leetcode-problemset/leetcode/originData/number-of-ways-to-paint-n-3-grid.json

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            "title": "Number of Ways to Paint N × 3 Grid",
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            "content": "<p>You have a <code>grid</code> of size <code>n x 3</code> and you want to paint each cell of the grid with exactly one of the three colors: <strong>Red</strong>, <strong>Yellow,</strong> or <strong>Green</strong> while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).</p>\n\n<p>Given <code>n</code> the number of rows of the grid, return <em>the number of ways</em> you can paint this <code>grid</code>. As the answer may grow large, the answer <strong>must be</strong> computed modulo <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/03/26/e1.png\" style=\"width: 400px; height: 257px;\" />\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> There are 12 possible way to paint the grid as shown.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 5000\n<strong>Output:</strong> 30228214\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == grid.length</code></li>\n\t<li><code>1 &lt;= n &lt;= 5000</code></li>\n</ul>\n",
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            "hints": [
                "We will use Dynamic programming approach. we will try all possible configuration.",
                "Let dp[idx][prev1col][prev2col][prev3col] be the number of ways to color the rows of the grid from idx to n-1 keeping in mind that the previous row (idx - 1) has colors prev1col, prev2col and prev3col. Build the dp array to get the answer."
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