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44 lines
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44 lines
2.0 KiB
HTML
<p>The chess knight has a <strong>unique movement</strong>, it may move two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of an <strong>L</strong>). The possible movements of chess knight are shown in this diagaram:</p>
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<p>A chess knight can move as indicated in the chess diagram below:</p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/chess.jpg" style="width: 402px; height: 402px;" />
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<p>We have a chess knight and a phone pad as shown below, the knight <strong>can only stand on a numeric cell</strong> (i.e. blue cell).</p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/phone.jpg" style="width: 242px; height: 322px;" />
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<p>Given an integer <code>n</code>, return how many distinct phone numbers of length <code>n</code> we can dial.</p>
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<p>You are allowed to place the knight <strong>on any numeric cell</strong> initially and then you should perform <code>n - 1</code> jumps to dial a number of length <code>n</code>. All jumps should be <strong>valid</strong> knight jumps.</p>
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<p>As the answer may be very large, <strong>return the answer modulo</strong> <code>10<sup>9</sup> + 7</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 = 1
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<strong>Output:</strong> 10
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<strong>Explanation:</strong> We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.
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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 = 2
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<strong>Output:</strong> 20
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<strong>Explanation:</strong> All the valid number we can dial are [04, 06, 16, 18, 27, 29, 34, 38, 40, 43, 49, 60, 61, 67, 72, 76, 81, 83, 92, 94]
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> n = 3131
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<strong>Output:</strong> 136006598
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<strong>Explanation:</strong> Please take care of the mod.
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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 <= 5000</code></li>
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</ul>
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