Number of Beautiful Partitions
<p>You are given a string <code>s</code> that consists of the digits <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code> and two integers <code>k</code> and <code>minLength</code>.</p>

<p>A partition of <code>s</code> is called <strong>beautiful</strong> if:</p>

<ul>
	<li><code>s</code> is partitioned into <code>k</code> non-intersecting substrings.</li>
	<li>Each substring has a length of <strong>at least</strong> <code>minLength</code>.</li>
	<li>Each substring starts with a <strong>prime</strong> digit and ends with a <strong>non-prime</strong> digit. Prime digits are <code>&#39;2&#39;</code>, <code>&#39;3&#39;</code>, <code>&#39;5&#39;</code>, and <code>&#39;7&#39;</code>, and the rest of the digits are non-prime.</li>
</ul>

<p>Return<em> the number of <strong>beautiful</strong> partitions of </em><code>s</code>. Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters within a string.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;23542185131&quot;, k = 3, minLength = 2
<strong>Output:</strong> 3
<strong>Explanation:</strong> There exists three ways to create a beautiful partition:
&quot;2354 | 218 | 5131&quot;
&quot;2354 | 21851 | 31&quot;
&quot;2354218 | 51 | 31&quot;
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;23542185131&quot;, k = 3, minLength = 3
<strong>Output:</strong> 1
<strong>Explanation:</strong> There exists one way to create a beautiful partition: &quot;2354 | 218 | 5131&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;3312958&quot;, k = 3, minLength = 1
<strong>Output:</strong> 1
<strong>Explanation:</strong> There exists one way to create a beautiful partition: &quot;331 | 29 | 58&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= k, minLength &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists of the digits <code>&#39;1&#39;</code> to <code>&#39;9&#39;</code>.</li>
</ul>
String; Dynamic Programming
func beautifulPartitions(s string, k int, minLength int) int {
	prime := func(c byte) bool {
		return c == '2' || c == '3' || c == '5' || c == '7'
	}
	n := len(s)
	if !prime(s[0]) || prime(s[n-1]) {
		return 0
	}
	const mod int = 1e9 + 7
	f := make([][]int, n+1)
	g := make([][]int, n+1)
	for i := range f {
		f[i] = make([]int, k+1)
		g[i] = make([]int, k+1)
	}
	f[0][0], g[0][0] = 1, 1
	for i := 1; i <= n; i++ {
		if i >= minLength && !prime(s[i-1]) && (i == n || prime(s[i])) {
			for j := 1; j <= k; j++ {
				f[i][j] = g[i-minLength][j-1]
			}
		}
		for j := 0; j <= k; j++ {
			g[i][j] = (g[i-1][j] + f[i][j]) % mod
		}
	}
	return f[n][k]
}