시간 제한메모리 제한제출정답맞힌 사람정답 비율
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문제

명우는 보안 업체의 직원이고, 강남역에 있는 상점 여러 개를 도보로 순찰하는 업무를 맡고 있다. 

강남역은 선분으로 나타낼 수 있고, 명우의 회사와 상점은 왼쪽부터 순서대로 선분 위의 점 pi로 나타낼 수 있다. 회사는 pa에 있고, s로 나타낸다. 명우는 s에서 순찰을 시작해서, 모든 상점 pi를 적어도 한 번 방문해야 한다. 각각의 i에 대해서, pi와 pi+1사이를 오가는데 걸리는 시간은 t[pi,pi+1]이다. pi의 대기 시간 ℓi는 s를 출발해서 pi에 처음 도착하기 까지 걸린 시간이다. 시작점 s = pa의 대기 시간 ℓa는 0이다. 명우는 모든 상점의 대기 시간의 합이 최소가 되게 하기 위해 순찰을 해야 한다.

아래 그림에는 총 6개의 상점 p1부터 p6까지가 있고, 시작점 s는 p3이다. 또, t[p1,p2] = 7, t[p2,p3] = 4, t[p3,p4] = 1, t[p4,p5] = 2, t[p5,p6] = 9이다. 명우가 s에서 오른쪽으로 걷기 시작한다면, 대기 시간 ℓ4와 ℓ5는 1과 3이 된다. 아래 그림에 나와있는 순서대로 순찰을 한다면, 대기 시간의 합은 71이 된다. 71보다 대기 시간의 합을 줄이는 방법은 없다.

점의 수 N과, pi와 pi+1 사이를 오가는데 걸리는 시간 t[pi,pi+1] (t = 1,...,N-1)이 주어졌을 때, 대기 시간을 최소로 하는 프로그램을 작성하시오.

입력

첫째 줄에 테스트 케이스의 개수 T가 주어진다. 각 테스트 케이스의 첫째 줄에는 상점의 수 N (1 ≤ N ≤ 100)이 주어진다. 둘째 줄에는 시작점의 위치 a (1 ≤ a ≤ N)가 주어진다. a번째 점, pa = s가 시작점이 된다. 다음 N-1개 줄의 i번째 줄에는 t[pi,pi+1]가 주어진다. (1 ≤ t[pi,pi+1] ≤ 15,000,000)

출력

각 테스트 케이스 마다, 모든 가게를 순찰하는 모든 순찰 방법 중 대기 시간의 최솟값을 출력한다.

예제 입력 1

2
6
3
7
4
1
2
9
9
5
96
24
6
2
1
3
12
48

예제 출력 1

71
605
[{"problem_id":"4243","problem_lang":"0","title":"\ubcf4\uc548 \uc5c5\uccb4","description":"<p>\uba85\uc6b0\ub294 \ubcf4\uc548 \uc5c5\uccb4\uc758 \uc9c1\uc6d0\uc774\uace0,&nbsp;\uac15\ub0a8\uc5ed\uc5d0 \uc788\ub294 \uc0c1\uc810 \uc5ec\ub7ec \uac1c\ub97c \ub3c4\ubcf4\ub85c \uc21c\ucc30\ud558\ub294 \uc5c5\ubb34\ub97c \ub9e1\uace0 \uc788\ub2e4.&nbsp;<\/p>\r\n\r\n<p>\uac15\ub0a8\uc5ed\uc740 \uc120\ubd84\uc73c\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\uace0, \uba85\uc6b0\uc758 \ud68c\uc0ac\uc640 \uc0c1\uc810\uc740 \uc67c\ucabd\ubd80\ud130 \uc21c\uc11c\ub300\ub85c&nbsp;\uc120\ubd84 \uc704\uc758 \uc810 p<sub>i<\/sub>\ub85c \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \ud68c\uc0ac\ub294 p<sub>a<\/sub>\uc5d0 \uc788\uace0, s\ub85c \ub098\ud0c0\ub0b8\ub2e4. \uba85\uc6b0\ub294 s\uc5d0\uc11c \uc21c\ucc30\uc744 \uc2dc\uc791\ud574\uc11c, \ubaa8\ub4e0 \uc0c1\uc810&nbsp;p<sub>i<\/sub>\ub97c \uc801\uc5b4\ub3c4 \ud55c \ubc88 \ubc29\ubb38\ud574\uc57c \ud55c\ub2e4. \uac01\uac01\uc758 i\uc5d0 \ub300\ud574\uc11c, p<sub>i<\/sub>\uc640 p<sub>i+1<\/sub>\uc0ac\uc774\ub97c \uc624\uac00\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04\uc740 t[p<sub>i<\/sub>,p<sub>i+1<\/sub>]\uc774\ub2e4. p<sub>i<\/sub>\uc758 \ub300\uae30 \uc2dc\uac04 \u2113<sub>i<\/sub>\ub294 s\ub97c \ucd9c\ubc1c\ud574\uc11c p<sub>i<\/sub>\uc5d0 \ucc98\uc74c \ub3c4\ucc29\ud558\uae30 \uae4c\uc9c0 \uac78\ub9b0 \uc2dc\uac04\uc774\ub2e4. \uc2dc\uc791\uc810 s = p<sub>a<\/sub>\uc758 \ub300\uae30 \uc2dc\uac04 \u2113<sub>a<\/sub>\ub294 0\uc774\ub2e4. \uba85\uc6b0\ub294 \ubaa8\ub4e0 \uc0c1\uc810\uc758 \ub300\uae30 \uc2dc\uac04\uc758 \ud569\uc774 \ucd5c\uc18c\uac00 \ub418\uac8c \ud558\uae30 \uc704\ud574 \uc21c\ucc30\uc744 \ud574\uc57c \ud55c\ub2e4.<\/p>\r\n\r\n<p>\uc544\ub798 \uadf8\ub9bc\uc5d0\ub294 \ucd1d 6\uac1c\uc758 \uc0c1\uc810 p<sub>1<\/sub>\ubd80\ud130 p<sub>6<\/sub>\uae4c\uc9c0\uac00 \uc788\uace0, \uc2dc\uc791\uc810 s\ub294 p<sub>3<\/sub>\uc774\ub2e4. \ub610, t[p<sub>1<\/sub>,p<sub>2<\/sub>] = 7, t[p<sub>2<\/sub>,p<sub>3<\/sub>] = 4, t[p<sub>3<\/sub>,p<sub>4<\/sub>] = 1, t[p<sub>4<\/sub>,p<sub>5<\/sub>] = 2, t[p<sub>5<\/sub>,p<sub>6<\/sub>] = 9\uc774\ub2e4. \uba85\uc6b0\uac00 s\uc5d0\uc11c \uc624\ub978\ucabd\uc73c\ub85c \uac77\uae30 \uc2dc\uc791\ud55c\ub2e4\uba74, \ub300\uae30 \uc2dc\uac04 \u2113<sub>4<\/sub>\uc640 \u2113<sub>5<\/sub>\ub294 1\uacfc 3\uc774 \ub41c\ub2e4. \uc544\ub798 \uadf8\ub9bc\uc5d0 \ub098\uc640\uc788\ub294 \uc21c\uc11c\ub300\ub85c&nbsp;\uc21c\ucc30\uc744 \ud55c\ub2e4\uba74, \ub300\uae30 \uc2dc\uac04\uc758 \ud569\uc740 71\uc774 \ub41c\ub2e4. 71\ubcf4\ub2e4 \ub300\uae30 \uc2dc\uac04\uc758 \ud569\uc744 \uc904\uc774\ub294 \ubc29\ubc95\uc740 \uc5c6\ub2e4.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images\/security.png\" style=\"height:100px; width:415px\" \/><\/p>\r\n\r\n<p>\uc810\uc758 \uc218 N\uacfc, p<sub>i<\/sub>\uc640 p<sub>i+1<\/sub> \uc0ac\uc774\ub97c \uc624\uac00\ub294\ub370 \uac78\ub9ac\ub294 \uc2dc\uac04 t[p<sub>i<\/sub>,p<sub>i+1<\/sub>] (t = 1,...,N-1)\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c, \ub300\uae30 \uc2dc\uac04\uc744 \ucd5c\uc18c\ub85c \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 \uc0c1\uc810\uc758 \uc218 N (1 &le; N &le; 100)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 \uc2dc\uc791\uc810\uc758 \uc704\uce58 a (1 &le; a &le; N)\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. a\ubc88\uc9f8 \uc810, p<sub>a<\/sub> = s\uac00 \uc2dc\uc791\uc810\uc774 \ub41c\ub2e4. \ub2e4\uc74c N-1\uac1c \uc904\uc758 i\ubc88\uc9f8 \uc904\uc5d0\ub294 t[p<sub>i<\/sub>,p<sub>i+1<\/sub>]\uac00 \uc8fc\uc5b4\uc9c4\ub2e4. (1 &le; t[p<sub>i<\/sub>,p<sub>i+1<\/sub>] &le; 15,000,000)<\/p>\r\n","output":"<p>\uac01 \ud14c\uc2a4\ud2b8 \ucf00\uc774\uc2a4 \ub9c8\ub2e4, \ubaa8\ub4e0 \uac00\uac8c\ub97c \uc21c\ucc30\ud558\ub294 \ubaa8\ub4e0 \uc21c\ucc30 \ubc29\ubc95 \uc911 \ub300\uae30 \uc2dc\uac04\uc758 \ucd5c\uc19f\uac12\uc744 \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"Korean"},{"problem_id":"4243","problem_lang":"1","title":"Security","description":"<p>Today most shopkeepers employ a security service. On a famous street, there are several shops. The shops are protected by a guard belonging to a security company, which is also located on the street.<\/p>\r\n\r\n<p>For simplicity, we consider the shops and the company as points p<sub>i<\/sub> on a line, running in order from left to right. The company is located at a point p<sub>a<\/sub> for some a, denote by s. Starting at the point s, the guard should visit each point p<sub>i<\/sub> at least once a day to protect the shops. For each i, it takes t[p<sub>i<\/sub>,p<sub>i+1<\/sub>] time for the guard to move between p<sub>i<\/sub> and p<sub>i+1<\/sub>. The latency \u2113<sub>i<\/sub> of p<sub>i<\/sub> is considered to be the time when the guard first visits p<sub>i<\/sub> after leaving s. Obviously the latency \u2113<sub>a<\/sub> of the starting point s = p<sub>a<\/sub> is 0. The guard shall travel to minimize the sum of latencies, which is &Sigma;<sub>i<\/sub>\u2113<sub>i<\/sub>.<\/p>\r\n\r\n<p>For example, in Figure 1, there are six points p<sub>1<\/sub> to p<sub>6<\/sub>, where the starting point s is p<sub>3<\/sub>. Alsot[p<sub>1<\/sub>,p<sub>2<\/sub>] = 7, t[p<sub>2<\/sub>,p<sub>3<\/sub>] = 4, t[p<sub>3<\/sub>,p<sub>4<\/sub>] = 1, t[p<sub>4<\/sub>,p<sub>5<\/sub>] = 2, t[p<sub>5<\/sub>,p<sub>6<\/sub>] = 9. When the guard first walks right from s, the latency \u2113<sub>4<\/sub> and \u2113<sub>5<\/sub> are determined as 1 and 3, respectively. if the guard travels as in Figure 1, then the sum of all the latencies is 71. It is minimum for all possible travels of the guard.<\/p>\r\n\r\n<p style=\"text-align: center;\"><img alt=\"\" src=\"\/upload\/images\/security.png\" style=\"height:100px; width:415px\" \/><\/p>\r\n\r\n<p style=\"text-align: center;\">Figure 1.<\/p>\r\n\r\n<p>Give an integer N, the number of points, and the times t[p<sub>i<\/sub>,p<sub>i+1<\/sub>] for the guard to move between p<sub>i<\/sub> and p<sub>i+1<\/sub>. i = 1, ..., N-1, write a program to minimize the sum of latencies of points when traveling from a starting point.<\/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 starts with an integer N (1 &le; N &le; 100), the number of points. The second line contains an integer a (1 &le; a &le; N), saying that the a-th point is the starting point, that is, p<sub>a<\/sub> = s. The i-th line of the following N-1 lines contains an integer t (1 &le; t &le; 15,000,000), representing the time t[p<sub>i<\/sub>,p<sub>i+1<\/sub>] for i=1,...,N-1.<\/p>\r\n","output":"<p>Your program is to write to standard output. Print exactly one line for each test case. The line should contain the minimum of the sum of latencies for all possible movements of the guard.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"English"}]

출처

ICPC > Regionals > Asia Pacific > Korea > Nationwide Internet Competition > Daejeon Nationalwide Internet Competition 2013 K번