Painting a Grid With Three Different Colors
<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>

<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>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1931.Painting%20a%20Grid%20With%20Three%20Different%20Colors/images/colorthegrid.png" style="width: 200px; height: 50px;" />
<pre>
<strong>Input:</strong> m = 1, n = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> The three possible colorings are shown in the image above.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/1900-1999/1931.Painting%20a%20Grid%20With%20Three%20Different%20Colors/images/copy-of-colorthegrid.png" style="width: 321px; height: 121px;" />
<pre>
<strong>Input:</strong> m = 1, n = 2
<strong>Output:</strong> 6
<strong>Explanation:</strong> The six possible colorings are shown in the image above.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> m = 5, n = 5
<strong>Output:</strong> 580986
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= m &lt;= 5</code></li>
	<li><code>1 &lt;= n &lt;= 1000</code></li>
</ul>
Dynamic Programming
func colorTheGrid(m int, n int) (ans int) {
	f1 := func(x int) bool {
		last := -1
		for i := 0; i < m; i++ {
			if x%3 == last {
				return false
			}
			last = x % 3
			x /= 3
		}
		return true
	}
	f2 := func(x, y int) bool {
		for i := 0; i < m; i++ {
			if x%3 == y%3 {
				return false
			}
			x /= 3
			y /= 3
		}
		return true
	}
	mx := int(math.Pow(3, float64(m)))
	valid := map[int]bool{}
	f := make([]int, mx)
	for i := 0; i < mx; i++ {
		if f1(i) {
			valid[i] = true
			f[i] = 1
		}
	}
	d := map[int][]int{}
	for i := range valid {
		for j := range valid {
			if f2(i, j) {
				d[i] = append(d[i], j)
			}
		}
	}
	const mod int = 1e9 + 7
	for k := 1; k < n; k++ {
		g := make([]int, mx)
		for i := range valid {
			for _, j := range d[i] {
				g[i] = (g[i] + f[j]) % mod
			}
		}
		f = g
	}
	for _, x := range f {
		ans = (ans + x) % mod
	}
	return
}