시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
2 초 128 MB 220 33 27 18.243%

문제

상근이는 자신의 이름을 딴 방송국 GSK를 만들었다. GSK는 스포츠 전문 방송국으로 곧 열리는 경기 N개를 모두 취재하려고 한다.

각각의 스포츠 경기 Ei(1 ≤ i ≤ n)의 시작 시간은 si, 경기 시간은 di, 경기장은 gi이다. gi에서 gj로 가는 이동 시간은 ti,j(1 ≤ i,j ≤ n)이며, ti,j = tj,i와 ti,j ≤ ti,k + tk,j (1 ≤ i,j,k ≤ n)을 만족한다.

리포터는 경기가 열리는 동안 그 경기장에서 계속 취재를 해야 한다. 즉, 한 리포터가 두 경기 Ei와 Ej를 취재하려면, si + di + ti,j ≤ sj 나 sj + dj + tj,i ≤ si를 만족해야 한다.

경기 정보가 모두 주어졌을 때, 한 리포터가 동시에 취재할 수 없는 가장 큰 경기의 부분집합을 구하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 경기의 수 n (1 ≤ n ≤ 1,000)이 주어진다. 둘째 줄에는 각 경기의 시작 시간 si, 셋째 줄에는 경기 시간 di가 주어진다. (1 ≤ si, di ≤ 1,000,000) 넷째 줄부터 총 n개 줄 중 i번째 줄에는 n-i+1개의 정수가 주어지며, ti,i, ti,i+1, ..., ti,n을 나타낸다. (0 ≤ ti,j ≤ 1,000,000) ti,i는 항상 0이다.

출력

각 테스트 케이스마다 두 줄을 출력한다. 첫째 줄은 한 리포터가 동시에 취재할 수 없는 가장 큰 경기의 부분집합의 크기 k이고, 둘째 줄에는 집합에 포함된 경기의 번호를 출력한다. (Ei에서 i) 가능한 정답이 여러가지인 경우에는 아무거나 출력한다.

예제 입력 1

2
3
7 8 9
1 1 1
0 2 2
0 1
0
2
7 12
3 2
0 2
0

예제 출력 1

3
2 3 1
1
2

힌트

[{"problem_id":"8898","problem_lang":"0","title":"\uc2a4\ud3ec\uce20 \uc804\ubb38 \ucc44\ub110 GSK","description":"<p>\uc0c1\uadfc\uc774\ub294 \uc790\uc2e0\uc758 \uc774\ub984\uc744 \ub534 \ubc29\uc1a1\uad6d GSK\ub97c \ub9cc\ub4e4\uc5c8\ub2e4. GSK\ub294 \uc2a4\ud3ec\uce20 \uc804\ubb38 \ubc29\uc1a1\uad6d\uc73c\ub85c \uace7 \uc5f4\ub9ac\ub294 \uacbd\uae30 N\uac1c\ub97c \ubaa8\ub450 \ucde8\uc7ac\ud558\ub824\uace0 \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uac01\uac01\uc758 \uc2a4\ud3ec\uce20 \uacbd\uae30 E<sub>i<\/sub>(1 &le; i &le; n)\uc758 \uc2dc\uc791 \uc2dc\uac04\uc740 s<sub>i<\/sub>, \uacbd\uae30 \uc2dc\uac04\uc740 d<sub>i<\/sub>, \uacbd\uae30\uc7a5\uc740 g<sub>i<\/sub>\uc774\ub2e4. g<sub>i<\/sub>\uc5d0\uc11c g<sub>j<\/sub>\ub85c \uac00\ub294 \uc774\ub3d9 \uc2dc\uac04\uc740 t<sub>i,j<\/sub>(1 &le; i,j &le; n)\uc774\uba70, t<sub>i,j<\/sub> = t<sub>j,i<\/sub>\uc640 t<sub>i,j<\/sub> &le; t<sub>i,k<\/sub> + t<sub>k,j<\/sub> (1 &le; i,j,k &le; n)\uc744 \ub9cc\uc871\ud55c\ub2e4.<\/p>\r\n\r\n<p>\ub9ac\ud3ec\ud130\ub294 \uacbd\uae30\uac00 \uc5f4\ub9ac\ub294 \ub3d9\uc548 \uadf8 \uacbd\uae30\uc7a5\uc5d0\uc11c \uacc4\uc18d \ucde8\uc7ac\ub97c \ud574\uc57c \ud55c\ub2e4. \uc989, \ud55c \ub9ac\ud3ec\ud130\uac00 \ub450 \uacbd\uae30 E<sub>i<\/sub>\uc640 E<sub>j<\/sub>\ub97c \ucde8\uc7ac\ud558\ub824\uba74, s<sub>i<\/sub> + d<sub>i<\/sub> + t<sub>i,j<\/sub> &le; s<sub>j<\/sub> \ub098 s<sub>j<\/sub> + d<sub>j<\/sub> + t<sub>j,i<\/sub> &le; s<sub>i<\/sub>\ub97c \ub9cc\uc871\ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uacbd\uae30 \uc815\ubcf4\uac00 \ubaa8\ub450 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ud55c \ub9ac\ud3ec\ud130\uac00 \ub3d9\uc2dc\uc5d0 \ucde8\uc7ac\ud560 \uc218 \uc5c6\ub294 \uac00\uc7a5 \ud070 \uacbd\uae30\uc758 \ubd80\ubd84\uc9d1\ud569\uc744 \uad6c\ud558\ub294 \ud504\ub85c\uadf8\ub7a8\uc744 \uc791\uc131\ud558\uc2dc\uc624.<\/p>\r\n","input":"<p>\uccab\uc9f8 \uc904\uc5d0 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uac1c\uc218 T\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. \uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\uc758 \uccab\uc9f8 \uc904\uc5d0\ub294 \uacbd\uae30\uc758 \uc218 n (1 &le; n &le; 1,000)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uac01 \uacbd\uae30\uc758 \uc2dc\uc791 \uc2dc\uac04 s<sub>i<\/sub>, \uc14b\uc9f8 \uc904\uc5d0\ub294 \uacbd\uae30 \uc2dc\uac04 d<sub>i<\/sub>\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; s<sub>i<\/sub>, d<sub>i<\/sub> &le; 1,000,000) \ub137\uc9f8 \uc904\ubd80\ud130 \ucd1d n\uac1c \uc904 \uc911 i\ubc88\uc9f8 \uc904\uc5d0\ub294 n-i+1\uac1c\uc758 \uc815\uc218\uac00 \uc8fc\uc5b4\uc9c0\uba70, t<sub>i,i<\/sub>, t<sub>i,i+1<\/sub>, ..., t<sub>i,n<\/sub>\uc744 \ub098\ud0c0\ub0b8\ub2e4. (0 &le; t<sub>i,j<\/sub> &le; 1,000,000) t<sub>i,i<\/sub>\ub294 \ud56d\uc0c1 0\uc774\ub2e4.<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4\ub9c8\ub2e4 \ub450 \uc904\uc744 \ucd9c\ub825\ud55c\ub2e4. \uccab\uc9f8 \uc904\uc740 \ud55c \ub9ac\ud3ec\ud130\uac00 \ub3d9\uc2dc\uc5d0 \ucde8\uc7ac\ud560 \uc218 \uc5c6\ub294 \uac00\uc7a5 \ud070 \uacbd\uae30\uc758 \ubd80\ubd84\uc9d1\ud569\uc758 \ud06c\uae30&nbsp;k\uc774\uace0, \ub458\uc9f8 \uc904\uc5d0\ub294 \uc9d1\ud569\uc5d0 \ud3ec\ud568\ub41c&nbsp;\uacbd\uae30\uc758 \ubc88\ud638\ub97c \ucd9c\ub825\ud55c\ub2e4. (E<sub>i<\/sub>\uc5d0\uc11c i) \uac00\ub2a5\ud55c \uc815\ub2f5\uc774 \uc5ec\ub7ec\uac00\uc9c0\uc778 \uacbd\uc6b0\uc5d0\ub294 \uc544\ubb34\uac70\ub098 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"8898","problem_lang":"1","title":"Sports Reporters","description":"<p>A news agency wishes to cover sporting events that will take place soon. For each event E<sub>i<\/sub>, 1 &le; i &le; n, its starting time s<sub>i<\/sub>, duration time d<sub>i<\/sub>, and geographical site g<sub>i<\/sub> are known in advance. In addition, the travel time t<sub>i,j<\/sub> from g<sub>i<\/sub> to g<sub>j<\/sub> is also known for all 1 &le; i,j &le; n, where t<sub>i,j<\/sub> = t<sub>j,i<\/sub> and t<sub>i,j<\/sub> &le; t<sub>i,k<\/sub> + t<sub>k,j<\/sub> for every 1 &le; i,j,k &le; n. In gathering news from an event, the news agency wants one reporter to fully take responsibility for the entire period of the event. This means that two events E<sub>i<\/sub> and E<sub>j<\/sub> may be assigned to the same reporter if s<sub>i<\/sub>&nbsp;+ d<sub>i<\/sub>&nbsp;+ t<sub>i,j<\/sub>&nbsp;&le; s<sub>j<\/sub> or s<sub>j<\/sub>&nbsp;+ d<sub>j<\/sub>&nbsp;+ t<sub>j,i<\/sub>&nbsp;&le; s<sub>i<\/sub>.&nbsp;<br \/>\r\n&nbsp;<br \/>\r\nUnder these constraints, a manager of the agency tries to identify a maximum subset of events such that no pair of events in the subset can be assigned to the same reporter. Write a program that solves the manager&rsquo;s problem.&nbsp;<\/p>\r\n","input":"<p>Your program is to read from standard input. The input consists of T test cases. The number of test cases T is given in the first line of the input. Each test case is described by a number of lines. The first line of a test case contains an integer n, indicating the number of sporting events (1 &le; n &le; 1,000). Then, the second line n contains integers s<sub>1<\/sub>, s<sub>2<\/sub>, ..., s<sub>n<\/sub> separated by spaces, where s<sub>i<\/sub> is the starting time of event E<sub>i<\/sub> (1 &le; s<sub>i<\/sub> &le; 1,000,000). Similary, the third line contains n integers d<sub>1<\/sub>, d<sub>2<\/sub>, ..., d<sub>n<\/sub>, where d<sub>i<\/sub> is the duration time of E<sub>i<\/sub> (1 &le; d<sub>i<\/sub> &le; 1,000,000). In the following n lines, the i-th line contains n-i+1 integers t<sub>i,i<\/sub>, t<sub>i,i+1<\/sub>, ..., t<sub>i,n<\/sub>, where t<sub>i,j<\/sub> is the travel time from g<sub>i<\/sub> to g<sub>j<\/sub> (0 &le; t<sub>i,j<\/sub> &le; 1,000,000). You may assume t<sub>i,i<\/sub> = 0 for every i.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly two lines per each test case. The first line should contain the maximum number k of events in which no two can be assigned to the same reporter. Then, the second line should contain the indices of such k events (i.e., i for E<sub>i<\/sub>), separated by a space. If there are multiple solutions, just output any one of them.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Korea > Asia Regional - Daejeon 2012 K번