시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 249 100 87 44.162%

문제

GSHS에서는 체력측정에서 제자리 멀리뛰기가 가장 중요하다. GSHS의 체육선생님께서는 학생들의 제자리 멀리뛰기 실력을 키워주게 하기 위해서 특수 훈련을 준비중이다.

특수 훈련장소는 GSHS특수 트레이닝 센터로 이 곳은 끓는 용암으로 가득 차 있다. 체육선생님께서는 이 용암으로 가득찬 방의 가운데 있는 돌섬에 학생들을 가두고 학생들이 탈출해 나오기를 기대하고 있다. 탈출할 수 있는 방법은 단 한가지 이다. 돌섬에서 탈출구까지 띄엄 띄엄 존재하는 작은 돌섬들로 점프하여 탈출구까지 가는 것이다.

돌섬에서 탈출구 사이에는 총 n개의 작은 돌섬이 있다. 선생님은 이 n개의 작은 돌섬들 중 m개를 제거하여 학생들이 최대한 멀리뛰기 연습의 효율을 높이기 위해서 학생들이 각 돌섬을 점프한 거리의 최솟값을 최대한 크게 하려고 한다. 물론 학생들은 체력이 좋기 때문에 두 돌섬이 아무리 멀더라도 점프할 수 있다. 즉, 빠지는 일은 없다.

그리고 학생들은 탈출 시 n-m개의 모든 돌섬을 밟으면서 탈출해야 한다.

학 생들이 갇힌 돌섬으로부터 탈출구까지의 거리 d가 주어지고, 각 n개의 작은 돌섬의 위치(갇힌 돌섬으로 부터의 거리)가 주어지며, 제거할 수 있는 작은 돌섬의 수 m이 주어질 때, m개를 제거한 후 학생들이 점프하는 최소거리의 최댓값을 구하는 프로그램을 작성하시오.

입력

첫 번째 줄에는 갇힌 돌섬으로부터 탈출구까지의 거리 d(1 ≤ d ≤ 1,000,000,000), 작은 돌섬의 수 n(0 ≤ n ≤ 50,000), 제거할 수 있는 작은 돌섬의 수 m (0 ≤ m ≤ n)이 공백으로 구분되어 주어진다.

두 번째 줄부터 n줄에 걸쳐서 갇힌섬으로부터 각 작은 돌섬이 얼마나 떨어져 있는지를 나타내는 하나의 정수가 한 줄에 하나씩 주어진다. (단, 두 돌섬은 같은 위치에 있을 수 없다.)

출력

m개의 작은섬을 제거한 뒤 학생들이 점프할 수 있는 최소거리의 최댓값을 출력한다.

예제 입력 1

25 5 2
2
14
11
21
17

예제 출력 1

4
[{"problem_id":"6209","problem_lang":"0","title":"\uc81c\uc790\ub9ac \uba40\ub9ac\ub6f0\uae30","description":"<p>GSHS\uc5d0\uc11c\ub294 \uccb4\ub825\uce21\uc815\uc5d0\uc11c \uc81c\uc790\ub9ac \uba40\ub9ac\ub6f0\uae30\uac00 \uac00\uc7a5 \uc911\uc694\ud558\ub2e4. GSHS\uc758 \uccb4\uc721\uc120\uc0dd\ub2d8\uaed8\uc11c\ub294 \ud559\uc0dd\ub4e4\uc758 \uc81c\uc790\ub9ac \uba40\ub9ac\ub6f0\uae30 \uc2e4\ub825\uc744 \ud0a4\uc6cc\uc8fc\uac8c \ud558\uae30 \uc704\ud574\uc11c \ud2b9\uc218 \ud6c8\ub828\uc744 \uc900\ube44\uc911\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud2b9\uc218 \ud6c8\ub828\uc7a5\uc18c\ub294 GSHS\ud2b9\uc218 \ud2b8\ub808\uc774\ub2dd \uc13c\ud130\ub85c \uc774 \uacf3\uc740 \ub053\ub294 \uc6a9\uc554\uc73c\ub85c \uac00\ub4dd \ucc28 \uc788\ub2e4. \uccb4\uc721\uc120\uc0dd\ub2d8\uaed8\uc11c\ub294 \uc774 \uc6a9\uc554\uc73c\ub85c \uac00\ub4dd\ucc2c \ubc29\uc758 \uac00\uc6b4\ub370 \uc788\ub294 \ub3cc\uc12c\uc5d0 \ud559\uc0dd\ub4e4\uc744 \uac00\ub450\uace0 \ud559\uc0dd\ub4e4\uc774 \ud0c8\ucd9c\ud574 \ub098\uc624\uae30\ub97c \uae30\ub300\ud558\uace0 \uc788\ub2e4. \ud0c8\ucd9c\ud560 \uc218 \uc788\ub294 \ubc29\ubc95\uc740 \ub2e8 \ud55c\uac00\uc9c0 \uc774\ub2e4. \ub3cc\uc12c\uc5d0\uc11c \ud0c8\ucd9c\uad6c\uae4c\uc9c0 \ub744\uc5c4 \ub744\uc5c4 \uc874\uc7ac\ud558\ub294 \uc791\uc740 \ub3cc\uc12c\ub4e4\ub85c \uc810\ud504\ud558\uc5ec \ud0c8\ucd9c\uad6c\uae4c\uc9c0 \uac00\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ub3cc\uc12c\uc5d0\uc11c \ud0c8\ucd9c\uad6c \uc0ac\uc774\uc5d0\ub294 \ucd1d n\uac1c\uc758 \uc791\uc740 \ub3cc\uc12c\uc774 \uc788\ub2e4. \uc120\uc0dd\ub2d8\uc740 \uc774 n\uac1c\uc758 \uc791\uc740 \ub3cc\uc12c\ub4e4 \uc911 m\uac1c\ub97c \uc81c\uac70\ud558\uc5ec \ud559\uc0dd\ub4e4\uc774 \ucd5c\ub300\ud55c \uba40\ub9ac\ub6f0\uae30 \uc5f0\uc2b5\uc758 \ud6a8\uc728\uc744 \ub192\uc774\uae30 \uc704\ud574\uc11c \ud559\uc0dd\ub4e4\uc774 \uac01 \ub3cc\uc12c\uc744 \uc810\ud504\ud55c \uac70\ub9ac\uc758 \ucd5c\uc19f\uac12\uc744 \ucd5c\ub300\ud55c \ud06c\uac8c \ud558\ub824\uace0 \ud55c\ub2e4. \ubb3c\ub860 \ud559\uc0dd\ub4e4\uc740 \uccb4\ub825\uc774 \uc88b\uae30 \ub54c\ubb38\uc5d0 \ub450 \ub3cc\uc12c\uc774 \uc544\ubb34\ub9ac \uba40\ub354\ub77c\ub3c4 \uc810\ud504\ud560 \uc218 \uc788\ub2e4. \uc989, \ube60\uc9c0\ub294 \uc77c\uc740 \uc5c6\ub2e4.<\/p>\r\n\r\n<p>\uadf8\ub9ac\uace0 \ud559\uc0dd\ub4e4\uc740 \ud0c8\ucd9c \uc2dc n-m\uac1c\uc758 \ubaa8\ub4e0 \ub3cc\uc12c\uc744 \ubc1f\uc73c\uba74\uc11c \ud0c8\ucd9c\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud559 \uc0dd\ub4e4\uc774 \uac07\ud78c \ub3cc\uc12c\uc73c\ub85c\ubd80\ud130 \ud0c8\ucd9c\uad6c\uae4c\uc9c0\uc758 \uac70\ub9ac d\uac00 \uc8fc\uc5b4\uc9c0\uace0, \uac01 n\uac1c\uc758 \uc791\uc740 \ub3cc\uc12c\uc758 \uc704\uce58(\uac07\ud78c \ub3cc\uc12c\uc73c\ub85c \ubd80\ud130\uc758 \uac70\ub9ac)\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uc81c\uac70\ud560 \uc218 \uc788\ub294 \uc791\uc740 \ub3cc\uc12c\uc758 \uc218 m\uc774 \uc8fc\uc5b4\uc9c8 \ub54c, m\uac1c\ub97c \uc81c\uac70\ud55c \ud6c4 \ud559\uc0dd\ub4e4\uc774 \uc810\ud504\ud558\ub294 \ucd5c\uc18c\uac70\ub9ac\uc758 \ucd5c\ub313\uac12\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0\ub294 \uac07\ud78c \ub3cc\uc12c\uc73c\ub85c\ubd80\ud130 \ud0c8\ucd9c\uad6c\uae4c\uc9c0\uc758 \uac70\ub9ac d(1 &le;&nbsp;d &le; 1,000,000,000), \uc791\uc740 \ub3cc\uc12c\uc758 \uc218 n(0 &le; n &le; 50,000), \uc81c\uac70\ud560 \uc218 \uc788\ub294 \uc791\uc740 \ub3cc\uc12c\uc758 \uc218 m (0 &le; m &le;&nbsp;n)\uc774 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\ubd80\ud130 n\uc904\uc5d0 \uac78\uccd0\uc11c \uac07\ud78c\uc12c\uc73c\ub85c\ubd80\ud130 \uac01 \uc791\uc740 \ub3cc\uc12c\uc774 \uc5bc\ub9c8\ub098 \ub5a8\uc5b4\uc838 \uc788\ub294\uc9c0\ub97c \ub098\ud0c0\ub0b4\ub294 \ud558\ub098\uc758 \uc815\uc218\uac00 \ud55c \uc904\uc5d0 \ud558\ub098\uc529 \uc8fc\uc5b4\uc9c4\ub2e4. (\ub2e8, \ub450 \ub3cc\uc12c\uc740 \uac19\uc740 \uc704\uce58\uc5d0 \uc788\uc744 \uc218 \uc5c6\ub2e4.)<\/p>\r\n","output":"<p>m\uac1c\uc758 \uc791\uc740\uc12c\uc744 \uc81c\uac70\ud55c \ub4a4 \ud559\uc0dd\ub4e4\uc774 \uc810\ud504\ud560 \uc218 \uc788\ub294 \ucd5c\uc18c\uac70\ub9ac\uc758 \ucd5c\ub313\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"6209","problem_lang":"1","title":"River Hopscotch","description":"<p>Every year the cows hold an event featuring a peculiar version of hopscotch that involves carefully jumping from rock to rock in a river. The excitement takes place on a long, straight river with a rock at the start and another rock at the end, L units away from the start (1 &lt;= L &lt;= 1,000,000,000). Along the river between the starting and ending rocks, N (0 &lt;= N &lt;= 50,000) more rocks appear, each at an integral distance Di from the start (0 &lt; Di &lt; L).<\/p>\r\n\r\n<p>To play the game, each cow in turn starts at the starting rock and tries to reach the finish at the ending rock, jumping only from rock to rock. Of course, less agile cows never make it to the final rock, ending up instead in the river.<\/p>\r\n\r\n<p>Farmer John is proud of his cows and watches this event each year. But as time goes by, he tires of watching the timid cows of the other farmers limp across the short distances between rocks placed too closely together. He plans to remove several rocks in order to increase the shortest distance a cow will have to jump to reach the end. He knows he cannot remove the starting and ending rocks, but he calculates that he has enough resources to remove up to M rocks (0 &lt;= M &lt;= N).<\/p>\r\n\r\n<p>FJ wants to know exactly how much he can increase the shortest distance *before* he starts removing the rocks. Help Farmer John determine the greatest possible shortest distance a cow has to jump after removing the optimal set of M rocks.<\/p>\r\n","input":"<ul>\r\n\t<li>Line 1: Three space-separated integers: L, N, and M<\/li>\r\n\t<li>Lines 2..N+1: Each line contains a single integer indicating how far some rock is away from the starting rock. No two rocks share the same position.<\/li>\r\n<\/ul>\r\n\r\n<p>&nbsp;<\/p>\r\n","output":"<ul>\r\n\t<li>Line 1: A single integer that is the maximum of the shortest distance a cow has to jump after removing M rocks<\/li>\r\n<\/ul>\r\n","hint":"<p>Before removing any rocks, the shortest jump was a jump of 2 from 0 (the start) to 2. After removing the rocks at 2 and 14, the shortest required jump is a jump of 4 (from 17 to 21 or from 21 to 25).<\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Olympiad > USA Computing Olympiad > 2006-2007 Season > USACO December 2006 Contest > Silver 3번