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문제

은기는 모바일 게임 개발자이다. 이번에 은기가 만드는 게임은 Chain Shot! 게임 (SameGame, Jawbreaker, Bubble Shot, ... 으로도 알려져 있다)을 응용한 "한번 쏘면 멈출 수 없어" 이다.

게임은 직사각형 게임판에서 진행되며, 각 칸에는 색칠된 구슬이 채워져 있다. 플레이어는 각 턴마다 같은 색으로 이루어진 인접한 구슬 그룹을 선택한다. 선택한 구슬은 모두 게임판에서 제거된다. 구슬이 떠있는 경우에는 모두 바닥으로 떨어지게 되고, 빈 열은 제거된다.

선택한 그룹 바닥으로 떨어지는 구슬 빈 열 최종 상태

각 턴마다 플레이어가 얻는 점수는 그룹을 구성하는 구슬 개수의 제곱이다. 예를 들어, 위의 그림에서 플레이어는 49점을 받게 된다.

게임판에 구슬이 모두 없어지면 게임은 끝나게 되고, 플레이어의 점수는 각 턴마다 얻은 점수의 합이 된다.

레벨의 설계도는 게임판의 크기와 각 구슬 색상의 수로 이루어져 있다.

레벨의 설계도가 주어졌을 때, 설계도로 만들 수 있는 레벨 중 얻을 수 있는 점수가 가장 높은 것을 구하는 프로그램을 작성하시오. 

입력

입력으로 레벨의 설계도가 주어진다.

첫째 줄에는 게임판의 행의 수 h와 열의 수 w, 색상의 수 c가 주어진다. (1 ≤ h, w ≤ 10, 1 ≤ c ≤ 9)

둘째 줄에는 c개의 양의 정수가 주어지며, 각 정수는 그 색상 구슬의 개수이다. 구슬 개수의 합은 h·w가 된다.

출력

만든 게임판을 출력한다. 첫 번째 색상은 1, 두 번째 색상은 2, ... 로 출력한다.

예제 입력 1

3 5 3
4 4 7

예제 출력 1

31233
12211
33233

힌트

최대 81점을 얻을 수 있다. 

16점 16점 49점
[{"problem_id":"3991","problem_lang":"0","title":"\ud55c\ubc88 \uc3d8\uba74 \uba48\ucd9c \uc218 \uc5c6\uc5b4","description":"<p>\uc740\uae30\ub294 \ubaa8\ubc14\uc77c \uac8c\uc784 \uac1c\ubc1c\uc790\uc774\ub2e4. \uc774\ubc88\uc5d0 \uc740\uae30\uac00 \ub9cc\ub4dc\ub294 \uac8c\uc784\uc740 Chain Shot! \uac8c\uc784 (SameGame, Jawbreaker, Bubble Shot, ... \uc73c\ub85c\ub3c4 \uc54c\ub824\uc838 \uc788\ub2e4)\uc744 \uc751\uc6a9\ud55c &quot;\ud55c\ubc88 \uc3d8\uba74 \uba48\ucd9c \uc218 \uc5c6\uc5b4&quot; \uc774\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\uc740 \uc9c1\uc0ac\uac01\ud615 \uac8c\uc784\ud310\uc5d0\uc11c \uc9c4\ud589\ub418\uba70, \uac01 \uce78\uc5d0\ub294 \uc0c9\uce60\ub41c \uad6c\uc2ac\uc774 \ucc44\uc6cc\uc838 \uc788\ub2e4. \ud50c\ub808\uc774\uc5b4\ub294 \uac01 \ud134\ub9c8\ub2e4 \uac19\uc740 \uc0c9\uc73c\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uc778\uc811\ud55c \uad6c\uc2ac \uadf8\ub8f9\uc744 \uc120\ud0dd\ud55c\ub2e4. \uc120\ud0dd\ud55c \uad6c\uc2ac\uc740 \ubaa8\ub450 \uac8c\uc784\ud310\uc5d0\uc11c \uc81c\uac70\ub41c\ub2e4. \uad6c\uc2ac\uc774 \ub5a0\uc788\ub294 \uacbd\uc6b0\uc5d0\ub294 \ubaa8\ub450 \ubc14\ub2e5\uc73c\ub85c \ub5a8\uc5b4\uc9c0\uac8c \ub418\uace0, \ube48 \uc5f4\uc740 \uc81c\uac70\ub41c\ub2e4.<\/p>\r\n\r\n<table class=\"table table-bordered td-center th-center\" style=\"width:100%;\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/290x202\/0,0\/-\/preview\/\" style=\"width: 145px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/289x202\/318,0\/-\/preview\/\" style=\"width: 145px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/291x202\/634,0\/-\/preview\/\" style=\"width: 146px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/246x202\/946,0\/-\/preview\/\" style=\"width: 123px; height: 101px;\" \/><\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n\t<tfoot>\r\n\t\t<tr>\r\n\t\t\t<th>\uc120\ud0dd\ud55c \uadf8\ub8f9<\/th>\r\n\t\t\t<th>\ubc14\ub2e5\uc73c\ub85c \ub5a8\uc5b4\uc9c0\ub294 \uad6c\uc2ac<\/th>\r\n\t\t\t<th>\ube48 \uc5f4<\/th>\r\n\t\t\t<th>\ucd5c\uc885 \uc0c1\ud0dc<\/th>\r\n\t\t<\/tr>\r\n\t<\/tfoot>\r\n<\/table>\r\n\r\n<p>\uac01 \ud134\ub9c8\ub2e4 \ud50c\ub808\uc774\uc5b4\uac00 \uc5bb\ub294 \uc810\uc218\ub294 \uadf8\ub8f9\uc744 \uad6c\uc131\ud558\ub294 \uad6c\uc2ac \uac1c\uc218\uc758 \uc81c\uacf1\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, \uc704\uc758 \uadf8\ub9bc\uc5d0\uc11c \ud50c\ub808\uc774\uc5b4\ub294 49\uc810\uc744 \ubc1b\uac8c \ub41c\ub2e4.<\/p>\r\n\r\n<p>\uac8c\uc784\ud310\uc5d0 \uad6c\uc2ac\uc774 \ubaa8\ub450 \uc5c6\uc5b4\uc9c0\uba74 \uac8c\uc784\uc740 \ub05d\ub098\uac8c \ub418\uace0, \ud50c\ub808\uc774\uc5b4\uc758 \uc810\uc218\ub294 \uac01 \ud134\ub9c8\ub2e4 \uc5bb\uc740 \uc810\uc218\uc758 \ud569\uc774 \ub41c\ub2e4.<\/p>\r\n\r\n<p>\ub808\ubca8\uc758 \uc124\uacc4\ub3c4\ub294 \uac8c\uc784\ud310\uc758 \ud06c\uae30\uc640 \uac01 \uad6c\uc2ac \uc0c9\uc0c1\uc758 \uc218\ub85c \uc774\ub8e8\uc5b4\uc838 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ub808\ubca8\uc758 \uc124\uacc4\ub3c4\uac00 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \uc124\uacc4\ub3c4\ub85c \ub9cc\ub4e4 \uc218 \uc788\ub294 \ub808\ubca8 \uc911 \uc5bb\uc744 \uc218 \uc788\ub294 \uc810\uc218\uac00 \uac00\uc7a5 \ub192\uc740 \uac83\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.&nbsp;<\/p>\r\n","input":"<p>\uc785\ub825\uc73c\ub85c \ub808\ubca8\uc758 \uc124\uacc4\ub3c4\uac00 \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\uccab\uc9f8 \uc904\uc5d0\ub294 \uac8c\uc784\ud310\uc758 \ud589\uc758 \uc218 h\uc640 \uc5f4\uc758 \uc218 w, \uc0c9\uc0c1\uc758 \uc218 c\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; h, w &le; 10, 1 &le; c &le; 9)<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0\ub294 c\uac1c\uc758 \uc591\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\uba70, \uac01 \uc815\uc218\ub294 \uadf8 \uc0c9\uc0c1 \uad6c\uc2ac\uc758 \uac1c\uc218\uc774\ub2e4. \uad6c\uc2ac \uac1c\uc218\uc758 \ud569\uc740 h&middot;w\uac00 \ub41c\ub2e4.<\/p>\r\n","output":"<p>\ub9cc\ub4e0 \uac8c\uc784\ud310\uc744 \ucd9c\ub825\ud55c\ub2e4. \uccab \ubc88\uc9f8 \uc0c9\uc0c1\uc740 1, \ub450 \ubc88\uc9f8 \uc0c9\uc0c1\uc740 2, ... \ub85c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\ucd5c\ub300 81\uc810\uc744 \uc5bb\uc744 \uc218 \uc788\ub2e4.&nbsp;<\/p>\r\n\r\n<table class=\"table table-bordered th-center td-center\" style=\"width:100%;\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/240x164\/10,0\/-\/preview\/\" style=\"width: 120px; height: 82px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/203x164\/273,0\/-\/preview\/\" style=\"width: 102px; height: 82px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/198x164\/496,0\/-\/preview\/\" style=\"width: 99px; height: 82px;\" \/><\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n\t<tfoot>\r\n\t\t<tr>\r\n\t\t\t<th>16\uc810<\/th>\r\n\t\t\t<th>16\uc810<\/th>\r\n\t\t\t<th>49\uc810<\/th>\r\n\t\t<\/tr>\r\n\t<\/tfoot>\r\n<\/table>\r\n","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"3991","problem_lang":"1","title":"Addictive Bubbles","description":"<p>Alice is a mobile game developer. She writes a new port of the Chain Shot! game (also known as SameGame, Jawbreaker, Bubble Shot, etc) called Addictive Bubbles.<\/p>\r\n\r\n<p>The game is played on a rectangular board \ufb01lled with color bubbles. On each turn player selects a group of adjacent bubbles of the same color. Selected bubbles are removed from the board. Bubbles that are no longer supported fall down. If there are empty columns, they are removed.<\/p>\r\n\r\n<table class=\"table table-bordered td-center th-center\" style=\"width:100%;\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/290x202\/0,0\/-\/preview\/\" style=\"width: 145px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/289x202\/318,0\/-\/preview\/\" style=\"width: 145px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/291x202\/634,0\/-\/preview\/\" style=\"width: 146px; height: 101px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/0de1c91f-73ee-4267-abe3-92ac506ccd84\/-\/crop\/246x202\/946,0\/-\/preview\/\" style=\"width: 123px; height: 101px;\" \/><\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n\t<tfoot>\r\n\t\t<tr>\r\n\t\t\t<th>Selected group<\/th>\r\n\t\t\t<th>Not supported bubbles<\/th>\r\n\t\t\t<th>Empty columns<\/th>\r\n\t\t\t<th>Final state<\/th>\r\n\t\t<\/tr>\r\n\t<\/tfoot>\r\n<\/table>\r\n\r\n<p>The number of points scored by the move is a square of the number of bubbles in the selected group. For the sample turn shown on the \ufb01gure, 49 points are scored.<\/p>\r\n\r\n<p>Turns are repeated until the board is empty. The total number of points is the sum of points scored on each turn.<\/p>\r\n\r\n<p>The blueprint of the level consists of board dimensions and the number of bubbles of each color.<\/p>\r\n\r\n<p>Your task is to help Alice write a bonus level generator. Given the blueprint, generator must produce a level that allows a skillful player to score the maximum possible number of points compared to all levels with the same blueprint.<\/p>\r\n","input":"<p>The input \ufb01le contains the blueprint.<\/p>\r\n\r\n<p>The \ufb01rst line of the input \ufb01le contains three positive integers h, w and c &mdash; number of rows and columns of the board, and the number of colors (1 &le; h, w &le; 10; 1 &le; c &le; 9).<\/p>\r\n\r\n<p>The second line of the input \ufb01le contains c positive integer numbers &mdash; the number of bubbles of each color. The total number of bubbles is h &middot; w.<\/p>\r\n","output":"<p>Output the designed level &mdash; a h&times;w matrix of characters. The bubbles of the \ufb01rst color must be denoted by &lsquo;1&rsquo;, the second color &mdash; by &lsquo;2&rsquo;, etc.<\/p>\r\n","hint":"<p>A sequence of turns, yielding the maximum possible number of points &mdash; 81:<\/p>\r\n\r\n<table class=\"table table-bordered th-center td-center\" style=\"width:100%;\">\r\n\t<tbody>\r\n\t\t<tr>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/240x164\/10,0\/-\/preview\/\" style=\"width: 120px; height: 82px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/203x164\/273,0\/-\/preview\/\" style=\"width: 102px; height: 82px;\" \/><\/td>\r\n\t\t\t<td><img alt=\"\" src=\"https:\/\/upload.acmicpc.net\/f82e41a5-5e31-47b2-b38d-07669fa5c6b3\/-\/crop\/198x164\/496,0\/-\/preview\/\" style=\"width: 99px; height: 82px;\" \/><\/td>\r\n\t\t<\/tr>\r\n\t<\/tbody>\r\n\t<tfoot>\r\n\t\t<tr>\r\n\t\t\t<th>16 points<\/th>\r\n\t\t\t<th>16 points<\/th>\r\n\t\t\t<th>49 points<\/th>\r\n\t\t<\/tr>\r\n\t<\/tfoot>\r\n<\/table>\r\n","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Northern Eurasia > Northern Eurasia Finals > NEERC 2012 A번