시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 256 MB 121 71 59 62.105%

문제

비트 문자열은 0, 1로만 이루어진 문자열이다. 여러분은 비트 문자열을 하나 받아서 특정한 문자열로 바꾸어야 한다. 이때, 여러분이 유일하게 할 수 있는 연산은 인접한 두 비트를 바꾸는 것이다.

초기 문자열의 상태는 그냥 비트의 순열로 주어진다. 하지만 바꾸고자 하는 문자열은 '연속 코드'의 형태로 주어진다. 연속 코드란, 문자열에 나타나는 연속된 0 또는 1의 개수를 차례대로 늘어놓은 순열이다. 예를 들어, "011100"의 연속 코드는 "1 3 2"가 된다. 이때, 여러분도 눈치챘겠지만 연속 코드가 같은 문자열은 0으로 시작하는 것 하나, 그리고 1로 시작하는 것 하나로 항상 두 개씩 있다.

초기 문자열에서 나중 문자열로 문자열을 바꾸는데 필요한 최소한의 연산의 수를 계산하여라.

입력

입력의 첫 줄에는 두 정수 N (1 ≤ N ≤ 15)과 M (1 ≤ M ≤ N)이 주어진다. 둘째 줄에는 N개의 비트가 공백을 사이에 두고 주어진다. 이는 초기 문자열을 의미한다. 셋째 줄에는 바꿔야 하는 문자열의 연속 코드가 M개의 정수로 차례대로 주어진다.

바꿔야 하는 연속 코드의 각 숫자는 항상 1보다 크거나 같고, 그 코드를 모두 더하면 N이 되고, 주어진 비트 문자열이 항상 연속 코드가 나타내는 비트 문자열로 변환될 수 있음이 보장된다.

출력

필요한 최소한의 연산 수를 출력한다.

예제 입력 1

6 3
1 0 0 1 0 1
1 3 2

예제 출력 1

1

예제 입력 2

7 2
1 1 1 0 0 0 0
4 3

예제 출력 2

12

예제 입력 3

15 14
1 0 1 0 1 0 1 0 1 0 1 0 1 0 1
1 1 1 1 1 1 1 1 1 1 1 1 1 2

예제 출력 3

7

예제 입력 4

1 1
0
1

예제 출력 4

0

힌트

예제 입력 1에서 비트 문자열 "100101"은 연속 코드가 "1 3 2"인 비트 문자열로 재배열되어야 한다. 즉, "100011"이나 "011100" 둘 중 한 가지 문자열로 재배열되어야 하는 것이다. "011100"으로 문자열을 바꾸기 위해서는 4번의 연산이 필요하지만 "100011"로 바꾸기 위해서는 1번의 연산이면 충분하다. 따라서 이 경우에는 1이 답이다.

[{"problem_id":"10330","problem_lang":"0","title":"\ube44\ud2b8 \ubb38\uc790\uc5f4 \uc7ac\ubc30\uc5f4\ud558\uae30","description":"<p>\ube44\ud2b8 \ubb38\uc790\uc5f4\uc740 0, 1\ub85c\ub9cc \uc774\ub8e8\uc5b4\uc9c4 \ubb38\uc790\uc5f4\uc774\ub2e4. \uc5ec\ub7ec\ubd84\uc740 \ube44\ud2b8 \ubb38\uc790\uc5f4\uc744 \ud558\ub098 \ubc1b\uc544\uc11c&nbsp;\ud2b9\uc815\ud55c \ubb38\uc790\uc5f4\ub85c \ubc14\uafb8\uc5b4\uc57c \ud55c\ub2e4. \uc774\ub54c, \uc5ec\ub7ec\ubd84\uc774 \uc720\uc77c\ud558\uac8c \ud560 \uc218 \uc788\ub294 \uc5f0\uc0b0\uc740 \uc778\uc811\ud55c \ub450 \ube44\ud2b8\ub97c \ubc14\uafb8\ub294 \uac83\uc774\ub2e4.<\/p>\r\n\r\n<p>\ucd08\uae30 \ubb38\uc790\uc5f4\uc758 \uc0c1\ud0dc\ub294 \uadf8\ub0e5 \ube44\ud2b8\uc758 \uc21c\uc5f4\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \ud558\uc9c0\ub9cc \ubc14\uafb8\uace0\uc790 \ud558\ub294 \ubb38\uc790\uc5f4\uc740 &#39;\uc5f0\uc18d \ucf54\ub4dc&#39;\uc758 \ud615\ud0dc\ub85c \uc8fc\uc5b4\uc9c4\ub2e4. \uc5f0\uc18d \ucf54\ub4dc\ub780, \ubb38\uc790\uc5f4\uc5d0 \ub098\ud0c0\ub098\ub294 \uc5f0\uc18d\ub41c 0 \ub610\ub294 1\uc758 \uac1c\uc218\ub97c \ucc28\ub840\ub300\ub85c \ub298\uc5b4\ub193\uc740 \uc21c\uc5f4\uc774\ub2e4. \uc608\ub97c \ub4e4\uc5b4, &quot;011100&quot;\uc758 \uc5f0\uc18d \ucf54\ub4dc\ub294 &quot;1 3 2&quot;\uac00 \ub41c\ub2e4. \uc774\ub54c, \uc5ec\ub7ec\ubd84\ub3c4 \ub208\uce58\ucc58\uaca0\uc9c0\ub9cc \uc5f0\uc18d \ucf54\ub4dc\uac00 \uac19\uc740 \ubb38\uc790\uc5f4\uc740&nbsp;0\uc73c\ub85c \uc2dc\uc791\ud558\ub294 \uac83 \ud558\ub098, \uadf8\ub9ac\uace0 1\ub85c \uc2dc\uc791\ud558\ub294 \uac83 \ud558\ub098\ub85c&nbsp;\ud56d\uc0c1 \ub450 \uac1c\uc529 \uc788\ub2e4.<\/p>\r\n\r\n<p>\ucd08\uae30 \ubb38\uc790\uc5f4\uc5d0\uc11c \ub098\uc911 \ubb38\uc790\uc5f4\ub85c \ubb38\uc790\uc5f4\uc744&nbsp;\ubc14\uafb8\ub294\ub370 \ud544\uc694\ud55c \ucd5c\uc18c\ud55c\uc758 \uc5f0\uc0b0\uc758 \uc218\ub97c \uacc4\uc0b0\ud558\uc5ec\ub77c.<\/p>\r\n","input":"<p>\uc785\ub825\uc758 \uccab \uc904\uc5d0\ub294 \ub450 \uc815\uc218&nbsp;N (1 &le; N &le; 15)\uacfc&nbsp;M (1 &le; M &le; N)\uc774 \uc8fc\uc5b4\uc9c4\ub2e4. \ub458\uc9f8 \uc904\uc5d0\ub294 N\uac1c\uc758 \ube44\ud2b8\uac00 \uacf5\ubc31\uc744 \uc0ac\uc774\uc5d0 \ub450\uace0 \uc8fc\uc5b4\uc9c4\ub2e4. \uc774\ub294 \ucd08\uae30 \ubb38\uc790\uc5f4\uc744 \uc758\ubbf8\ud55c\ub2e4. \uc14b\uc9f8 \uc904\uc5d0\ub294 \ubc14\uafd4\uc57c \ud558\ub294 \ubb38\uc790\uc5f4\uc758 \uc5f0\uc18d \ucf54\ub4dc\uac00 M\uac1c\uc758 \uc815\uc218\ub85c \ucc28\ub840\ub300\ub85c \uc8fc\uc5b4\uc9c4\ub2e4.<\/p>\r\n\r\n<p>\ubc14\uafd4\uc57c \ud558\ub294 \uc5f0\uc18d \ucf54\ub4dc\uc758 \uac01 \uc22b\uc790\ub294 \ud56d\uc0c1 1\ubcf4\ub2e4 \ud06c\uac70\ub098 \uac19\uace0, \uadf8 \ucf54\ub4dc\ub97c \ubaa8\ub450 \ub354\ud558\uba74 N\uc774 \ub418\uace0, \uc8fc\uc5b4\uc9c4 \ube44\ud2b8 \ubb38\uc790\uc5f4\uc774 \ud56d\uc0c1 \uc5f0\uc18d \ucf54\ub4dc\uac00 \ub098\ud0c0\ub0b4\ub294 \ube44\ud2b8 \ubb38\uc790\uc5f4\ub85c \ubcc0\ud658\ub420 \uc218 \uc788\uc74c\uc774 \ubcf4\uc7a5\ub41c\ub2e4.<\/p>\r\n","output":"<p>\ud544\uc694\ud55c \ucd5c\uc18c\ud55c\uc758 \uc5f0\uc0b0 \uc218\ub97c \ucd9c\ub825\ud55c\ub2e4.<\/p>\r\n","hint":"<p>\uc608\uc81c \uc785\ub825 1\uc5d0\uc11c \ube44\ud2b8 \ubb38\uc790\uc5f4 &quot;100101&quot;\uc740 \uc5f0\uc18d \ucf54\ub4dc\uac00 &quot;1 3 2&quot;\uc778 \ube44\ud2b8 \ubb38\uc790\uc5f4\ub85c \uc7ac\ubc30\uc5f4\ub418\uc5b4\uc57c \ud55c\ub2e4. \uc989, &quot;100011&quot;\uc774\ub098 &quot;011100&quot; \ub458 \uc911 \ud55c \uac00\uc9c0 \ubb38\uc790\uc5f4\ub85c \uc7ac\ubc30\uc5f4\ub418\uc5b4\uc57c \ud558\ub294 \uac83\uc774\ub2e4. &quot;011100&quot;\uc73c\ub85c \ubb38\uc790\uc5f4\uc744 \ubc14\uafb8\uae30 \uc704\ud574\uc11c\ub294 4\ubc88\uc758 \uc5f0\uc0b0\uc774 \ud544\uc694\ud558\uc9c0\ub9cc &quot;100011&quot;\ub85c \ubc14\uafb8\uae30 \uc704\ud574\uc11c\ub294 1\ubc88\uc758 \uc5f0\uc0b0\uc774\uba74 \ucda9\ubd84\ud558\ub2e4. \ub530\ub77c\uc11c \uc774 \uacbd\uc6b0\uc5d0\ub294 1\uc774 \ub2f5\uc774\ub2e4.<\/p>\r\n","original":"0","problem_lang_code":"\ud55c\uad6d\uc5b4"},{"problem_id":"10330","problem_lang":"1","title":"Bit String Reordering","description":"<p>You have to reorder a given bit string as specified. The only operation allowed is swapping adjacent bit pairs. Please write a program that calculates the minimum number of swaps required.<\/p>\r\n\r\n<p>The initial bit string is simply represented by a sequence of bits, while the target is specified by a run-length code. The run-length code of a bit string is a sequence of the lengths of maximal consecutive sequences of zeros or ones in the bit string. For example, the run-length code of &ldquo;011100&rdquo; is &ldquo;1 3 2&rdquo;. Note that there are two different bit strings with the same run-length code, one starting with zero and the other starting with one. The target is either of these two.<\/p>\r\n\r\n<p>In Sample Input 1, bit string &ldquo;100101&rdquo; should be reordered so that its run-length code is &ldquo;1 3 2&rdquo;, which means either &ldquo;100011&rdquo; or &ldquo;011100&rdquo;. At least four swaps are required to obtain &ldquo;011100&rdquo;. On the other hand, only one swap is required to make &ldquo;100011&rdquo;. Thus, in this example, 1 is the answer.<\/p>\r\n","input":"<p>The input consists of a single test case. The test case is formatted as follows.<\/p>\r\n\r\n<pre>\r\nN M\r\nb<sub>1<\/sub> b<sub>2<\/sub> ... b<sub>N<\/sub>\r\np<sub>1<\/sub> p<sub>2<\/sub> ... p<sub>M<\/sub><\/pre>\r\n\r\n<p>The first line contains two integers N (1 &le; N &le; 15) and M (1 &le; M &le; N). The second line specifies the initial bit string by N integers. Each integer bi is either 0 or 1. The third line contains the run-length code, consisting of M integers. Integers p<sub>1<\/sub> through p<sub>M<\/sub> represent the lengths of consecutive sequences of zeros or ones in the bit string, from left to right. Here, 1 &le; p<sub>j<\/sub> for 1 &le; j &le; M and &Sigma;p<sub>j<\/sub> = N hold. It is guaranteed that the initial bit string can be reordered into a bit string with its run-length code p<sub>1<\/sub>, ... , p<sub>M<\/sub>.<\/p>\r\n","output":"<p>Output the minimum number of swaps required.<\/p>\r\n","hint":"","original":"1","problem_lang_code":"\uc601\uc5b4"}]

출처

ACM-ICPC > Regionals > Asia > Japan > Asia Regional Contest 2014 in Tokyo A번