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문제

넓은 창고에 상자들을 쌓으려고 한다. 상자는 하나씩 창고에 입고되며, 입고되는 순서대로 쌓아 나가야 한다. 또, 각 상자마다 그 상자를 쌓아야 하는 위치가 정확히 지정되어 있으며, 쌓을 때 회전시킬 수도 없다. 상자들은 직육면체 모양으로, 가로, 세로, 높이의 길이가 다양하다. 상자를 쌓아 둘 창고 역시 직육면체 모양이지만, 그 높이는 충분히 높다고 가정하자.

편의상 창고 바닥의 남서쪽 코너를 원점으로 하여 좌표계를 구성하도록 한다. 창고의 각 모서리는 x, y, z 각 좌표축에 평행하거나 수직하다. x축은 동쪽 방향, y축은 북쪽 방향, z축은 하늘 방향으로 잡는다. 물론 상자들도 각 모서리가 x, y, z축에 평행하거나 수직하게 되도록 쌓을 것이다.

여러분이 할 일은, 주어진 순서대로 각 상자들을 쌓았을 때, 가장 높은 위치의 고도를 알아내는 것이다. 이를 위한 프로그램을 작성하라.

입력

첫 줄에 세 정수 Lx, Ly, N이 주어진다. (1 ≤ Lx, Ly ≤ 1,000, 1 ≤ N ≤ 20,000) Lx와 Ly는 창고의 가로, 세로 길이이며, N은 입고되는 상자의 개수이다. 이후 N개의 줄에 각 상자의 정보가 입고되는 순서로 주어진다. 이는 다섯 개의 정수 lx, ly, lz, px, py 로 이루어진다. (1 ≤ lx, 0 ≤ px, px+lx ≤ Lx, 1 ≤ ly, 0 ≤ py, py+ly ≤ Ly, 1 ≤ lz ≤ 100,000) lx, ly, lz는 각각 상자의 가로, 세로, 높이 길이를 나타낸다. px, py는 상자를 쌓아야 하는 위치를 나타낸다. 상자 바닥의 네 꼭짓점 중 가장 남서쪽에 있는 것의 x, y좌표를 px, py에 맞추어 쌓으면 된다.

출력

첫 줄에 상자를 모두 쌓았을 때, 가장 높은 곳의 고도를 출력한다.

예제 입력 1

7 5 4
4 3 2 0 0
3 3 1 3 0
7 1 2 0 3
2 3 3 2 2

예제 출력 1

6

힌트

네 개의 상자를 순서대로 모두 쌓고 난 뒤, 각 상자의 꼭짓점 좌표는 다음과 같다.

  • 첫 번째 상자 : (0,0,0), (4,0,0), (4,3,0), (0,3,0), (0,0,2), (4,0,2), (4,3,2), (0,3,2)
  • 두 번째 상자 : (3,0,2), (6,0,2), (6,3,2), (3,3,2), (3,0,3), (6,0,3), (6,3,3), (3,3,3)
  • 세 번째 상자 :(0,3,0), (7,3,0), (7,4,0), (0,4,0), (0,3,2), (7,3,2), (7,4,2), (0,4,2)
  • 네 번째 상자 : (2,2,3), (4,2,3), (4,5,3), (2,5,3), (2,2,6), (4,2,6), (4,5,6), (2,5,6)
[{"problem_id":"1905","problem_lang":"0","title":"\uc0c1\uc790 \uc313\uae30","description":"<p>\ub113\uc740 \ucc3d\uace0\uc5d0 \uc0c1\uc790\ub4e4\uc744 \uc313\uc73c\ub824\uace0 \ud55c\ub2e4. \uc0c1\uc790\ub294 \ud558\ub098\uc529 \ucc3d\uace0\uc5d0 \uc785\uace0\ub418\uba70, \uc785\uace0\ub418\ub294 \uc21c\uc11c\ub300\ub85c \uc313\uc544 \ub098\uac00\uc57c \ud55c\ub2e4. \ub610, \uac01 \uc0c1\uc790\ub9c8\ub2e4 \uadf8 \uc0c1\uc790\ub97c \uc313\uc544\uc57c \ud558\ub294 \uc704\uce58\uac00 \uc815\ud655\ud788 \uc9c0\uc815\ub418\uc5b4 \uc788\uc73c\uba70, \uc313\uc744 \ub54c \ud68c\uc804\uc2dc\ud0ac \uc218\ub3c4 \uc5c6\ub2e4. \uc0c1\uc790\ub4e4\uc740 \uc9c1\uc721\uba74\uccb4 \ubaa8\uc591\uc73c\ub85c, \uac00\ub85c, \uc138\ub85c, \ub192\uc774\uc758 \uae38\uc774\uac00 \ub2e4\uc591\ud558\ub2e4. \uc0c1\uc790\ub97c \uc313\uc544 \ub458 \ucc3d\uace0 \uc5ed\uc2dc \uc9c1\uc721\uba74\uccb4 \ubaa8\uc591\uc774\uc9c0\ub9cc, \uadf8 \ub192\uc774\ub294 \ucda9\ubd84\ud788 \ub192\ub2e4\uace0 \uac00\uc815\ud558\uc790.<\/p>\r\n\r\n<p>\ud3b8\uc758\uc0c1 \ucc3d\uace0 \ubc14\ub2e5\uc758 \ub0a8\uc11c\ucabd \ucf54\ub108\ub97c \uc6d0\uc810\uc73c\ub85c \ud558\uc5ec \uc88c\ud45c\uacc4\ub97c \uad6c\uc131\ud558\ub3c4\ub85d \ud55c\ub2e4. \ucc3d\uace0\uc758 \uac01 \ubaa8\uc11c\ub9ac\ub294 x, y, z \uac01 \uc88c\ud45c\ucd95\uc5d0 \ud3c9\ud589\ud558\uac70\ub098 \uc218\uc9c1\ud558\ub2e4. x\ucd95\uc740 \ub3d9\ucabd \ubc29\ud5a5, y\ucd95\uc740 \ubd81\ucabd \ubc29\ud5a5, z\ucd95\uc740 \ud558\ub298 \ubc29\ud5a5\uc73c\ub85c \uc7a1\ub294\ub2e4. \ubb3c\ub860 \uc0c1\uc790\ub4e4\ub3c4 \uac01 \ubaa8\uc11c\ub9ac\uac00 x, y, z\ucd95\uc5d0 \ud3c9\ud589\ud558\uac70\ub098 \uc218\uc9c1\ud558\uac8c \ub418\ub3c4\ub85d \uc313\uc744 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\uc5ec\ub7ec\ubd84\uc774 \ud560 \uc77c\uc740, \uc8fc\uc5b4\uc9c4 \uc21c\uc11c\ub300\ub85c \uac01 \uc0c1\uc790\ub4e4\uc744 \uc313\uc558\uc744 \ub54c, \uac00\uc7a5 \ub192\uc740 \uc704\uce58\uc758 \uace0\ub3c4\ub97c \uc54c\uc544\ub0b4\ub294 \uac83\uc774\ub2e4. \uc774\ub97c \uc704\ud55c \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\ub77c.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uc138 \uc815\uc218 Lx, Ly, N\uc774&nbsp;\uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; Lx, Ly &le; 1,000,&nbsp;1 &le; N &le; 20,000) Lx\uc640 Ly\ub294 \ucc3d\uace0\uc758 \uac00\ub85c, \uc138\ub85c \uae38\uc774\uc774\uba70, N\uc740 \uc785\uace0\ub418\ub294 \uc0c1\uc790\uc758 \uac1c\uc218\uc774\ub2e4. \uc774\ud6c4 N\uac1c\uc758 \uc904\uc5d0 \uac01 \uc0c1\uc790\uc758 \uc815\ubcf4\uac00 \uc785\uace0\ub418\ub294 \uc21c\uc11c\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \ub2e4\uc12f \uac1c\uc758 \uc815\uc218 lx, ly, lz, px,&nbsp;py \ub85c \uc774\ub8e8\uc5b4\uc9c4\ub2e4. (1 &le; lx, 0 &le; px, px+lx &le; Lx, 1 &le; ly, 0 &le; py, py+ly &le; Ly, 1 &le; lz &le; 100,000) lx, ly, lz\ub294 \uac01\uac01 \uc0c1\uc790\uc758 \uac00\ub85c, \uc138\ub85c, \ub192\uc774 \uae38\uc774\ub97c \ub098\ud0c0\ub0b8\ub2e4. px, py\ub294 \uc0c1\uc790\ub97c \uc313\uc544\uc57c \ud558\ub294 \uc704\uce58\ub97c \ub098\ud0c0\ub0b8\ub2e4. \uc0c1\uc790 \ubc14\ub2e5\uc758 \ub124 \uaf2d\uc9d3\uc810 \uc911 \uac00\uc7a5 \ub0a8\uc11c\ucabd\uc5d0 \uc788\ub294 \uac83\uc758 x, y\uc88c\ud45c\ub97c px, py\uc5d0 \ub9de\ucd94\uc5b4 \uc313\uc73c\uba74 \ub41c\ub2e4.<\/p>\r\n","output":"<p>\uccab \uc904\uc5d0 \uc0c1\uc790\ub97c \ubaa8\ub450 \uc313\uc558\uc744 \ub54c, \uac00\uc7a5 \ub192\uc740 \uacf3\uc758 \uace0\ub3c4\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ub124 \uac1c\uc758 \uc0c1\uc790\ub97c \uc21c\uc11c\ub300\ub85c \ubaa8\ub450 \uc313\uace0 \ub09c \ub4a4, \uac01 \uc0c1\uc790\uc758 \uaf2d\uc9d3\uc810 \uc88c\ud45c\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\uccab \ubc88\uc9f8 \uc0c1\uc790 : (0,0,0), (4,0,0), (4,3,0), (0,3,0), (0,0,2), (4,0,2), (4,3,2), (0,3,2)<\/li>\r\n\t<li>\ub450 \ubc88\uc9f8 \uc0c1\uc790 : (3,0,2), (6,0,2), (6,3,2), (3,3,2), (3,0,3), (6,0,3), (6,3,3), (3,3,3)<\/li>\r\n\t<li>\uc138 \ubc88\uc9f8 \uc0c1\uc790 :(0,3,0), (7,3,0), (7,4,0), (0,4,0), (0,3,2), (7,3,2), (7,4,2), (0,4,2)<\/li>\r\n\t<li>\ub124 \ubc88\uc9f8 \uc0c1\uc790 : (2,2,3), (4,2,3), (4,5,3), (2,5,3), (2,2,6), (4,2,6), (4,5,6), (2,5,6)<\/li>\r\n<\/ul>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"1905","problem_lang":"1","title":"Tetris 3D","description":"<p>The authors of the game &quot;Tetris&quot; have decided to make a new, three-dimensional version, in which cuboids would fall down on a rectangular platform. The blocks fall down separately in a certain order, just like in the two-dimensional game. A block falls down until it reaches an obstacle: the platform or another block, that has already stopped - then it stops and remains in this exact position till the game is over.<\/p>\r\n\r\n<p>However, the authors wanted to change the spirit of the game, turning it from a simple arcade-game into a play far more puzzling. Knowing the order of the falling blocks and their flight path the player&#39;s task is to tell the height of the highest point of the arrangement after all blocks have fallen down (and stopped). All the blocks are falling down vertically and do not rotate while falling. For convenience we&#39;ll introduce a cartesian coordinate system on the platform, with the center in one of the platform&#39;s corners and the axes parallel to the platform&#39;s edges.<\/p>\r\n\r\n<p>Write a programme that automates verification of the player&#39;s answer.<\/p>\r\n\r\n<p>Write a programme that:<\/p>\r\n\r\n<ul>\r\n\t<li>reads the descriptions of subsequent falling blocks from the standard input,<\/li>\r\n\t<li>determines the height of the highest point of the arrangement of blocks after all have fallen down and stopped,<\/li>\r\n\t<li>writes the result to the standard output.<\/li>\r\n<\/ul>\r\n","input":"<p>In the first line of the input there are three integers D, S and N (1 &le; N &le; 20 000, 1 &le; D,S &le; 1 000), separated by single spaces and denoting respectively: the length and the depth of the platform and the number of blocks that are going to fall down on it. In the following N lines the descriptions of subsequent block are give, one in each line.<\/p>\r\n\r\n<p>Each description of a block consists of five integers: d, s, w, x and y (1 &le; d, 0 &le; x, d + x &le; D, 1 &le; s, 0 &le; y, s + y &le; S, 1 &le; w &le; 100 000), representing a block of length d depth s and height w. This very block will be be falling down on the platform with this d &times; s face as the bottom, where the length and depth of the block are parallel to those of the platform. The coordinates of the vertices of the projection of the block on the platform are: (x, y), (x+d, y), (x, y+s), and (x+d, y+s).<\/p>\r\n","output":"<p>The first and only line of the standard output should contain exactly one integer, the height of the highest point of the arrangement of blocks after all have fallen down and stopped.<\/p>\r\n\r\n<p>&nbsp;<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

Olympiad > Polish Olympiad in Informatics > POI 2005/2006 > Stage 1 4번

  • 문제의 오타를 찾은 사람: kazel