문제
어떤 수열이 다른 수열의 부분 수열이라는 것은 다음을 의미합니다.
- 해당 수열의 원소들이 다른 수열 내에서 순서대로 등장합니다.
- 예를 들어, $\{1,1,5\}$는 $\{3,\underline{\color{blue} 1} ,4,\underline{\color{blue} 1} ,\underline{\color{blue} 5} ,9\}$의 부분 수열이지만, $\{1,5,1\}$의 부분 수열은 아닙니다.
또한, 어떤 수열이 다른 수열보다 사전 순으로 나중이라는 것은 다음을 의미합니다.
- 두 수열 중 첫 번째 수가 큰 쪽은 사전 순으로 나중입니다.
- 두 수열의 첫 번째 수가 같다면, 첫 번째 수를 빼고 두 수열을 다시 비교했을 때 사전 순으로 나중인 쪽이 사전 순으로 나중입니다.
- 길이가 0ドル$인 수열과 다른 수열을 비교하면, 다른 수열이 사전 순으로 나중입니다.
양의 정수로 이루어진 길이가 $N$인 수열 $\{A_1,\cdots ,A_N\}$이 주어집니다. 마찬가지로 양의 정수로 이루어진 길이가 $M$인 수열 $\{B_1,\cdots ,B_M\}$이 주어집니다.
수열 $A$와 수열 $B$가 공통으로 갖는 부분 수열들 중 사전 순으로 가장 나중인 것을 구하세요.
출력
$A$와 $B$의 공통 부분 수열 중 사전 순으로 가장 나중인 수열의 크기 $K$를 출력하세요.
$K \ne 0$이라면, 다음 줄에 $K$개의 수를 공백으로 구분해 출력하세요. $i$번째 수는 $A$와 $B$의 공통 부분 수열 중 사전 순으로 가장 나중인 수열의 $i$번째 수입니다.
다음 수열들은 모두 $A$와 $B$의 공통 부분 수열입니다.
$$\begin{array}{cccc}\{\} & \{1\} & \{1,3\} & \{1,7\} \\\{1,7,3\} & \{3\} & \{7\} & \{7,3\} \\\end{array}$$
이 중 사전 순으로 가장 나중인 수열은 $\{7,3\}$입니다.
[{"problem_id":"30805","problem_lang":"0","title":"\uc0ac\uc804 \uc21c \ucd5c\ub300 \uacf5\ud1b5 \ubd80\ubd84 \uc218\uc5f4","description":"<p>\uc5b4\ub5a4 \uc218\uc5f4\uc774 \ub2e4\ub978 \uc218\uc5f4\uc758 \ubd80\ubd84 \uc218\uc5f4\uc774\ub77c\ub294 \uac83\uc740 \ub2e4\uc74c\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ud574\ub2f9 \uc218\uc5f4\uc758 \uc6d0\uc18c\ub4e4\uc774 \ub2e4\ub978 \uc218\uc5f4 \ub0b4\uc5d0\uc11c \uc21c\uc11c\ub300\ub85c \ub4f1\uc7a5\ud569\ub2c8\ub2e4.<\/li>\r\n\t<li>\uc608\ub97c \ub4e4\uc5b4, $\\{1,1,5\\}$\ub294 $\\{3,\\underline{\\color{blue} 1} ,4,\\underline{\\color{blue} 1} ,\\underline{\\color{blue} 5} ,9\\}$\uc758 \ubd80\ubd84 \uc218\uc5f4\uc774\uc9c0\ub9cc, $\\{1,5,1\\}$\uc758 \ubd80\ubd84 \uc218\uc5f4\uc740 \uc544\ub2d9\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\ub610\ud55c, \uc5b4\ub5a4 \uc218\uc5f4\uc774 \ub2e4\ub978 \uc218\uc5f4\ubcf4\ub2e4 \uc0ac\uc804 \uc21c\uc73c\ub85c \ub098\uc911\uc774\ub77c\ub294 \uac83\uc740 \ub2e4\uc74c\uc744 \uc758\ubbf8\ud569\ub2c8\ub2e4.<\/p>\r\n\r\n<ul>\r\n\t<li>\ub450 \uc218\uc5f4 \uc911 \uccab \ubc88\uc9f8 \uc218\uac00 \ud070 \ucabd\uc740 \uc0ac\uc804 \uc21c\uc73c\ub85c \ub098\uc911\uc785\ub2c8\ub2e4.<\/li>\r\n\t<li>\ub450 \uc218\uc5f4\uc758 \uccab \ubc88\uc9f8 \uc218\uac00 \uac19\ub2e4\uba74, \uccab \ubc88\uc9f8 \uc218\ub97c \ube7c\uace0 \ub450 \uc218\uc5f4\uc744 \ub2e4\uc2dc \ube44\uad50\ud588\uc744 \ub54c \uc0ac\uc804 \uc21c\uc73c\ub85c \ub098\uc911\uc778 \ucabd\uc774 \uc0ac\uc804 \uc21c\uc73c\ub85c \ub098\uc911\uc785\ub2c8\ub2e4.<\/li>\r\n\t<li>\uae38\uc774\uac00 $0$\uc778 \uc218\uc5f4\uacfc \ub2e4\ub978 \uc218\uc5f4\uc744 \ube44\uad50\ud558\uba74, \ub2e4\ub978 \uc218\uc5f4\uc774 \uc0ac\uc804 \uc21c\uc73c\ub85c \ub098\uc911\uc785\ub2c8\ub2e4.<\/li>\r\n<\/ul>\r\n\r\n<p>\uc591\uc758 \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uae38\uc774\uac00 $N$\uc778 \uc218\uc5f4 $\\{A_1,\\cdots ,A_N\\}$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. \ub9c8\ucc2c\uac00\uc9c0\ub85c \uc591\uc758 \uc815\uc218\ub85c \uc774\ub8e8\uc5b4\uc9c4 \uae38\uc774\uac00 $M$\uc778 \uc218\uc5f4 $\\{B_1,\\cdots ,B_M\\}$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4.<\/p>\r\n\r\n<p>\uc218\uc5f4 $A$\uc640 \uc218\uc5f4 $B$\uac00 \uacf5\ud1b5\uc73c\ub85c \uac16\ub294 \ubd80\ubd84 \uc218\uc5f4\ub4e4 \uc911 \uc0ac\uc804 \uc21c\uc73c\ub85c \uac00\uc7a5 \ub098\uc911\uc778 \uac83\uc744 \uad6c\ud558\uc138\uc694.<\/p>\r\n","input":"<p>\uccab \uc904\uc5d0 \uc218\uc5f4 $A$\uc758 \uae38\uc774 $N$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(1 \\le N \\le 100)$<\/p>\r\n\r\n<p>\ub458\uc9f8 \uc904\uc5d0 $N$\uac1c\uc758 \uc591\uc758 \uc815\uc218 $A_1,A_2,\\cdots,A_N$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(1 \\le A_i \\le 100)$<\/p>\r\n\r\n<p>\uc14b\uc9f8 \uc904\uc5d0 \uc218\uc5f4 $B$\uc758 \uae38\uc774 $M$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(1 \\le M \\le 100)$<\/p>\r\n\r\n<p>\ub137\uc9f8 \uc904\uc5d0 $M$\uac1c\uc758 \uc591\uc758 \uc815\uc218 $B_1,B_2,\\cdots,B_M$\uc774 \uc8fc\uc5b4\uc9d1\ub2c8\ub2e4. $(1 \\le B_i \\le 100)$<\/p>\r\n","output":"<p>$A$\uc640 $B$\uc758 \uacf5\ud1b5 \ubd80\ubd84 \uc218\uc5f4 \uc911 \uc0ac\uc804 \uc21c\uc73c\ub85c \uac00\uc7a5 \ub098\uc911\uc778 \uc218\uc5f4\uc758 \ud06c\uae30 $K$\ub97c \ucd9c\ub825\ud558\uc138\uc694.<\/p>\r\n\r\n<p>$K \\ne 0$\uc774\ub77c\uba74, \ub2e4\uc74c \uc904\uc5d0 $K$\uac1c\uc758 \uc218\ub97c \uacf5\ubc31\uc73c\ub85c \uad6c\ubd84\ud574 \ucd9c\ub825\ud558\uc138\uc694. $i$\ubc88\uc9f8 \uc218\ub294 $A$\uc640 $B$\uc758 \uacf5\ud1b5 \ubd80\ubd84 \uc218\uc5f4 \uc911 \uc0ac\uc804 \uc21c\uc73c\ub85c \uac00\uc7a5 \ub098\uc911\uc778 \uc218\uc5f4\uc758 $i$\ubc88\uc9f8 \uc218\uc785\ub2c8\ub2e4.<\/p>\r\n","hint":"","original":"1","html_title":"0","problem_lang_tcode":"Korean","sample_explain_1":"<p>\ub2e4\uc74c \uc218\uc5f4\ub4e4\uc740 \ubaa8\ub450 $A$\uc640 $B$\uc758 \uacf5\ud1b5 \ubd80\ubd84 \uc218\uc5f4\uc785\ub2c8\ub2e4.<\/p>\r\n\r\n<p>$$\\begin{array}{cccc}\\{\\} &amp; \\{1\\} &amp; \\{1,3\\} &amp; \\{1,7\\} \\\\\\{1,7,3\\} &amp; \\{3\\} &amp; \\{7\\} &amp; \\{7,3\\} \\\\\\end{array}$$<\/p>\r\n\r\n<p>\uc774 \uc911 \uc0ac\uc804 \uc21c\uc73c\ub85c \uac00\uc7a5 \ub098\uc911\uc778 \uc218\uc5f4\uc740 $\\{7,3\\}$\uc785\ub2c8\ub2e4.<\/p>\r\n"},{"problem_id":"30805","problem_lang":"1","title":"Lexicographically Largest Common Subsequence","description":"<p>If a sequence is a subsequence of another sequence, it meets the following conditions.<\/p>\r\n\r\n<ul>\r\n\t<li>The elements of the sequence appears in the other sequence in order.<\/li>\r\n\t<li>For example, $\\{1,1,5\\}$ is a subsequence of $\\{3,\\underline{\\color{blue} 1} ,4,\\underline{\\color{blue} 1} ,\\underline{\\color{blue} 5} ,9\\}$ but it is not a subsequence of $\\{1,5,1\\}$.<\/li>\r\n<\/ul>\r\n\r\n<p>In addition, if a sequence comes later in lexicographical order compared to another sequence, it meets the following conditions.<\/p>\r\n\r\n<ul>\r\n\t<li>For two sequences, the sequence&nbsp;whose&nbsp;first element is larger comes later in lexicographical order.<\/li>\r\n\t<li>If their first elements are equal, remove the first element&nbsp;from both sequences and compare them again. The one which comes later in lexicographical order after the removal&nbsp;comes later in lexicographical order.<\/li>\r\n\t<li>If a sequence of length $0$ is compared to another sequence, the other sequence always comes later in lexicographical order.<\/li>\r\n<\/ul>\r\n\r\n<p>You are given a sequence of length $N$ consisting of positive integers $\\{A_1,\\cdots ,A_N\\}$. You are also given another sequence of length $M$ consisting of positive integers $\\{B_1,\\cdots ,B_M\\}$.<\/p>\r\n\r\n<p>Find the common subsequence of $A$ and $B$ which comes last in lexicographical order.<\/p>\r\n","input":"<p>The first line of input contains a single integer $N$, denoting the length of sequence $A$. $(1 \\le N \\le 100)$<\/p>\r\n\r\n<p>The second line of input contains $N$ space-separated positive integers $A_1,A_2,\\cdots,A_N$. $(1 \\le A_i \\le 100)$<\/p>\r\n\r\n<p>The third line of input contains a single integer $M$, denoting the length of sequence $B$. $(1 \\le M \\le 100)$<\/p>\r\n\r\n<p>The fourth line of input contains $M$ space-separated positive integers $B_1,B_2,\\cdots,B_M$. $(1 \\le B_i \\le 100)$<\/p>\r\n","output":"<p>Print the length $K$ of the common subsequence of $A$ and $B$ which comes last in lexicographical order.&nbsp;<\/p>\r\n\r\n<p>If $K \\ne 0$, print $K$ space-separated integers in the next line. The $i$-th of the integers should be the $i$-th element of the common subsequence of $A$ and $B$ which comes last in lexicographical order.<\/p>\r\n","hint":"","original":"0","html_title":"0","problem_lang_tcode":"English","sample_explain_1":"<p>The following are all common subsequences of $A$ and $B$.<\/p>\r\n\r\n<p>$$ \\begin{array}{cccc} \\{\\} &amp; \\{1\\} &amp; \\{1,3\\} &amp; \\{1,7\\} \\\\ \\{1,7,3\\} &amp; \\{3\\} &amp; \\{7\\} &amp; \\{7,3\\} \\\\ \\end{array} $$<\/p>\r\n\r\n<p>The one which comes last in lexicographical order among them is $\\{7,3\\}$.<\/p>\r\n"}]