시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 20 13 11 64.706%

문제

엄청난 벼락을 맞아 많은 전선들이 끊어져 현재 전력 공급이 중단된 상태이다. 가장 심각한 문제는 1번 발전소에서 N번 발전소로 가는 중간의 전선이 끊어진 것이기에 일단 이 두 발전소를 다시 연결하는게 현재 해결해야할 첫 번째 과제이다.

발전소는 1번부터 N번까지 번호로 매겨져 2차원 격자 좌표 위에 있다. 그리고 몇몇 전선은 보존된 채 몇몇 발전소를 잇고 있다. 문제는 현재 전선과 발전소의 위치가 주어졌을 때 최소의 전선 길이를 추가로 사용하여 1번 발전소와 N번 발전소를 연결짓는 것이다. 물론 연결 짓는 중간에 다른 발전소를 거쳐갈 수 있다. 단, 안정성 문제로 어떠한 두 발전소 사이의 전선의 길이가 M을 초과할 수는 없다. 아래에 이에 대한 예를 그려놓았다.

         연결 전                          연결 후

3  . . . 7 9 . . . . .          3  . . . 7 9 . . . . .
                                          /
2  . . 5 6 . . . . . .          2  . . 5 6 . . . . . .
                                        /
1  2-3-4 . 8 . . . . .          1  2-3-4 . 8 . . . . .
   |                               |
0  1 . . . . . . . . .          0  1 . . . . . . . . .

   0 1 2 3 4 5 6 7 8 9             0 1 2 3 4 5 6 7 8 9

입력

첫 줄에는 발전소의 수 N(1 ≤ N ≤ 1,000)과 현재 남아있는 전선의 수 W(1≤ W ≤ 10,000)가 주어진다. 두 번째 줄에는 제한 길이 M(0.0 < M < 200,000.0)가 주어진다. 다음 N개의 줄에는 1번 발전소부터 N번 발전소까지 각각의 발전소의 X좌표와 Y좌표(-100,000 ≤ xi,yi  ≤ 100,000)가 차례대로 주어진다. 다음 W개의 줄에 대해 각 줄에는 두 개의 정수가 입력되어지는데 이는 현재 남아있는 전선이 잇고 있는 두 발전소를 의미한다.

출력

첫 줄에 1번 발전소와 N번 발전소를 잇는데 필요한 추가 전선 길이의 최솟값을 1000배하여 출력한다. (단, 1000배하고 난 후 나머지 소수는 반올림이 아닌 버림을 한다)

예제 입력 1

9 3
2.0
0 0
0 1
1 1
2 1
2 2
3 2
3 3
4 1
4 3
1 2
2 3
3 4

예제 출력 1

2828
[{"problem_id":"1277","problem_lang":"0","title":"\ubc1c\uc804\uc18c \uc124\uce58","description":"<p>\uc5c4\uccad\ub09c \ubcbc\ub77d\uc744 \ub9de\uc544 \ub9ce\uc740 \uc804\uc120\ub4e4\uc774 \ub04a\uc5b4\uc838 \ud604\uc7ac \uc804\ub825 \uacf5\uae09\uc774 \uc911\ub2e8\ub41c \uc0c1\ud0dc\uc774\ub2e4. \uac00\uc7a5 \uc2ec\uac01\ud55c \ubb38\uc81c\ub294 1\ubc88 \ubc1c\uc804\uc18c\uc5d0\uc11c N\ubc88 \ubc1c\uc804\uc18c\ub85c \uac00\ub294 \uc911\uac04\uc758 \uc804\uc120\uc774 \ub04a\uc5b4\uc9c4 \uac83\uc774\uae30\uc5d0 \uc77c\ub2e8 \uc774 \ub450 \ubc1c\uc804\uc18c\ub97c \ub2e4\uc2dc \uc5f0\uacb0\ud558\ub294\uac8c \ud604\uc7ac \ud574\uacb0\ud574\uc57c\ud560 \uccab \ubc88\uc9f8 \uacfc\uc81c\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubc1c\uc804\uc18c\ub294 1\ubc88\ubd80\ud130 N\ubc88\uae4c\uc9c0 \ubc88\ud638\ub85c \ub9e4\uaca8\uc838 2\ucc28\uc6d0 \uaca9\uc790 \uc88c\ud45c \uc704\uc5d0 \uc788\ub2e4. \uadf8\ub9ac\uace0 \uba87\uba87 \uc804\uc120\uc740 \ubcf4\uc874\ub41c \ucc44 \uba87\uba87 \ubc1c\uc804\uc18c\ub97c \uc787\uace0 \uc788\ub2e4. \ubb38\uc81c\ub294 \ud604\uc7ac \uc804\uc120\uacfc \ubc1c\uc804\uc18c\uc758 \uc704\uce58\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c \ucd5c\uc18c\uc758 \uc804\uc120 \uae38\uc774\ub97c \ucd94\uac00\ub85c \uc0ac\uc6a9\ud558\uc5ec 1\ubc88 \ubc1c\uc804\uc18c\uc640 N\ubc88 \ubc1c\uc804\uc18c\ub97c \uc5f0\uacb0\uc9d3\ub294 \uac83\uc774\ub2e4. \ubb3c\ub860 \uc5f0\uacb0 \uc9d3\ub294 \uc911\uac04\uc5d0 \ub2e4\ub978 \ubc1c\uc804\uc18c\ub97c \uac70\uccd0\uac08 \uc218 \uc788\ub2e4. \ub2e8, \uc548\uc815\uc131 \ubb38\uc81c\ub85c \uc5b4\ub5a0\ud55c \ub450 \ubc1c\uc804\uc18c \uc0ac\uc774\uc758 \uc804\uc120\uc758 \uae38\uc774\uac00 M\uc744 \ucd08\uacfc\ud560 \uc218\ub294 \uc5c6\ub2e4. \uc544\ub798\uc5d0 \uc774\uc5d0 \ub300\ud55c \uc608\ub97c \uadf8\ub824\ub193\uc558\ub2e4.<\/p>\r\n\r\n<pre>\r\n         \uc5f0\uacb0 \uc804                          \uc5f0\uacb0 \ud6c4\r\n\r\n3  . . . 7 9 . . . . .          3  . . . 7 9 . . . . .\r\n                                          \/\r\n2  . . 5 6 . . . . . .          2  . . 5 6 . . . . . .\r\n                                        \/\r\n1  2-3-4 . 8 . . . . .          1  2-3-4 . 8 . . . . .\r\n   |                               |\r\n0  1 . . . . . . . . .          0  1 . . . . . . . . .\r\n\r\n   0 1 2 3 4 5 6 7 8 9             0 1 2 3 4 5 6 7 8 9\r\n<\/pre>\r\n","input":"<p>\uccab \uc904\uc5d0\ub294 \ubc1c\uc804\uc18c\uc758 \uc218 N(1 &le; N &le; 1,000)\uacfc \ud604\uc7ac \ub0a8\uc544\uc788\ub294 \uc804\uc120\uc758 \uc218 W(1&le; W &le; 10,000)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub450 \ubc88\uc9f8 \uc904\uc5d0\ub294 \uc81c\ud55c \uae38\uc774 M(0.0 &lt; M &lt; 200,000.0)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c N\uac1c\uc758 \uc904\uc5d0\ub294 1\ubc88 \ubc1c\uc804\uc18c\ubd80\ud130 N\ubc88 \ubc1c\uc804\uc18c\uae4c\uc9c0 \uac01\uac01\uc758 \ubc1c\uc804\uc18c\uc758 X\uc88c\ud45c\uc640 Y\uc88c\ud45c(-100,000 &le; xi,yi&nbsp; &le; 100,000)\uac00 \ucc28\ub840\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c W\uac1c\uc758 \uc904\uc5d0 \ub300\ud574 \uac01 \uc904\uc5d0\ub294 \ub450 \uac1c\uc758 \uc815\uc218\uac00 \uc785\ub825\ub418\uc5b4\uc9c0\ub294\ub370 \uc774\ub294 \ud604\uc7ac \ub0a8\uc544\uc788\ub294 \uc804\uc120\uc774 \uc787\uace0 \uc788\ub294 \ub450 \ubc1c\uc804\uc18c\ub97c \uc758\ubbf8\ud55c\ub2e4.<\/p>\r\n","output":"<p>\uccab \uc904\uc5d0 1\ubc88 \ubc1c\uc804\uc18c\uc640 N\ubc88 \ubc1c\uc804\uc18c\ub97c \uc787\ub294\ub370 \ud544\uc694\ud55c \ucd94\uac00 \uc804\uc120 \uae38\uc774\uc758 \ucd5c\uc19f\uac12\uc744 1000\ubc30\ud558\uc5ec \ucd9c\ub825\ud55c\ub2e4. (\ub2e8, 1000\ubc30\ud558\uace0 \ub09c \ud6c4 \ub098\uba38\uc9c0 \uc18c\uc218\ub294 \ubc18\uc62c\ub9bc\uc774 \uc544\ub2cc \ubc84\ub9bc\uc744 \ud55c\ub2e4)<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"1277","problem_lang":"1","title":"Power Failure","description":"<p>A vicious thunderstorm has destroyed some of the wires of the farm&#39;s electrical power grid! Farmer John has a map of all N (2 &lt;= N &lt;= 1,000) of the powerpoles, which are conveniently numbered 1..N and located on integer plane coordinates x_i,y_i (-100,000 &lt;= x_i &lt;= 100000; -100,000 &lt;= y_i &lt;= 100,000).<\/p>\r\n\r\n<p>Some W (1 &lt;= W &lt;= 10,000) power wires connect pairs of power poles Pi and Pj (1 &lt;= Pi &lt;= N; 1 &lt;= Pj &lt;= N).<\/p>\r\n\r\n<p>He needs to get power from pole 1 to pole N (which means that some series of wires can traverse from pole 1 to pole N, probably through some intermediate set of poles).<\/p>\r\n\r\n<p>Given the locations of the N poles and the list of remaining power wires, determine the minimum length of power wire required to restore the electrical connection so that electricity can flow from pole 1 to pole N. &nbsp;No wire can be longer than some real number M (0.0 &lt; M &lt;= 200,000.0).<\/p>\r\n\r\n<p>As an example, below on the left is a map of the 9 poles and 3 wires after the storm. For this task, M = 2.0. The best set of wires to add would connect poles 4 and 6 and also poles 6 and 9.<\/p>\r\n\r\n<pre>\r\n      After the storm              Optimally reconnected\r\n\r\n3  . . . 7 9 . . . . .          3  . . . 7 9 . . . . .\r\n                                          \/\r\n2  . . 5 6 . . . . . .          2  . . 5 6 . . . . . .\r\n                                        \/\r\n1  2-3-4 . 8 . . . . .          1  2-3-4 . 8 . . . . .\r\n   |                               |\r\n0  1 . . . . . . . . .          0  1 . . . . . . . . .\r\n\r\n   0 1 2 3 4 5 6 7 8 9             0 1 2 3 4 5 6 7 8 9\r\n<\/pre>\r\n\r\n<p>The total length is then 1.414213562 + 1.414213562 = 2.828427124 .<\/p>\r\n\r\n","input":"<p>* Line 1: Two space-separated integers: N and W<\/p>\r\n\r\n<p>* Line 2: A single real number: M<\/p>\r\n\r\n<p>* Lines 3..N+2: Each line contains two space-separated integers: x_i and y_i<\/p>\r\n\r\n<p>* Lines N+3..N+2+W: Two space-separated integers: Pi and Pj<\/p>\r\n","output":"<p>* Line 1: A single integer on a single line. &nbsp;If restoring connection is impossible, output -1. Otherwise, output a single integer that is 1000 times the total minimum cost to restore electricity. Do not perform any rounding; truncate the resulting product.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]