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65 lines
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65 lines
3.1 KiB
HTML
<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>
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<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>
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<ol>
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<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>
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<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>
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<li>Remove a train car from <strong>anywhere</strong> in the sequence which takes 2 units of time.</li>
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</ol>
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<p>Return <em>the <strong>minimum</strong> time to remove all the cars containing illegal goods</em>.</p>
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<p>Note that an empty sequence of cars is considered to have no cars containing illegal goods.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> s = "<strong><u>11</u></strong>00<strong><u>1</u></strong>0<strong><u>1</u></strong>"
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<strong>Output:</strong> 5
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<strong>Explanation:</strong>
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One way to remove all the cars containing illegal goods from the sequence is to
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- remove a car from the left end 2 times. Time taken is 2 * 1 = 2.
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- remove a car from the right end. Time taken is 1.
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- remove the car containing illegal goods found in the middle. Time taken is 2.
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This obtains a total time of 2 + 1 + 2 = 5.
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An alternative way is to
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- remove a car from the left end 2 times. Time taken is 2 * 1 = 2.
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- remove a car from the right end 3 times. Time taken is 3 * 1 = 3.
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This also obtains a total time of 2 + 3 = 5.
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5 is the minimum time taken to remove all the cars containing illegal goods.
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There are no other ways to remove them with less time.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> s = "00<strong><u>1</u></strong>0"
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<strong>Output:</strong> 2
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<strong>Explanation:</strong>
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One way to remove all the cars containing illegal goods from the sequence is to
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- remove a car from the left end 3 times. Time taken is 3 * 1 = 3.
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This obtains a total time of 3.
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Another way to remove all the cars containing illegal goods from the sequence is to
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- remove the car containing illegal goods found in the middle. Time taken is 2.
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This obtains a total time of 2.
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Another way to remove all the cars containing illegal goods from the sequence is to
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- remove a car from the right end 2 times. Time taken is 2 * 1 = 2.
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This obtains a total time of 2.
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2 is the minimum time taken to remove all the cars containing illegal goods.
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There are no other ways to remove them with less time.</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= s.length <= 2 * 10<sup>5</sup></code></li>
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<li><code>s[i]</code> is either <code>'0'</code> or <code>'1'</code>.</li>
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</ul>
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