774 \ud569\uccd0\uc9c0\uac70\ub098 \ub098\ub204\uc5b4\uc9c0\ub294 \uacf3, \ubc14\ub2e4\uc640 \ub9cc\ub098\ub294 \uacf3\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/strahler.png\" style=\"height:299px; width:354px\" \/><\/p>\r\n\r\n<p>\ub124\ubaa8 \uc548\uc758 \uc22b\uc790\ub294 \uc21c\uc11c\ub97c \ub098\ud0c0\ub0b4\uace0, \ub3d9\uadf8\ub77c\ubbf8 \uc548\uc758 \uc22b\uc790\ub294 \ub178\ub4dc \ubc88\ud638\ub97c \ub098\ud0c0\ub0b8\ub2e4.<\/p>\r\n\r\n<p>\ud558\ucc9c\uacc4\uc758 Strahler \uc21c\uc11c\ub294 \ub2e4\uc74c\uacfc \uac19\uc774 \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uac15\uc758 \uadfc\uc6d0\uc778 \ub178\ub4dc\uc758 \uc21c\uc11c\ub294 1\uc774\ub2e4.<\/li>\r\n\t<li>\ub098\uba38\uc9c0 \ub178\ub4dc\ub294 \uadf8 \ub178\ub4dc\ub85c \ub4e4\uc5b4\uc624\ub294 \uac15\uc758 \uc21c\uc11c \uc911 \uac00\uc7a5 \ud070 \uac12\uc744 i\ub77c\uace0 \ud588\uc744 \ub54c, \ub4e4\uc5b4\uc624\ub294 \ubaa8\ub4e0 \uac15 \uc911\uc5d0\uc11c Strahler \uc21c\uc11c\uac00 i\uc778 \uac15\uc774&nbsp;1\uac1c\uc774\uba74 \uc21c\uc11c\ub294 i, 2\uac1c \uc774\uc0c1\uc774\uba74 \uc21c\uc11c\ub294 i+1\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ud558\ucc9c\uacc4\uc758 \uc21c\uc11c\ub294 \ubc14\ub2e4\uc640 \ub9cc\ub098\ub294 \ub178\ub4dc\uc758 \uc21c\uc11c\uc640 \uac19\ub2e4. \ubc14\ub2e4\uc640 \ub9cc\ub098\ub294 \ub178\ub4dc\ub294 \ud56d\uc0c1 1\uac1c\uc774\uba70, \uc704\uc758 \uadf8\ub9bc\uc758 Strahler \uc21c\uc11c\ub294 3\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud558\ucc9c\uacc4\uc758 \uc815\ubcf4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, Strahler \uc21c\uc11c\ub97c \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n\r\n<p>\uc2e4\uc81c \uac15 \uc911\uc5d0\uc11c Strahler \uc21c\uc11c\uac00 \uac00\uc7a5 \ud070 \uac15\uc740&nbsp;\uc544\ub9c8\uc874 \uac15(12)\uc774\uba70, \ubbf8\uad6d\uc5d0\uc11c \uac00\uc7a5 \ud070 \uac12\uc744 \uac16\ub294 \uac15\uc740 \ubbf8\uc2dc\uc2dc\ud53c \uac15(10)\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub178\ub4dc M\uc740 \ud56d\uc0c1 \ubc14\ub2e4\uc640 \ub9cc\ub098\ub294 \ub178\ub4dc\uc774\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uc218 T (1 &le; T &le; 1000)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 K, M, P\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. K\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638, M\uc740 \ub178\ub4dc\uc758 \uc218, P\ub294 \uac04\uc120\uc758 \uc218\uc774\ub2e4. (2 &le; M &le; 1000) \ub2e4\uc74c P\uac1c \uc904\uc5d0\ub294 \uac04\uc120\uc758 \uc815\ubcf4\ub97c \ub098\ud0c0\ub0b4\ub294 A, B\uac00 \uc8fc\uc5b4\uc9c0\uba70, A\uc5d0\uc11c B\ub85c \ubb3c\uc774 \ud750\ub978\ub2e4\ub294 \ub73b\uc774\ub2e4. (1 &le; A, B &le; M) M\uc740 \ud56d\uc0c1 \ubc14\ub2e4\uc640 \ub9cc\ub098\ub294 \ub178\ub4dc\uc774\uba70, \ubc16\uc73c\ub85c \ud5a5\ud558\ub294 \uac04\uc120\uc740 \uc874\uc7ac\ud558\uc9c0 \uc54a\ub294\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ubc88\ud638\uc640 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \ud558\ucc9c\uacc4\uc758 Strahler \uc21c\uc11c\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"9470","problem_lang":"1","title":"Strahler Order","description":"<p>In geology, a river system can be represented as a directed graph. Each river segment is an edge;with the edge pointing the same way the water flows. Nodes are either the source of a river segment(for example, a lake or spring), where river segments merge or diverge, or the mouth of the river<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/strahler.png\" style=\"height:299px; width:354px\" \/><\/p>\r\n\r\n<p>Note: The number in a box is the order. The number in a circle is the node number.<\/p>\r\n\r\n<p>The Strahler order of a river system is computed as follows.<\/p>\r\n\r\n<ul>\r\n\t<li>The order of each source node is 1.<\/li>\r\n\t<li>For every other node, let i be the highest order of all its upstream nodes. If just one upstreamnode has order i, then this node also has order i. If two or more upstream nodes have orderi, then this node has order i+1.<\/li>\r\n<\/ul>\r\n\r\n<p>The order of the entire river system is the order of the mouth node. In this problem, the river systemwill have just one mouth. In the picture above, the Strahler order is three (3).<\/p>\r\n\r\n<p>You must write a program to determine the order of a given river system.<\/p>\r\n\r\n<p>The actual river with the highest order is the Amazon, with order 12. The highest in the U.S. is theMississippi, with order 10.<\/p>\r\n\r\n<p>Node M is the mouth of the river. It has no outgoing edges.<\/p>\r\n","input":"<p>The first line of input contains a single integer K, (1 &le; K &le; 1000), which is the number of data setsthat follow. Each data set should be processed identically and independently.<\/p>\r\n\r\n<p>Each data set consists of multiple lines of input. The first line of each data set contains three positiveintegers, K, M and P (2 &le; M &le; 1000). K is the data set number. M is the number of nodes in thegraph and P is the number of edges. The first line is followed by P lines, each describing an edge ofthe graph. The line will contain two positive integers, A and B, indicating that water flows from node Ato node B (1 &le; A, B &le; M). Node M is the mouth of the river. It has no outgoing edges.<\/p>\r\n","output":"<p>For each data set there is a single line of output. The line consists of the data set number, a singlespace and the order of the river system.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > North America > Greater New York Region > 2013 Greater New York Programming Contest C번