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leetcode-problemset/leetcode/originData/count-number-of-ways-to-place-houses.json
2022-06-29 22:54:34 +08:00

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{
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"title": "Count Number of Ways to Place Houses",
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"content": "<p>There is a street with <code>n * 2</code> <strong>plots</strong>, where there are <code>n</code> plots on each side of the street. The plots on each side are numbered from <code>1</code> to <code>n</code>. On each plot, a house can be placed.</p>\n\n<p>Return <em>the number of ways houses can be placed such that no two houses are adjacent to each other on the same side of the street</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Note that if a house is placed on the <code>i<sup>th</sup></code> plot on one side of the street, a house can also be placed on the <code>i<sup>th</sup></code> plot on the other side of the street.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> \nPossible arrangements:\n1. All plots are empty.\n2. A house is placed on one side of the street.\n3. A house is placed on the other side of the street.\n4. Two houses are placed, one on each side of the street.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/12/arrangements.png\" style=\"width: 500px; height: 500px;\" />\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 9\n<strong>Explanation:</strong> The 9 possible arrangements are shown in the diagram above.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n &lt;= 10<sup>4</sup></code></li>\n</ul>\n",
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"hints": [
"Try coming up with a DP solution for one side of the street.",
"The DP for one side of the street will bear resemblance to the Fibonacci sequence.",
"The number of different arrangements on both side of the street is the same."
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