mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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196 lines
18 KiB
JSON
196 lines
18 KiB
JSON
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"questionId": "2251",
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"title": "Number of Ways to Divide a Long Corridor",
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"content": "<p>Along a long library corridor, there is a line of seats and decorative plants. You are given a <strong>0-indexed</strong> string <code>corridor</code> of length <code>n</code> consisting of letters <code>'S'</code> and <code>'P'</code> where each <code>'S'</code> represents a seat and each <code>'P'</code> represents a plant.</p>\n\n<p>One room divider has <strong>already</strong> been installed to the left of index <code>0</code>, and <strong>another</strong> to the right of index <code>n - 1</code>. Additional room dividers can be installed. For each position between indices <code>i - 1</code> and <code>i</code> (<code>1 <= i <= n - 1</code>), at most one divider can be installed.</p>\n\n<p>Divide the corridor into non-overlapping sections, where each section has <strong>exactly two seats</strong> with any number of plants. There may be multiple ways to perform the division. Two ways are <strong>different</strong> if there is a position with a room divider installed in the first way but not in the second way.</p>\n\n<p>Return <em>the number of ways to divide the corridor</em>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>. If there is no way, return <code>0</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/04/1.png\" style=\"width: 410px; height: 199px;\" />\n<pre>\n<strong>Input:</strong> corridor = "SSPPSPS"\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> There are 3 different ways to divide the corridor.\nThe black bars in the above image indicate the two room dividers already installed.\nNote that in each of the ways, <strong>each</strong> section has exactly <strong>two</strong> seats.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/04/2.png\" style=\"width: 357px; height: 68px;\" />\n<pre>\n<strong>Input:</strong> corridor = "PPSPSP"\n<strong>Output:</strong> 1\n<strong>Explanation:</strong> There is only 1 way to divide the corridor, by not installing any additional dividers.\nInstalling any would create some section that does not have exactly two seats.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/12/3.png\" style=\"width: 115px; height: 68px;\" />\n<pre>\n<strong>Input:</strong> corridor = "S"\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> There is no way to divide the corridor because there will always be a section that does not have exactly two seats.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == corridor.length</code></li>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>corridor[i]</code> is either <code>'S'</code> or <code>'P'</code>.</li>\n</ul>\n",
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"Divide the corridor into segments. Each segment has two seats, starts precisely with one seat, and ends precisely with the other seat.",
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"How many dividers can you install between two adjacent segments? You must install precisely one. Otherwise, you would have created a section with not exactly two seats.",
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"If there are k plants between two adjacent segments, there are k + 1 positions (ways) you could install the divider you must install.",
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"The problem now becomes: Find the product of all possible positions between every two adjacent segments."
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