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47 lines
1.8 KiB
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47 lines
1.8 KiB
HTML
<p>Given two positive integers <code>n</code> and <code>k</code>, the binary string <code>S<sub>n</sub></code> is formed as follows:</p>
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<ul>
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<li><code>S<sub>1</sub> = "0"</code></li>
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<li><code>S<sub>i</sub> = S<sub>i - 1</sub> + "1" + reverse(invert(S<sub>i - 1</sub>))</code> for <code>i > 1</code></li>
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</ul>
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<p>Where <code>+</code> denotes the concatenation operation, <code>reverse(x)</code> returns the reversed string <code>x</code>, and <code>invert(x)</code> inverts all the bits in <code>x</code> (<code>0</code> changes to <code>1</code> and <code>1</code> changes to <code>0</code>).</p>
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<p>For example, the first four strings in the above sequence are:</p>
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<ul>
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<li><code>S<sub>1 </sub>= "0"</code></li>
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<li><code>S<sub>2 </sub>= "0<strong>1</strong>1"</code></li>
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<li><code>S<sub>3 </sub>= "011<strong>1</strong>001"</code></li>
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<li><code>S<sub>4</sub> = "0111001<strong>1</strong>0110001"</code></li>
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</ul>
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<p>Return <em>the</em> <code>k<sup>th</sup></code> <em>bit</em> <em>in</em> <code>S<sub>n</sub></code>. It is guaranteed that <code>k</code> is valid for the given <code>n</code>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> n = 3, k = 1
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<strong>Output:</strong> "0"
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<strong>Explanation:</strong> S<sub>3</sub> is "<strong><u>0</u></strong>111001".
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The 1<sup>st</sup> bit is "0".
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</pre>
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<p><strong>Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> n = 4, k = 11
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<strong>Output:</strong> "1"
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<strong>Explanation:</strong> S<sub>4</sub> is "0111001101<strong><u>1</u></strong>0001".
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The 11<sup>th</sup> bit is "1".
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</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 <= n <= 20</code></li>
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<li><code>1 <= k <= 2<sup>n</sup> - 1</code></li>
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</ul>
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