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leetcode-problemset/算法题(国外版)/painting-a-grid-with-three-different-colors.json
2022-03-27 18:52:06 +08:00

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JSON

{
"data": {
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"title": "Painting a Grid With Three Different Colors",
"titleSlug": "painting-a-grid-with-three-different-colors",
"content": "<p>You are given two integers <code>m</code> and <code>n</code>. Consider an <code>m x n</code> grid where each cell is initially white. You can paint each cell <strong>red</strong>, <strong>green</strong>, or <strong>blue</strong>. All cells <strong>must</strong> be painted.</p>\n\n<p>Return<em> the number of ways to color the grid with <strong>no two adjacent cells having the same color</strong></em>. Since the answer can be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/22/colorthegrid.png\" style=\"width: 200px; height: 50px;\" />\n<pre>\n<strong>Input:</strong> m = 1, n = 1\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The three possible colorings are shown in the image above.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/06/22/copy-of-colorthegrid.png\" style=\"width: 321px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> m = 1, n = 2\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The six possible colorings are shown in the image above.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> m = 5, n = 5\n<strong>Output:</strong> 580986\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= m &lt;= 5</code></li>\n\t<li><code>1 &lt;= n &lt;= 1000</code></li>\n</ul>\n",
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"hints": [
"Represent each colored column by a bitmask based on each cell color.",
"Use bitmasks DP with state (currentCell, prevColumn)."
],
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Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. 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