"content":"<p>There is a safe protected by a password. The password is a sequence of <code>n</code> digits where each digit can be in the range <code>[0, k - 1]</code>.</p>\n\n<p>The safe has a peculiar way of checking the password. When you enter in a sequence, it checks the <strong>most recent </strong><code>n</code><strong> digits</strong> that were entered each time you type a digit.</p>\n\n<ul>\n\t<li>For example, the correct password is <code>"345"</code> and you enter in <code>"012345"</code>:\n\n\t<ul>\n\t\t<li>After typing <code>0</code>, the most recent <code>3</code> digits is <code>"0"</code>, which is incorrect.</li>\n\t\t<li>After typing <code>1</code>, the most recent <code>3</code> digits is <code>"01"</code>, which is incorrect.</li>\n\t\t<li>After typing <code>2</code>, the most recent <code>3</code> digits is <code>"012"</code>, which is incorrect.</li>\n\t\t<li>After typing <code>3</code>, the most recent <code>3</code> digits is <code>"123"</code>, which is incorrect.</li>\n\t\t<li>After typing <code>4</code>, the most recent <code>3</code> digits is <code>"234"</code>, which is incorrect.</li>\n\t\t<li>After typing <code>5</code>, the most recent <code>3</code> digits is <code>"345"</code>, which is correct and the safe unlocks.</li>\n\t</ul>\n\t</li>\n</ul>\n\n<p>Return <em>any string of <strong>minimum length</strong> that will unlock the safe <strong>at some point</strong> of entering it</em>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1, k = 2\n<strong>Output:</strong> "10"\n<strong>Explanation:</strong> The password is a single digit, so enter each digit. "01" would also unlock the safe.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2, k = 2\n<strong>Output:</strong> "01100"\n<strong>Explanation:</strong> For each possible password:\n- "00" is typed in starting from the 4<sup>th</sup> digit.\n- "01" is typed in starting from the 1<sup>st</sup> digit.\n- "10" is typed in starting from the 3<sup>rd</sup> digit.\n- "11" is typed in starting from the 2<sup>nd</sup> digit.\nThus "01100" will unlock the safe. "01100", "10011", and "11001" would also unlock the safe.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 4</code></li>\n\t<li><code>1 <= k <= 10</code></li>\n\t<li><code>1 <= k<sup>n</sup> <= 4096</code></li>\n</ul>\n",
"We can think of this problem as the problem of finding an Euler path (a path visiting every edge exactly once) on the following graph: there are $$k^{n-1}$$ nodes with each node having $$k$$ edges. It turns out this graph always has an Eulerian circuit (path starting where it ends.)\r\n\r\nWe should visit each node in \"post-order\" so as to not get stuck in the graph prematurely."
"envInfo":"{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code> OpenJDK 17 </code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"c\": [\"C\", \"<p>Compiled with <code>gcc 8.2</code> using the gnu99 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level one optimization (<code>-O1</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n\\r\\n<p>For hash table operations, you may use <a href=\\\"https://troydhanson.github.io/uthash/\\\" target=\\\"_blank\\\">uthash</a>. \\\"uthash.h\\\" is included by default. Below are some examples:</p>\\r\\n\\r\\n<p><b>1. Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https:
