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
class Solution {
public:
    int beautifulPartitions(string s, int k, int minLength) {
        int n = s.size();
        auto prime = [](char c) {
            return c == '2' || c == '3' || c == '5' || c == '7';
        };
        if (!prime(s[0]) || prime(s[n - 1])) return 0;
        vector<vector<int>> f(n + 1, vector<int>(k + 1));
        vector<vector<int>> g(n + 1, vector<int>(k + 1));
        f[0][0] = g[0][0] = 1;
        const int mod = 1e9 + 7;
        for (int i = 1; i <= n; ++i) {
            if (i >= minLength && !prime(s[i - 1]) && (i == n || prime(s[i]))) {
                for (int j = 1; j <= k; ++j) {
                    f[i][j] = g[i - minLength][j - 1];
                }
            }
            for (int j = 0; j <= k; ++j) {
                g[i][j] = (g[i - 1][j] + f[i][j]) % mod;
            }
        }
        return f[n][k];
    }
};