"content":"<p>You are given a <strong>0-indexed</strong> binary string <code>s</code> which represents a sequence of train cars. <code>s[i] = '0'</code> denotes that the <code>i<sup>th</sup></code> car does <strong>not</strong> contain illegal goods and <code>s[i] = '1'</code> denotes that the <code>i<sup>th</sup></code> car does contain illegal goods.</p>\n\n<p>As the train conductor, you would like to get rid of all the cars containing illegal goods. You can do any of the following three operations <strong>any</strong> number of times:</p>\n\n<ol>\n\t<li>Remove a train car from the <strong>left</strong> end (i.e., remove <code>s[0]</code>) which takes 1 unit of time.</li>\n\t<li>Remove a train car from the <strong>right</strong> end (i.e., remove <code>s[s.length - 1]</code>) which takes 1 unit of time.</li>\n\t<li>Remove a train car from <strong>anywhere</strong> in the sequence which takes 2 units of time.</li>\n</ol>\n\n<p>Return <em>the <strong>minimum</strong> time to remove all the cars containing illegal goods</em>.</p>\n\n<p>Note that an empty sequence of cars is considered to have no cars containing illegal goods.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = "<strong><u>11</u></strong>00<strong><u>1</u></strong>0<strong><u>1</u></strong>"\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> \nOne way to remove all the cars containing illegal goods from the sequence is to\n- remove a car from the left end 2 times. Time taken is 2 * 1 = 2.\n- remove a car from the right end. Time taken is 1.\n- remove the car containing illegal goods found in the middle. Time taken is 2.\nThis obtains a total time of 2 + 1 + 2 = 5. \n\nAn alternative way is to\n- remove a car from the left end 2 times. Time taken is 2 * 1 = 2.\n- remove a car from the right end 3 times. Time taken is 3 * 1 = 3.\nThis also obtains a total time of 2 + 3 = 5.\n\n5 is the minimum time taken to remove all the cars containing illegal goods. \nThere are no other ways to remove them with less time.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = "00<strong><u>1</u></strong>0"\n<strong>Output:</strong> 2\n<strong>Explanation:</strong>\nOne way to remove all the cars containing illegal goods from the sequence is to\n- remove a car from the left end 3 times. Time taken is 3 * 1 = 3.\nThis obtains a total time of 3.\n\nAnother way to remove all the cars containing illegal goods from the sequence is to\n- remove the car containing illegal goods found in the middle. Time taken is 2.\nThis obtains a total time of 2.\n\nAnother way to remove all the cars containing illegal goods from the sequence is to \n- remove a car from the right end 2 times. Time taken is 2 * 1 = 2. \nThis obtains a total time of 2.\n\n2 is the minimum time taken to remove all the cars containing illegal goods. \nThere are no other ways to remove them with less time.</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= s.length <= 2 * 10<sup>5</sup></code></li>\n\t<li><code>s[i]</code> is either <code>'0'</code> or <code>'1'</code>.</li>\n</ul>\n",
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"Build an array withoutFirst where withoutFirst[i] stores the minimum time to remove all the cars containing illegal goods from the ‘suffix’ of the sequence starting from the ith car without using any type 1 operations.",
"Next, build an array onlyFirst where onlyFirst[i] stores the minimum time to remove all the cars containing illegal goods from the ‘prefix’ of the sequence ending on the ith car using only type 1 operations.",
"Finally, we can compare the best way to split the operations amongst these two types by finding the minimum time across all onlyFirst[i] + withoutFirst[i + 1]."
"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:
