문제
태인이의 옷장에는 $N$개의 옷이 일렬로 걸려 있다. 현재 왼쪽에서 $i$번째 옷의 색은 $c_i$이다.
태인이는 어떤 정수 $k$ (1ドル\le k\le N$)가 존재해 $c_1\leq c_2\leq\cdots\leq c_k\geq c_{k+1}\geq\cdots\geq c_N$를 만족하면 옷장이 아름답다고 생각한다.
하지만 옷장을 아름다운 상태로 정리하는 것은 꽤 귀찮다. 그래서 태인이는 옷장에서 최대 $M$개의 옷을 제거해 남은 옷들을 거의 아름다운 상태로 만들기로 했다.
최대 $M$개의 옷을 제거한 후, 남은 옷들의 개수를 $L,ドル 왼쪽에서 $j$번째 옷의 색을 $d_j$라 하자. 태인이는 인접한 두 옷의 색의 차가 $x$ 이하라면 두 옷을 같은 색으로 인식하기로 했다. 즉, 다음을 만족하는 정수 $k$ (1ドル\le k\le L$)가 존재한다면 옷장이 거의 아름다운 상태라고 한다.
- 1ドル\leq j<k$인 모든 정수 $j$에 대해 $d_j-d_{j+1}\leq x$.
- $k\leq j<L$인 모든 정수 $j$에 대해 $d_{j+1}-d_j\leq x$.
$M$개 이하의 옷을 제거해 옷장을 거의 아름다운 상태로 만들 수 있는 가장 작은 음이 아닌 정수 $x$의 값을 구하자.
출력
옷장을 거의 아름다운 상태로 만들 수 있는 가장 작은 $x$ ($x\ge 0$)의 값을 출력한다.
제한
- 1ドル\leq N\leq 10^5$
- 0ドル\leq M\leq N$
- 1ドル\leq c_i\leq 10^9$ (1ドル\leq i\leq N$)
서브태스크
| 번호 | 배점 | 제한 | | 1 | 4 | $M=0$
|
| 2 | 21 | 1ドル \leq N \leq 1,000円$
|
| 3 | 16 | 1ドル \leq c_i \leq 100$ (1ドル \leq i \leq N$)
|
| 4 | 59 | 추가적인 제약 조건이 없다.
|
노트
$x=2$일 때, 왼쪽에서 5번째 옷과 9번째 옷을 제거하면 옷장은 거의 아름다운 상태가 된다. 이보다 더 작은 $x$로는 옷장을 거의 아름다운 상태로 만들 수 없다.
[{"problem_id":"31816","problem_lang":"0","title":"Closet","description":"<p>\ud0dc\uc778\uc774\uc758 \uc637\uc7a5\uc5d0\ub294 $N$\uac1c\uc758 \uc637\uc774 \uc77c\ub82c\ub85c \uac78\ub824 \uc788\ub2e4. \ud604\uc7ac \uc67c\ucabd\uc5d0\uc11c $i$\ubc88\uc9f8 \uc637\uc758 \uc0c9\uc740 $c_i$\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud0dc\uc778\uc774\ub294 \uc5b4\ub5a4 \uc815\uc218 $k$ ($1\\le k\\le N$)\uac00 \uc874\uc7ac\ud574 $c_1\\leq c_2\\leq\\cdots\\leq c_k\\geq c_{k+1}\\geq\\cdots\\geq c_N$\ub97c \ub9cc\uc871\ud558\uba74 \uc637\uc7a5\uc774 \uc544\ub984\ub2f5\ub2e4\uace0 \uc0dd\uac01\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ud558\uc9c0\ub9cc \uc637\uc7a5\uc744 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc\ub85c \uc815\ub9ac\ud558\ub294 \uac83\uc740 \uaf64 \uadc0\ucc2e\ub2e4. \uadf8\ub798\uc11c \ud0dc\uc778\uc774\ub294 \uc637\uc7a5\uc5d0\uc11c \ucd5c\ub300 $M$\uac1c\uc758 \uc637\uc744 \uc81c\uac70\ud574 \ub0a8\uc740 \uc637\ub4e4\uc744 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\ub85c \ub9cc\ub4e4\uae30\ub85c \ud588\ub2e4.<\/p>\r\n\r\n<p>\ucd5c\ub300 $M$\uac1c\uc758 \uc637\uc744 \uc81c\uac70\ud55c \ud6c4, \ub0a8\uc740 \uc637\ub4e4\uc758 \uac1c\uc218\ub97c $L$, \uc67c\ucabd\uc5d0\uc11c $j$\ubc88\uc9f8 \uc637\uc758 \uc0c9\uc744 $d_j$\ub77c \ud558\uc790. \ud0dc\uc778\uc774\ub294 \uc778\uc811\ud55c \ub450 \uc637\uc758 \uc0c9\uc758 \ucc28\uac00 $x$ \uc774\ud558\ub77c\uba74 \ub450 \uc637\uc744 \uac19\uc740 \uc0c9\uc73c\ub85c \uc778\uc2dd\ud558\uae30\ub85c \ud588\ub2e4. \uc989, \ub2e4\uc74c\uc744 \ub9cc\uc871\ud558\ub294 \uc815\uc218 $k$ ($1\\le k\\le L$)\uac00 \uc874\uc7ac\ud55c\ub2e4\uba74 \uc637\uc7a5\uc774 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>$1\\leq j&lt;k$\uc778 \ubaa8\ub4e0 \uc815\uc218 $j$\uc5d0 \ub300\ud574 $d_j-d_{j+1}\\leq x$.<\/li>\r\n\t<li>$k\\leq j&lt;L$\uc778 \ubaa8\ub4e0 \uc815\uc218 $j$\uc5d0 \ub300\ud574 $d_{j+1}-d_j\\leq x$.<\/li>\r\n<\/ul>\r\n\r\n<p>$M$\uac1c \uc774\ud558\uc758 \uc637\uc744 \uc81c\uac70\ud574 \uc637\uc7a5\uc744 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 \uc74c\uc774 \uc544\ub2cc \uc815\uc218 $x$\uc758 \uac12\uc744 \uad6c\ud558\uc790.<\/p>\r\n","input":"<p>\uccab \ubc88\uc9f8 \uc904\uc5d0 \ub450 \uc815\uc218 $N$\uacfc $M$\uc774 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ub450 \ubc88\uc9f8 \uc904\uc5d0 $N$\uac1c\uc758 \uc815\uc218 $c_1,c_2,\\ldots ,c_N$\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uc637\uc7a5\uc744 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 \uac00\uc7a5 \uc791\uc740 $x$ ($x\\ge 0$)\uc758 \uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>$x=2$\uc77c \ub54c, \uc67c\ucabd\uc5d0\uc11c 5\ubc88\uc9f8 \uc637\uacfc 9\ubc88\uc9f8 \uc637\uc744 \uc81c\uac70\ud558\uba74 \uc637\uc7a5\uc740 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\uac00 \ub41c\ub2e4. \uc774\ubcf4\ub2e4 \ub354 \uc791\uc740 $x$\ub85c\ub294 \uc637\uc7a5\uc744 <strong>\uac70\uc758 \uc544\ub984\ub2e4\uc6b4 \uc0c1\ud0dc<\/strong>\ub85c \ub9cc\ub4e4 \uc218 \uc5c6\ub2e4.<\/p>\r\n","original":"1","html_title":"0","problem_lang_tcode":"Korean","limit":"<ul>\r\n\t<li>$1\\leq N\\leq 10^5$<\/li>\r\n\t<li>$0\\leq M\\leq N$<\/li>\r\n\t<li>$1\\leq c_i\\leq 10^9$ ($1\\leq i\\leq N$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$M=0$<\/p>\r\n","subtask2":"<p>$1 \\leq N \\leq 1\\,000$<\/p>\r\n","subtask3":"<p>$1 \\leq c_i \\leq 100$ ($1 \\leq i \\leq N$)<\/p>\r\n","subtask4":"<p>\ucd94\uac00\uc801\uc778 \uc81c\uc57d \uc870\uac74\uc774 \uc5c6\ub2e4.<\/p>\r\n"},{"problem_id":"31816","problem_lang":"1","title":"Closet","description":"<p>Taein has a closet with $N$ clothes hanging in it. Currently, the $i$-th clothes from the left has color $c_i$.<\/p>\r\n\r\n<p>Taein considers his closet beautiful if there exists an integer $k$ ($1\\le k\\le N$) such that $c_1\\leq c_2\\leq\\cdots\\leq c_k\\geq c_{k+1}\\geq\\cdots\\geq c_N$.<\/p>\r\n\r\n<p>However, organizing the closet into a beautiful state is quite tedious. So, Taein decided to remove at most $M$ clothes from the closet to make the remaining clothes <strong>almost beautiful<\/strong>.<\/p>\r\n\r\n<p>After removing at most $M$ clothes, let $L$ be the number of remaining clothes, and let $d_j$ be the color of the $j$-th clothes from the left. Taein decided to recognize two adjacent clothes as the same color if the difference in color between them is at most $x$. In other words, the closet is called <strong>almost beautiful<\/strong> if there exists an integer $k$ ($1\\le k\\le L$) for which the following holds:<\/p>\r\n\r\n<ul>\r\n\t<li>$d_j-d_{j+1}\\leq x$ for each integer $j$ such that $1\\leq j&lt;k$.<\/li>\r\n\t<li>$d_{j+1}-d_j\\leq x$ for each integer $j$ such that $k\\leq j&lt;L$.<\/li>\r\n<\/ul>\r\n\r\n<p>Let&rsquo;s find the smallest value of non-negative integer $x$ that can make the closet <strong>almost beautiful<\/strong> by removing $M$ or fewer clothes.<\/p>\r\n","input":"<p>The first line contains two integers $N$ and $M$ separated by a space.<\/p>\r\n\r\n<p>The second line contains $N$ integers $c_1,c_2,\\ldots ,c_N$ separated by a space.<\/p>\r\n","output":"<p>Print the smallest value of $x$ ($x\\ge 0$) that can make the closet <strong>almost beautiful<\/strong>.<\/p>\r\n","hint":"<p>When $x=2$, Taein can make the closet <strong>almost beautiful<\/strong> by removing the 5th and 9th clothes from the left. There are no smaller values of $x$ which make it possible to make the closet <strong>almost beautiful<\/strong>.<\/p>\r\n","original":"0","html_title":"0","problem_lang_tcode":"English","limit":"<ul>\r\n\t<li>$1\\leq N\\leq 10^5$<\/li>\r\n\t<li>$0\\leq M\\leq N$<\/li>\r\n\t<li>$1\\leq c_i\\leq 10^9$ ($1\\leq i\\leq N$)<\/li>\r\n<\/ul>\r\n","subtask1":"<p>$M=0$<\/p>\r\n","subtask2":"<p>$1 \\leq N \\leq 1\\,000$<\/p>\r\n","subtask3":"<p>$1 \\leq c_i \\leq 100$ ($1 \\leq i \\leq N$)<\/p>\r\n","subtask4":"<p>No additional constraints.<\/p>\r\n"}]