시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 9 2 2 100.000%

문제

질량이 mi, 길이가 2, 높이가 h인 직사각형이 N개가 있다. 이 직사각형은 2차원 평면에 다음과 같이 쌓여져 있다.

  • 직사각형의 변은 모두 축에 평행하다.
  • 직사각형 아랫변의 y좌표는 모두 다르고, 다음이 0, h, 2h, 3h, ..., (N-1)h값을 갖는다.
  • 가장 아래에 있는 직사각형의 왼쪽 아래 좌표는 (-2,0)이고, 오른쪽 아래의 좌표는 (0,0)이다.

직사각형의 x중심은 아랫변의 중점이다.

하나 또는 그 이상 직사각형의 무게중심은 직사각형의 x좌표와 무게를 이용해서 아래와 같이 계산할 수 있다.

각 직사각형 A보다 위에 있는 직사각형의 무게중심과 A의 x중심의 거리가 많아야 1이 되도록 직사각형을 쌓는다면, 안정한 쌓기라고 한다.

직사각형을 안정하게 쌓는다면, 직사각형은 무너지지 않을 것이다. 왼쪽 그림은 안정한 배치가 아니다. 그 이유는 가장 위의 두 직사각형의 무게중심과 바로 아래있는 직사각형의 x중심의 거리가 1을 넘기 때문이다. 오른족 그림은 안정한 쌓기이다.

모든 직사각형의 질량이 주어졌을 때, 모든 직사각형의 꼭짓점 중 가장 오른쪽에 있는 꼭짓점이 크게 쌓는 방법을 구하는 프로그램을 작성하시오. 이때, 직사각형은 안정한 쌓기이어야 하고, 입력으로 주어진 순서대로 쌓아야 한다.

입력

첫째 줄에 직사각형의 개수 N이 주어진다. (2 ≤ N ≤ 300,000)

다음 N개 줄에는 직사각형의 질량이 아래 직사각형부터 위 직사각형까지 순서대로 주어진다. 질량은 10,000보다 작거나 같은 양의 정수이다.

출력

첫째 줄에 안정하게 쌓는 방법 중에서 가장 오른쪽 꼭짓점이 클 때의 오른쪽 꼭짓점의 x좌표를 출력한다. 정답과의 오차는 0.000001까지 허용한다.

예제 입력 1

2
1
1

예제 출력 1

1.000000
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(2 &le; N &le; 300,000)<\/p>\r\n\r\n<p>\ub2e4\uc74c N\uac1c \uc904\uc5d0\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 \uc9c8\ub7c9\uc774 \uc544\ub798 \uc9c1\uc0ac\uac01\ud615\ubd80\ud130 \uc704 \uc9c1\uc0ac\uac01\ud615\uae4c\uc9c0 \uc21c\uc11c\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc9c8\ub7c9\uc740 10,000\ubcf4\ub2e4 \uc791\uac70\ub098 \uac19\uc740 \uc591\uc758 \uc815\uc218\uc774\ub2e4.<\/p>\r\n","output":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc548\uc815\ud558\uac8c \uc313\ub294 \ubc29\ubc95 \uc911\uc5d0\uc11c \uac00\uc7a5 \uc624\ub978\ucabd \uaf2d\uc9d3\uc810\uc774 \ud074 \ub54c\uc758 \uc624\ub978\ucabd \uaf2d\uc9d3\uc810\uc758 x\uc88c\ud45c\ub97c \ucd9c\ub825\ud55c\ub2e4. \uc815\ub2f5\uacfc\uc758 \uc624\ucc28\ub294&nbsp;0.000001\uae4c\uc9c0 \ud5c8\uc6a9\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"2808","problem_lang":"1","title":"BLOKOVI","description":"<p>N rectangles with given masses (m<sub>i<\/sub>) and equal lengths (2) and heights (h) are arranged in a Cartesian plane such that:<\/p>\r\n\r\n<p>rectangle edges are parallel to the coordinate axes;<br \/>\r\nthe y-coordinates of lower horizontal edges are distinct and assume the following values: 0, h, 2h, 3h, &hellip;, (N - 1)h;<br \/>\r\nthe lowest rectangle\u201fs lower left corner has coordinates (-2, 0), while the lower right corner coincides with the origin<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/book.png\" style=\"height:204px; width:553px\" \/><\/p>\r\n\r\n<p>The X-centre of a rectangle is the x-coordinate of the midpoint of its lower edge.<\/p>\r\n\r\n<p>The X-barycentre of one or more rectangles is the weighted average of their X-centres. It is computed as<\/p>\r\n\r\n<p>\\[Xbarycentre=\\frac{\\sum_{i}{m_{i} \\cdot Xcentre(i)} }{\\sum_{i}{m_{i}}}\\]<\/p>\r\n\r\n<p>In other words, the mass of each rectangle is multiplied by its X-centre and the sum of these products is then divided by the total mass of the rectangles.<\/p>\r\n\r\n<p>An arrangement is stable if, for each rectangle A:<\/p>\r\n\r\n<ul>\r\n\t<li>the X-barycentre of rectangles above A has distance of at most 1 from the X-centre of A (i.e. is contained in the x-interval that covers A).<\/li>\r\n<\/ul>\r\n\r\n<p>Intuitively, stability of an arrangement can be understood as the precondition for the arrangement to not fall apart. The arrangement in the figure on the left is unstable since the X-barycentre of the top two rectangles falls outside the rectangle underneath (the distance of the X-barycentre to the X-centre of the underlying rectangle is greater than 1). The arrangement in the figure on the right is stable.<\/p>\r\n\r\n<p>Given the masses of all rectangles, find the largest (&ldquo;rightmost&rdquo;) possible x-coordinate of any rectangle corner in a stable arrangement. You are not allowed to change the order of rectangles (they are given from the lowest to the highest one).<\/p>\r\n","input":"<p>The first line of input contains the positive integer N (2 &le; N &le; 300 000), the number of rectangles.<\/p>\r\n\r\n<p>Each of the next N lines contains a single positive integer less than 10 000, the mass of a rectangle. The masses are given in order from the lowest to the highest rectangle.<\/p>\r\n","output":"<p>The first and only line of output must contain the required rightmost x-coordinate. The given result must be within 0.000001 of the official solution.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]