leetcode-problemset/leetcode-cn/originData/minimum-time-to-remove-all-cars-containing-illegal-goods.json

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            "categoryTitle": "Algorithms",
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            "title": "Minimum Time to Remove All Cars Containing Illegal Goods",
            "titleSlug": "minimum-time-to-remove-all-cars-containing-illegal-goods",
            "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] = &#39;0&#39;</code> denotes that the <code>i<sup>th</sup></code> car does <strong>not</strong> contain illegal goods and <code>s[i] = &#39;1&#39;</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>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> s = &quot;<strong><u>11</u></strong>00<strong><u>1</u></strong>0<strong><u>1</u></strong>&quot;\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 = &quot;00<strong><u>1</u></strong>0&quot;\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>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 2 * 10<sup>5</sup></code></li>\n\t<li><code>s[i]</code> is either <code>&#39;0&#39;</code> or <code>&#39;1&#39;</code>.</li>\n</ul>\n",
            "translatedTitle": "移除所有载有违禁货物车厢所需的最少时间",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的二进制字符串 <code>s</code> ，表示一个列车车厢序列。<code>s[i] = '0'</code> 表示第 <code>i</code> 节车厢 <strong>不</strong> 含违禁货物，而 <code>s[i] = '1'</code> 表示第 <code>i</code> 节车厢含违禁货物。</p>\n\n<p>作为列车长，你需要清理掉所有载有违禁货物的车厢。你可以不限次数执行下述三种操作中的任意一个：</p>\n\n<ol>\n\t<li>从列车 <strong>左</strong> 端移除一节车厢（即移除 <code>s[0]</code>），用去 1 单位时间。</li>\n\t<li>从列车 <strong>右</strong> 端移除一节车厢（即移除 <code>s[s.length - 1]</code>），用去 1 单位时间。</li>\n\t<li>从列车车厢序列的 <strong>任意位置</strong> 移除一节车厢，用去 2 单位时间。</li>\n</ol>\n\n<p>返回移除所有载有违禁货物车厢所需要的 <strong>最少</strong> 单位时间数。</p>\n\n<p>注意，空的列车车厢序列视为没有车厢含违禁货物。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>s = \"<em><strong>11</strong></em>00<em><strong>1</strong></em>0<em><strong>1</strong></em>\"\n<strong>输出：</strong>5\n<strong>解释：</strong>\n一种从序列中移除所有载有违禁货物的车厢的方法是：\n- 从左端移除一节车厢 2 次。所用时间是 2 * 1 = 2 。\n- 从右端移除一节车厢 1 次。所用时间是 1 。\n- 移除序列中间位置载有违禁货物的车厢。所用时间是 2 。\n总时间是 2 + 1 + 2 = 5 。\n\n一种替代方法是：\n- 从左端移除一节车厢 2 次。所用时间是 2 * 1 = 2 。\n- 从右端移除一节车厢 3 次。所用时间是 3 * 1 = 3 。\n总时间也是 2 + 3 = 5 。\n\n5 是移除所有载有违禁货物的车厢所需要的最少单位时间数。\n没有其他方法能够用更少的时间移除这些车厢。</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>s = \"00<em><strong>1</strong></em>0\"\n<strong>输出：</strong>2\n<strong>解释：</strong>\n一种从序列中移除所有载有违禁货物的车厢的方法是：\n- 从左端移除一节车厢 3 次。所用时间是 3 * 1 = 3 。\n总时间是 3.\n\n另一种从序列中移除所有载有违禁货物的车厢的方法是：\n- 移除序列中间位置载有违禁货物的车厢。所用时间是 2 。\n总时间是 2.\n\n另一种从序列中移除所有载有违禁货物的车厢的方法是：\n- 从右端移除一节车厢 2 次。所用时间是 2 * 1 = 2 。\n总时间是 2.\n\n2 是移除所有载有违禁货物的车厢所需要的最少单位时间数。\n没有其他方法能够用更少的时间移除这些车厢。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= s.length &lt;= 2 * 10<sup>5</sup></code></li>\n\t<li><code>s[i]</code> 为 <code>'0'</code> 或 <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]."
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