시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 128 MB 8 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 꼭지점 중 가장 오른쪽에 있는 꼭지점이 크게 쌓는 방법을 구하는 프로그램을 작성하시오. 이 때, 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 꼭지점이 클 때의 오른쪽 꼭지점의 x좌표를 출력한다. 정답과의 오차는 0.000001까지 허용한다.

예제 입력 1

2
1
1

예제 출력 1

1.000000
[{"problem_id":"2808","problem_lang":"0","title":"\ucc45 \uc313\uae30","description":"<p>\uc9c8\ub7c9\uc774 m<sub>i<\/sub>, \uae38\uc774\uac00 2, \ub192\uc774\uac00 h\uc778 \uc9c1\uc0ac\uac01\ud615\uc774 N\uac1c\uac00 \uc788\ub2e4. \uc774 \uc9c1\uc0ac\uac01\ud615\uc740 2\ucc28\uc6d0 \ud3c9\uba74\uc5d0 \ub2e4\uc74c\uacfc \uac19\uc774 \uc313\uc5ec\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uc9c1\uc0ac\uac01\ud615\uc758 \ubcc0\uc740 \ubaa8\ub450 \ucd95\uc5d0 \ud3c9\ud589\ud558\ub2e4.<\/li>\r\n\t<li>\uc9c1\uc0ac\uac01\ud615 \uc544\ub7ab\ubcc0\uc758 y\uc88c\ud45c\ub294 \ubaa8\ub450 \ub2e4\ub974\uace0, \ub2e4\uc74c\uc774 0, h, 2h, 3h, ..., (N-1)h\uac12\uc744 \uac16\ub294\ub2e4.<\/li>\r\n\t<li>\uac00\uc7a5 \uc544\ub798\uc5d0 \uc788\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 \uc67c\ucabd \uc544\ub798 \uc88c\ud45c\ub294 (-2,0)\uc774\uace0, \uc624\ub978\ucabd \uc544\ub798\uc758 \uc88c\ud45c\ub294 (0,0)\uc774\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/book.png\" style=\"height:204px; width:553px\" \/><\/p>\r\n\r\n<p>\uc9c1\uc0ac\uac01\ud615\uc758 x\uc911\uc2ec\uc740 \uc544\ub7ab\ubcc0\uc758 \uc911\uc810\uc774\ub2e4.<\/p>\r\n\r\n<p>\ud558\ub098 \ub610\ub294 \uadf8 \uc774\uc0c1 \uc9c1\uc0ac\uac01\ud615\uc758 \ubb34\uac8c\uc911\uc2ec\uc740 \uc9c1\uc0ac\uac01\ud615\uc758 x\uc88c\ud45c\uc640 \ubb34\uac8c\ub97c \uc774\uc6a9\ud574\uc11c \uc544\ub798\uc640 \uac19\uc774 \uacc4\uc0b0\ud560 \uc218 \uc788\ub2e4.<\/p>\r\n\r\n<p><img alt=\"\" src=\"\/upload\/images\/daum_equation_1363184024520.png\" style=\"height:143px; width:470px\" \/><\/p>\r\n\r\n<p>\uac01 \uc9c1\uc0ac\uac01\ud615 A\ubcf4\ub2e4 \uc704\uc5d0 \uc788\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 \ubb34\uac8c\uc911\uc2ec\uacfc A\uc758 x\uc911\uc2ec\uc758 \uac70\ub9ac\uac00 \ub9ce\uc544\uc57c 1\uc774 \ub418\ub3c4\ub85d \uc9c1\uc0ac\uac01\ud615\uc744 \uc313\ub294\ub2e4\uba74, \uc548\uc815\ud55c \uc313\uae30\ub77c\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc9c1\uc0ac\uac01\ud615\uc744 \uc548\uc815\ud558\uac8c \uc313\ub294\ub2e4\uba74, \uc9c1\uc0ac\uac01\ud615\uc740 \ubb34\ub108\uc9c0\uc9c0 \uc54a\uc744 \uac83\uc774\ub2e4. \uc67c\ucabd \uadf8\ub9bc\uc740 \uc548\uc815\ud55c \ubc30\uce58\uac00 \uc544\ub2c8\ub2e4. \uadf8 \uc774\uc720\ub294 \uac00\uc7a5 \uc704\uc758 \ub450 \uc9c1\uc0ac\uac01\ud615\uc758 \ubb34\uac8c\uc911\uc2ec\uacfc \ubc14\ub85c \uc544\ub798\uc788\ub294 \uc9c1\uc0ac\uac01\ud615\uc758 x\uc911\uc2ec\uc758 \uac70\ub9ac\uac00 1\uc744 \ub118\uae30 \ub54c\ubb38\uc774\ub2e4. \uc624\ub978\uc871 \uadf8\ub9bc\uc740 \uc548\uc815\ud55c \uc313\uae30\uc774\ub2e4.<\/p>\r\n\r\n<p>\ubaa8\ub4e0 \uc9c1\uc0ac\uac01\ud615\uc758 \uc9c8\ub7c9\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ubaa8\ub4e0 \uc9c1\uc0ac\uac01\ud615\uc758 \uaf2d\uc9c0\uc810 \uc911 \uac00\uc7a5 \uc624\ub978\ucabd\uc5d0 \uc788\ub294 \uaf2d\uc9c0\uc810\uc774 \ud06c\uac8c \uc313\ub294 \ubc29\ubc95\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624. \uc774 \ub54c, \uc9c1\uc0ac\uac01\ud615\uc740 \uc548\uc815\ud55c \uc313\uae30\uc774\uc5b4\uc57c \ud558\uace0, \uc785\ub825\uc73c\ub85c \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c \uc313\uc544\uc57c \ud55c\ub2e4.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \uc9c1\uc0ac\uac01\ud615\uc758 \uac1c\uc218 N\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. (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\uc9c0\uc810\uc774 \ud074 \ub54c\uc758 \uc624\ub978\ucabd \uaf2d\uc9c0\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"}]