시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

수평선 상에 N개의 점이 있다. N개의 점은 서로 다른 위치에 존재하며, 왼쪽부터 1번부터 N번까지의 번호가 붙어 있다. 각 점에는 색이 있어 i번 점의 색깔은 Ai이다. 당신은 두 점을 연결하는 선을 여러개 긋고 싶어한다. 그러나 점을 연결하는 선에는 다음과 같은 제한이 존재한다.

  • 동일한 색을 가진 두 점은 이을 수 없다.
  • 점들을 잇는 선은 수평선보다 위에 있어야 한다. 즉, 집들이 있는 수평선을 y=0이라고 할 때, 점을 잇는 선들은 양 끝점을 제외한 모든 부분이 y>0 영역 내에 존재하는 곡선이라고 생각할 수 있다.
  • 점들을 잇는 선들끼리는 교차할 수 없다. (끝점을 공유하는 것은 가능하다)

예를 들어, 아래와 같이 4개의 점이 있고 1, 2번 점은 붉은색, 3, 4번 점은 푸른색인 경우 1번 점과 4번 점, 2번 점과 3번 점, 2번 점과 4번 점 사이에 선을 연결하여 총 3개를 그을 수 있다.

선을 4개 그으려면 3가지 제한 중 적어도 하나 이상을 위반하게 되므로 이 경우 3개가 최대이다. 각 점의 색깔이 주어질 때, 어떤 제한도 위반하지 않으면서 두 점 사이를 연결하는 선을 최대한 많이 그리는 방법을 찾아 각 선이 어떤 두 점을 연결하는지 출력하라. 가능한 여러 방법이 존재하는 경우, 그 중 하나를 출력하면 정답으로 인정된다.

입력

첫 줄에는 테스트 케이스의 개수 T(1T≤101) 주어진다.

각 테스트 케이스의 첫 줄에는 집의 수 N과 색의 종류 M이 주어진다. (2≤N≤30,000, 2≤MN).

각 테스트 케이스의 둘째 줄에는 각 점의 색깔 A1,A2, ..., AN이 주어진다. (1≤AiM).

출력

각 테스트 케이스마다 첫 줄에는 “Case #C”를 출력하여야 한다. 이때 C는 테스트 케이스의 번호이다.

그 다음 줄에는 두 점 사이를 연결하는 선의 최대 개수 K를 출력한다.

그 다음 K줄에 걸쳐 각 선이 연결하는 두 점의 번호를 출력한다.

예제 입력 1

3
4 2
1 1 2 2
4 2
1 2 1 2
3 3
1 2 3

예제 출력 1

Case #1
3
1 4
2 3
2 4
Case #2
4
1 2
1 4
2 3
3 4
Case #3
3
1 2
2 3
1 3
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(\ub05d\uc810\uc744 \uacf5\uc720\ud558\ub294 \uac83\uc740 \uac00\ub2a5\ud558\ub2e4)<\/li>\r\n<\/ul>\r\n\r\n<p dir=\"ltr\">\uc608\ub97c \ub4e4\uc5b4, \uc544\ub798\uc640 \uac19\uc774 4\uac1c\uc758 \uc810\uc774 \uc788\uace0 1, 2\ubc88 \uc810\uc740 \ubd89\uc740\uc0c9, 3, 4\ubc88 \uc810\uc740 \ud478\ub978\uc0c9\uc778 \uacbd\uc6b0  1\ubc88 \uc810\uacfc 4\ubc88 \uc810, 2\ubc88 \uc810\uacfc 3\ubc88 \uc810, 2\ubc88 \uc810\uacfc 4\ubc88 \uc810 \uc0ac\uc774\uc5d0 \uc120\uc744 \uc5f0\uacb0\ud558\uc5ec \ucd1d 3\uac1c\ub97c \uadf8\uc744 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\"><b id=\"docs-internal-guid-09dcf727-7fff-67d5-4536-a36b6236c486\"><img height=\"164\" src=\"https:\/\/lh3.googleusercontent.com\/uCKvXdUXmwSUOGJ7A-8bM1JZ0V7QdjZBoHoKghhBM4sU_qRlJsCcFJS3OtbNkAzqZ7KcTBbai2Czt-3iE9ARwYt4gQj8-lgklNTojAYf5bGbKU416DU-8UEjWmlqgkIyKlwMdqlA52aV18E49eSGIQ\" width=\"602\" \/><\/b><\/p>\r\n\r\n<p dir=\"ltr\">\uc120\uc744 4\uac1c \uadf8\uc73c\ub824\uba74 3\uac00\uc9c0 \uc81c\ud55c \uc911 \uc801\uc5b4\ub3c4 \ud558\ub098 \uc774\uc0c1\uc744 \uc704\ubc18\ud558\uac8c \ub418\ubbc0\ub85c \uc774 \uacbd\uc6b0 3\uac1c\uac00 \ucd5c\ub300\uc774\ub2e4. \uac01 \uc810\uc758 \uc0c9\uae54\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, \uc5b4\ub5a4 \uc81c\ud55c\ub3c4 \uc704\ubc18\ud558\uc9c0 \uc54a\uc73c\uba74\uc11c \ub450 \uc810 \uc0ac\uc774\ub97c \uc5f0\uacb0\ud558\ub294 \uc120\uc744 \ucd5c\ub300\ud55c \ub9ce\uc774 \uadf8\ub9ac\ub294 \ubc29\ubc95\uc744 \ucc3e\uc544 \uac01 \uc120\uc774 \uc5b4\ub5a4 \ub450 \uc810\uc744 \uc5f0\uacb0\ud558\ub294\uc9c0 \ucd9c\ub825\ud558\ub77c. \uac00\ub2a5\ud55c \uc5ec\ub7ec \ubc29\ubc95\uc774 \uc874\uc7ac\ud558\ub294 \uacbd\uc6b0, \uadf8 \uc911 \ud558\ub098\ub97c \ucd9c\ub825\ud558\uba74 \uc815\ub2f5\uc73c\ub85c \uc778\uc815\ub41c\ub2e4.<\/p>\r\n","input":"<p dir=\"ltr\">\uccab \uc904\uc5d0\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 <em>T(1<\/em>&le;<em>T<\/em>&le;101)<i>\uac00<\/i> \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p dir=\"ltr\">\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab \uc904\uc5d0\ub294 \uc9d1\uc758 \uc218 <em>N<\/em>\uacfc \uc0c9\uc758 \uc885\ub958 <em>M<\/em>\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (2&le;<em>N<\/em>&le;30,000, 2&le;<em>M<\/em>&le;<em>N<\/em>).<\/p>\r\n\r\n<p dir=\"ltr\">\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \uc810\uc758 \uc0c9\uae54 \b<em>A<sub>1<\/sub><\/em>,<em>A<span style=\"font-size: 10.8333px;\">2<\/span><\/em>, ..., <em>A<span style=\"font-size: 10.8333px;\">N<\/span><\/em>\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (1&le;<em>A<span style=\"font-size: 10.8333px;\">i<\/span><\/em>&le;<em>M<\/em>).<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \uccab \uc904\uc5d0\ub294 &ldquo;Case #C&rdquo;\ub97c \ucd9c\ub825\ud558\uc5ec\uc57c \ud55c\ub2e4. \uc774\ub54c C\ub294 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \ubc88\ud638\uc774\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \ub2e4\uc74c \uc904\uc5d0\ub294 \ub450 \uc810 \uc0ac\uc774\ub97c \uc5f0\uacb0\ud558\ub294 \uc120\uc758 \ucd5c\ub300 \uac1c\uc218 <em>K<\/em>\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uadf8 \ub2e4\uc74c <em>K<\/em>\uc904\uc5d0 \uac78\uccd0 \uac01 \uc120\uc774 \uc5f0\uacb0\ud558\ub294 \ub450 \uc810\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"25397","problem_lang":"1","title":"Connect the Dots","description":"<p>Consider $N$ different points on the $Ox$ axis, numbered $1, 2, \\ldots, N$ from left to right. Each point has a color: the color of point $i$ is $A_i$.<\/p>\r\n\r\n<p>You want to draw several curves, each curve connecting two points. However, there are the following restrictions.<\/p>\r\n\r\n<ul>\r\n\t<li>Two points of the same color cannot be connected.<\/li>\r\n\t<li>Each curve connecting the points must be above the x-axis. In other words, each interior point of each curve has $y &gt; 0$. (Endpoints have $y = 0$.)<\/li>\r\n\t<li>Two different curves cannot have a common interior point. (It is possible to share endpoints.)<\/li>\r\n<\/ul>\r\n\r\n<p>For example, if there are 4 points as shown below, points 1 and 2 are red, and points 3 and 4 are blue, you can draw a total of 3 curves: between points 1 and 4, 2 and 3, 2 and 4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/4a1d7f3a-5802-433d-8a65-fefbdb6e4dcd\/-\/preview\/\" style=\"width: 458px; height: 125px;\" \/><\/p>\r\n\r\n<p>Drawing 4 curves would violate at least one of the three restrictions above, so 3 is the maximum in this case.<\/p>\r\n\r\n<p>Given the color of each point, find a way to draw as many curves connecting two points as possible without violating any restrictions, and print which two points each curve connects.<\/p>\r\n","input":"<p>The first line contains an integer $T$, the number of test cases ($1 \\le T \\le 101$). The test cases follow.<\/p>\r\n\r\n<p>The first line of each test case has the number of points $N$ and the number of colors $M$ ($2 \\le N \\le 200\\,000$, $2 \\le M \\le N$).<\/p>\r\n\r\n<p>The next line contains $N$ integers $A_1, A_2, \\ldots, A_N$ ($1 \\le A_i \\le M$).<\/p>\r\n\r\n<p>The sum of $N$ over all test cases does not exceed $200\\,000$.<\/p>\r\n","output":"<p>For each test case, start with a line containing an integer $K$: the maximum number of curves connecting two points.<\/p>\r\n\r\n<p>In each of the next $K$ lines, print the indices of the two points connected by a curve. The curves must satisfy all the restrictions above. If there are several possible answers, print any one of them.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English"}]

출처

Camp > Petrozavodsk Programming Camp > Winter 2023 > Day 2: GP of ainta K번

  • 문제를 만든 사람: ainta