시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 143 22 15 62.500%

문제

상근이는 새 화면 보호기를 설치했다. 컴퓨터를 5분동안 사용하지 않으면 화면 보호기가 실행된다. 이 화면 보호기는 수족관 그림과 움직이는 물고기를 보여준다. 화면 보호기 설정 화면에서는 바닥의 모양과 수면의 높이를 설정할 수 있다.

수족관은 너비가 N-1인 2차원 평면으로 나타낼 수 있다. 이 때, N은 양의 정수이다. 수족관의 가장 왼쪽 x좌표는 0이고, 가장 오른쪽 x좌표는 N-1이다. 각 정수 x좌표 i는 바닥의 높이 Hi를 갖는다. 이 높이는 설정에서 바꿀 수 있다. 바닥은 인접한 두 x좌표 i와 i+1를 이용해서 (i, Hi)와 (i+1, Hi+1)을 연결하는 선분으로 나타낼 수 있다.

수면의 높이가 h라면, 수족관의 바닥과 y=h 사이의 모든 공간이 물로 채워지게 된다. 만약, h보다 높은 바닥이 있다면, 그 곳은 섬이다.

상근이는 설정에서 수족관 바닥 좌표와 수면의 높이를 바꿀 때 마다 물로 채워지는 곳의 넓이를 구하려고 한다.

입력

첫째 줄에 두 양의 정수 N과 상근이가 설정을 바꾼 횟수 M이 주어진다. (3 ≤ N ≤ 100,000, 1 ≤ M ≤ 100,000)

둘째 줄에는 N개의 정수 바닥의 초기 높이 Hi가 공백으로 구분되어 주어진다. (0 ≤ Hi ≤ 1000)

다음 M개 줄에는 상근이가 설정에서 무엇을 바꾸었는 지가 주어진다.

Q h는 수면의 높이를 h로 바꾸었다는 뜻이다. (0 ≤ h ≤ 1000)

U i h는 x좌표가 i인 곳의 바닥의 높이를 h로 바꾸었다는 뜻이다. (0 ≤ i ≤ N-1, 0 ≤ h ≤ 1000) 즉, Hi = h

출력

Q로 시작하는 변경이 주어질 때 마다, 물로 채워지는 곳의 넓이를 소수점 셋째 자리까지 출력한다.

예제 입력 1

7 7
0 2 1 3 2 1 0
Q 1
Q 2
Q 3
U 3 0
Q 1
Q 2
Q 3

예제 출력 1

0.750
3.750
9.000
1.500
6.000
12.000

힌트

왼쪽 그림은 입력으로 주어졌을 때의 상태이며, 오른쪽 그림은 U로 시작하는 설졍 변경을 수행한 뒤의 모습이다.

[{"problem_id":"3990","problem_lang":"0","title":"\ud654\uba74 \ubcf4\ud638\uae30","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc0c8 \ud654\uba74 \ubcf4\ud638\uae30\ub97c \uc124\uce58\ud588\ub2e4. \ucef4\ud4e8\ud130\ub97c 5\ubd84\ub3d9\uc548 \uc0ac\uc6a9\ud558\uc9c0 \uc54a\uc73c\uba74 \ud654\uba74 \ubcf4\ud638\uae30\uac00 \uc2e4\ud589\ub41c\ub2e4. \uc774 \ud654\uba74 \ubcf4\ud638\uae30\ub294 \uc218\uc871\uad00 \uadf8\ub9bc\uacfc \uc6c0\uc9c1\uc774\ub294 \ubb3c\uace0\uae30\ub97c \ubcf4\uc5ec\uc900\ub2e4. \ud654\uba74 \ubcf4\ud638\uae30 \uc124\uc815 \ud654\uba74\uc5d0\uc11c\ub294 \ubc14\ub2e5\uc758 \ubaa8\uc591\uacfc \uc218\uba74\uc758 \ub192\uc774\ub97c \uc124\uc815\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc218\uc871\uad00\uc740 \ub108\ube44\uac00 N-1\uc778 2\ucc28\uc6d0 \ud3c9\uba74\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774 \ub54c, N\uc740 \uc591\uc758 \uc815\uc218\uc774\ub2e4. \uc218\uc871\uad00\uc758 \uac00\uc7a5 \uc67c\ucabd x\uc88c\ud45c\ub294 0\uc774\uace0, \uac00\uc7a5 \uc624\ub978\ucabd x\uc88c\ud45c\ub294 N-1\uc774\ub2e4. \uac01 \uc815\uc218 x\uc88c\ud45c i\ub294 \ubc14\ub2e5\uc758 \ub192\uc774 H<sub>i<\/sub>\ub97c \uac16\ub294\ub2e4. \uc774 \ub192\uc774\ub294 \uc124\uc815\uc5d0\uc11c \ubc14\uafc0 \uc218 \uc788\ub2e4. \ubc14\ub2e5\uc740 \uc778\uc811\ud55c \ub450 x\uc88c\ud45c i\uc640 i+1\ub97c \uc774\uc6a9\ud574\uc11c (i, H<sub>i<\/sub>)\uc640 (i+1, H<sub>i+1<\/sub>)\uc744 \uc5f0\uacb0\ud558\ub294 \uc120\ubd84\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc218\uba74\uc758 \ub192\uc774\uac00 h\ub77c\uba74, \uc218\uc871\uad00\uc758 \ubc14\ub2e5\uacfc y=h \uc0ac\uc774\uc758 \ubaa8\ub4e0 \uacf5\uac04\uc774 \ubb3c\ub85c \ucc44\uc6cc\uc9c0\uac8c \ub41c\ub2e4. \ub9cc\uc57d, h\ubcf4\ub2e4 \ub192\uc740 \ubc14\ub2e5\uc774 \uc788\ub2e4\uba74, \uadf8 \uacf3\uc740 \uc12c\uc774\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>\uc0c1\uadfc\uc774\ub294 \uc124\uc815\uc5d0\uc11c \uc218\uc871\uad00 \ubc14\ub2e5 \uc88c\ud45c\uc640 \uc218\uba74\uc758 \ub192\uc774\ub97c \ubc14\uafc0 \ub54c \ub9c8\ub2e4 \ubb3c\ub85c \ucc44\uc6cc\uc9c0\ub294 \uacf3\uc758 \ub113\uc774\ub97c \uad6c\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ub450 \uc591\uc758 \uc815\uc218 N\uacfc \uc0c1\uadfc\uc774\uac00 \uc124\uc815\uc744 \ubc14\uafbc \ud69f\uc218 M\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (3 &le; N &le; 100,000, 1 &le; M &le; 100,000)<\/p>\r\n\r\n\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 N\uac1c\uc758 \uc815\uc218 \ubc14\ub2e5\uc758 \ucd08\uae30 \ub192\uc774 Hi\uac00 \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ub418\uc5b4 \uc8fc\uc5b4\uc9c4\ub2e4. (0 &le; Hi &le; 1000)<\/p>\r\n\r\n\r\n\r\n<p>\ub2e4\uc74c M\uac1c \uc904\uc5d0\ub294 \uc0c1\uadfc\uc774\uac00 \uc124\uc815\uc5d0\uc11c \ubb34\uc5c7\uc744 \ubc14\uafb8\uc5c8\ub294 \uc9c0\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n\r\n\r\n<p>Q h\ub294 \uc218\uba74\uc758 \ub192\uc774\ub97c h\ub85c \ubc14\uafb8\uc5c8\ub2e4\ub294 \ub73b\uc774\ub2e4. (0 &le; h &le; 1000)<\/p>\r\n\r\n\r\n\r\n<p>U i h\ub294 x\uc88c\ud45c\uac00 i\uc778 \uacf3\uc758 \ubc14\ub2e5\uc758 \ub192\uc774\ub97c h\ub85c \ubc14\uafb8\uc5c8\ub2e4\ub294 \ub73b\uc774\ub2e4. (0 &le; i &le; N-1, 0 &le; h &le; 1000) \uc989, Hi = h<\/p>\r\n","output":"<p>Q\ub85c \uc2dc\uc791\ud558\ub294 \ubcc0\uacbd\uc774 \uc8fc\uc5b4\uc9c8 \ub54c \ub9c8\ub2e4, \ubb3c\ub85c \ucc44\uc6cc\uc9c0\ub294 \uacf3\uc758 \ub113\uc774\ub97c \uc18c\uc218\uc810 \uc14b\uc9f8 \uc790\ub9ac\uae4c\uc9c0 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc67c\ucabd \uadf8\ub9bc\uc740 \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc84c\uc744 \ub54c\uc758 \uc0c1\ud0dc\uc774\uba70, \uc624\ub978\ucabd \uadf8\ub9bc\uc740 U\ub85c \uc2dc\uc791\ud558\ub294 \uc124\uc84d \ubcc0\uacbd\uc744 \uc218\ud589\ud55c \ub4a4\uc758 \ubaa8\uc2b5\uc774\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ssd.png\" style=\"height:209px; width:668px\" \/><\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3990","problem_lang":"1","title":"AKVARIJ","description":"<p>Mirko has recently installed a new screensaver. If he is away from the keyboard for five minutes, the screen shows a picture of an aquarium with animated fish. The screensaver has settings for customizingthe shape of the (virtual, sandy) aquarium bottom, as well as the water level.&nbsp;<\/p>\r\n\r\n<p>The aquarium can be represented in a 2D Cartesian coordinate system as a shape N - 1 columns wide, where N is a positive integer. The left wall of the aquarium has the x-coordinate of 0, and the right wall has the x-coordinate of N - 1. Each integer-valued x-coordinate of the aquarium bottom (let us denote it by i) from 0 to N - 1 has a separately adjustable height of H<sub>i<\/sub>. Between any two adjacent integervalued x-coordinates i and i + 1, the bottom can be described by a line segment between points (i, H<sub>i<\/sub>) and (i + 1, H<sub>i + 1<\/sub>).&nbsp;<\/p>\r\n\r\n<p>If the water level is set to h, the water fills the area between the line y = h and the aquarium bottom. If a part of the aquarium bottom is above the water level h, it forms an island and is not submerged.&nbsp;<\/p>\r\n\r\n<p>For different shapes of the aquarium bottom, Mirko would like to know the totalarea of his screen covered by water. Help Mirko find answers to his questions (other than 42).&nbsp;<\/p>\r\n","input":"<p>The first line of input contains two positive integers, N (3 &le; N &le; 100 000, the length of the bottom) and M (1 &le; M &le; 100 000, the number of queries).&nbsp;<\/p>\r\n\r\n<p>The second line of input contains N space-separated nonnegative integers H<sub>i<\/sub> (0 &le; H<sub>i<\/sub> &le; 1000), the starting bottom heights.&nbsp;<\/p>\r\n\r\n<p>Each of the following M lines contains a single query with one of the following two types:&nbsp;<\/p>\r\n\r\n<p>Q h &ndash; if the water level is set to h (0 &le; h &le; 1000), assuming the current bottom shape, what is the total screen area covered by water?&nbsp;<\/p>\r\n\r\n<p>U i h &ndash; Mirko has decided to change the bottom height at x-coordinate i (0 &le; i &le; N - 1) to h (0 &le; h &le; 1000); in other words, set H<sub>i<\/sub> = h<\/p>\r\n","output":"<p>or each query with type Q, output a single line containing the required area, rounded to exactly three decimals. The area given is allowed to differ by at most 0.001 from the official solution.&nbsp;<\/p>\r\n","hint":"<p>The left image below shows the situation before, and the right one after the U-type query, for water level h = 2 (query Q 2). In the first image, the submerged area equals 3.75, and in the second image it is 6.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ssd.png\" style=\"height:209px; width:668px\" \/><\/p>\r\n","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

Contest > Croatian Open Competition in Informatics > COCI 2012/2013 > Contest #4 6번