시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
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문제

성공한 벤쳐회사 "봉씨"의 데이터 분석원 이석원은 매일매일 전세계 사용자에 대한 정보를 받은뒤 이를 시각화한다. 이석원은 자신이 만든 시각화 툴을 이용한다.

아래 그림은 이석원의 시각화 툴을 이용해서 만든 히스토그램이다.

위의 예에서 구간 0-9는 5번 발생했고, 10-19는 3번, 20-29와 30-39는 한 번씩 발생한 것이다.

이석원의 히스토그램 생성 프로그램은 매우 간단하다. 먼저, 히스토그램의 높이는 고정되어 있다. 즉, 가장 높은 막대의 높이는 항상 일정하고, 나머지 막대의 높이는 그 막대와의 비율에 의해 정해진다. 또, 막대의 너비도 고정되어있다. 그렇기 때문에 구간의 크기는 항상 정해져 있다. (위의 그림에선 10이다) 

마지막으로, 각각의 막대는 가장 왼쪽이 검정색 (밝기: 1), 오른쪽이 흰색 (밝기: 0)이고, 그 사이 막대는 왼쪽에서 오른쪽으로 갈 수록 일정한 비율에 따라서 밝기가 감소한다. 예를 들어, 위의 그림에서 막대의 검은 정도는 1, 2/3, 1/3, 0이다.

히스토그램을 출력하는데 필요한 잉크의 양을 구하는 프로그램을 작성하시오. 각 막대를 그리는데 필요한 잉크의 양은 면적과 검은 정도에 비례한다.

입력

입력은 여러 개의 테스트 케이스로 이루어져 있다. 각 테스트 케이스의 첫째 줄에는 히스토그램의 값의 개수 n과 구간의 크기 w가 주어진다. 다음 줄에는 자료의 값이 주어진다. 첫 막대의 구간은 0 ≤ v < w, 두 번째 막대의 구간은 w ≤ v < 2w이고, 나머지 막대의 구간도 이와 같이 정할 수 있다. 어떤 막대에 포함되는 값의 개수가 0개이더라도 그 막대를 그리지 않으면 안된다. (1 ≤ n ≤ 100, 10 ≤ w ≤ 50, 0 ≤ 값 ≤ 100)

값의 최댓값은 w보다 작지 않다. 따라서, 히스토그램은 한 개보다 많은 구간을 가지고 있다.

입력의 마지막 줄에는 0이 두 개 주어진다.

출력

각 테스트 케이스에 대해서 히스토그램을 그리는데 필요한 잉크의 양을 출력한다.

가장 높은 막대를 검정색으로 드는데 잉크가 1만큼 필요하다. 또, 히스토그램에서 축과 글자를 그리는데 필요한 잉크의 양은 0.01이다. 예를 들어, 위에서 주어진 히스토그을 그리는데 필요한 잉크의 양은 다음과 같다.

정답과의 오차가 10-5보다 작은 경우에 정답이다.

예제 입력 1

3 50
100
0
100
3 50
100
100
50
10 10
1
2
3
4
5
16
17
18
29
30
0 0

예제 출력 1

0.51
0.26
1.4766666666666667
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(\uc704\uc758 \uadf8\ub9bc\uc5d0\uc120 10\uc774\ub2e4)&nbsp;<\/p>\r\n\r\n<p>\ub9c8\uc9c0\ub9c9\uc73c\ub85c, \uac01\uac01\uc758 \ub9c9\ub300\ub294 \uac00\uc7a5 \uc67c\ucabd\uc774 \uac80\uc815\uc0c9 (\ubc1d\uae30: 1), \uc624\ub978\ucabd\uc774 \ud770\uc0c9 (\ubc1d\uae30: 0)\uc774\uace0, \uadf8 \uc0ac\uc774 \ub9c9\ub300\ub294 \uc67c\ucabd\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uac08 \uc218\ub85d \uc77c\uc815\ud55c \ube44\uc728\uc5d0 \ub530\ub77c\uc11c \ubc1d\uae30\uac00 \uac10\uc18c\ud55c\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c \ub9c9\ub300\uc758 \uac80\uc740 \uc815\ub3c4\ub294 1, 2\/3, 1\/3, 0\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud788\uc2a4\ud1a0\uadf8\ub7a8\uc744 \ucd9c\ub825\ud558\ub294\ub370 \ud544\uc694\ud55c \uc789\ud06c\uc758 \uc591\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uac01 \ub9c9\ub300\ub97c \uadf8\ub9ac\ub294\ub370 \ud544\uc694\ud55c \uc789\ud06c\uc758 \uc591\uc740 \uba74\uc801\uacfc \uac80\uc740 \uc815\ub3c4\uc5d0 \ube44\ub840\ud55c\ub2e4.<\/p>\r\n","input":"<p>\uc785\ub825\uc740 \uc5ec\ub7ec \uac1c\uc758 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc758 \uac12\uc758 \uac1c\uc218 n\uacfc \uad6c\uac04\uc758 \ud06c\uae30 w\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \ub2e4\uc74c \uc904\uc5d0\ub294 \uc790\ub8cc\uc758 \uac12\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \uccab \ub9c9\ub300\uc758 \uad6c\uac04\uc740 0 &le; v &lt; w, \ub450 \ubc88\uc9f8 \ub9c9\ub300\uc758 \uad6c\uac04\uc740 w &le; v &lt; 2w\uc774\uace0, \ub098\uba38\uc9c0 \ub9c9\ub300\uc758 \uad6c\uac04\ub3c4 \uc774\uc640 \uac19\uc774 \uc815\ud560 \uc218 \uc788\ub2e4. \uc5b4\ub5a4 \ub9c9\ub300\uc5d0 \ud3ec\ud568\ub418\ub294 \uac12\uc758 \uac1c\uc218\uac00 0\uac1c\uc774\ub354\ub77c\ub3c4 \uadf8 \ub9c9\ub300\ub97c \uadf8\ub9ac\uc9c0 \uc54a\uc73c\uba74 \uc548\ub41c\ub2e4. (1 &le; n &le; 100, 10 &le; w &le; 50, 0 &le; \uac12 &le; 100)<\/p>\r\n\r\n<p>\uac12\uc758 \ucd5c\ub313\uac12\uc740 w\ubcf4\ub2e4 \uc791\uc9c0 \uc54a\ub2e4. \ub530\ub77c\uc11c, \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc740 \ud55c \uac1c\ubcf4\ub2e4 \ub9ce\uc740 \uad6c\uac04\uc744 \uac00\uc9c0\uace0 \uc788\ub2e4.<\/p>\r\n\r\n<p>\uc785\ub825\uc758 \ub9c8\uc9c0\ub9c9 \uc904\uc5d0\ub294 0\uc774 \ub450 \uac1c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc5d0 \ub300\ud574\uc11c \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc744 \uadf8\ub9ac\ub294\ub370 \ud544\uc694\ud55c \uc789\ud06c\uc758 \uc591\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac00\uc7a5 \ub192\uc740 \ub9c9\ub300\ub97c \uac80\uc815\uc0c9\uc73c\ub85c \ub4dc\ub294\ub370 \uc789\ud06c\uac00 1\ub9cc\ud07c \ud544\uc694\ud558\ub2e4. \ub610, \ud788\uc2a4\ud1a0\uadf8\ub7a8\uc5d0\uc11c \ucd95\uacfc \uae00\uc790\ub97c \uadf8\ub9ac\ub294\ub370 \ud544\uc694\ud55c \uc789\ud06c\uc758 \uc591\uc740 0.01\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc5d0\uc11c \uc8fc\uc5b4\uc9c4 \ud788\uc2a4\ud1a0\uadf8\uc744 \uadf8\ub9ac\ub294\ub370 \ud544\uc694\ud55c \uc789\ud06c\uc758 \uc591\uc740 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ink.png\" style=\"width: 284px; height: 109px;\" \/><\/p>\r\n\r\n<p>\uc815\ub2f5\uacfc\uc758 \uc624\ucc28\uac00 10<sup>-5<\/sup>\ubcf4\ub2e4 \uc791\uc740 \uacbd\uc6b0\uc5d0 \uc815\ub2f5\uc774\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"3885","problem_lang":"1","title":"Grey Area","description":"<p>Dr. Grey is a data analyst, who visualizes various aspects of data received from all over the world everyday. He is extremely good at sophisticated visualization tools, but yet his favorite is a simple self-made histogram generator.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/gre.png\" style=\"height:273px; width:370px\" \/><\/p>\r\n\r\n<p>Figure 1: A histogram<\/p>\r\n\r\n<p>Figure 1 is an example of histogram automatically produced by his histogram generator. A histogram is a visual display of frequencies of value occurrences as bars. In this example, values in the interval 0&ndash;9 occur five times, those in the interval 10&ndash;19 occur three times, and 20&ndash;29 and 30&ndash;39 once each.<\/p>\r\n\r\n<p>Dr. Grey&rsquo;s histogram generator is a simple tool. First, the height of the histogram is fixed, that is, the height of the highest bar is always the same and those of the others are automatically adjusted proportionately. Second, the widths of bars are also fixed. It can only produce a histogram of uniform intervals, that is, each interval of a histogram should have the same width (10 in the above example). Finally, the bar for each interval is painted in a grey color, where the colors of the leftmost and the rightmost intervals are black and white, respectively, and the darkness of bars monotonically decreases at the same rate from left to right. For instance, in Figure 1, the darkness levels of the four bars are 1, 2\/3, 1\/3, and 0, respectively.<\/p>\r\n\r\n<p>In this problem, you are requested to estimate ink consumption when printing a histogram on paper. The amount of ink necessary to draw a bar is proportional to both its area and darkness.<\/p>\r\n","input":"<p>The input consists of multiple datasets, each of which contains integers and specifies a value table and intervals for the histogram generator, in the following format.<\/p>\r\n\r\n<pre>\r\nn w\r\nv<sub>1<\/sub>\r\nv<sub>2<\/sub>\r\n...\r\nv<sub>n<\/sub>\r\n<\/pre>\r\n\r\n<p>w is the interval width. A value v is in the first (i.e. leftmost) interval if 0 &le; v &lt; w, the second one if w &le; v &lt; 2w, and so on. Note that the interval from 0 (inclusive) to w (exclusive) should be regarded as the leftmost even if no values occur in this interval. The last (i.e. rightmost) interval is the one that includes the largest value in the dataset.<\/p>\r\n\r\n<p>You may assume the following.<\/p>\r\n\r\n<pre>\r\n1 &le; n &le; 100\r\n10 &le; w &le; 50\r\n0 &le; vi &le; 100 for 1 &le; i &le; n<\/pre>\r\n\r\n<p>You can also assume that the maximum value is no less than w. This means that the histogram has more than one interval.<\/p>\r\n\r\n<p>The end of the input is indicated by a line containing two zeros.<\/p>\r\n","output":"<p>For each dataset, output a line containing the amount of ink consumed in printing the histogram.<\/p>\r\n\r\n<p>One unit of ink is necessary to paint one highest bar black. Assume that 0:01 units of ink per histogram is consumed for various purposes except for painting bars such as drawing lines and characters (see Figure 1). For instance, the amount of ink consumed in printing the histogram in Figure 1 is:<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/ink.png\" style=\"height:109px; width:284px\" \/><\/p>\r\n\r\n<p>Each output value should be in a decimal fraction and may have an error less than 10<sup>&minus;5<\/sup>.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Japan > Asia Regional Contest 2008 in Aizu A번