Number of Strings Which Can Be Rearranged to Contain Substring
<p>You are given an integer <code>n</code>.</p>

<p>A string <code>s</code> is called <strong>good </strong>if it contains only lowercase English characters <strong>and</strong> it is possible to rearrange the characters of <code>s</code> such that the new string contains <code>&quot;leet&quot;</code> as a <strong>substring</strong>.</p>

<p>For example:</p>

<ul>
	<li>The string <code>&quot;lteer&quot;</code> is good because we can rearrange it to form <code>&quot;leetr&quot;</code> .</li>
	<li><code>&quot;letl&quot;</code> is not good because we cannot rearrange it to contain <code>&quot;leet&quot;</code> as a substring.</li>
</ul>

<p>Return <em>the <strong>total</strong> number of good strings of length </em><code>n</code>.</p>

<p>Since the answer may be 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>

<div class="notranslate" style="all: initial;">&nbsp;</div>

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

<pre>
<strong>Input:</strong> n = 4
<strong>Output:</strong> 12
<strong>Explanation:</strong> The 12 strings which can be rearranged to have &quot;leet&quot; as a substring are: &quot;eelt&quot;, &quot;eetl&quot;, &quot;elet&quot;, &quot;elte&quot;, &quot;etel&quot;, &quot;etle&quot;, &quot;leet&quot;, &quot;lete&quot;, &quot;ltee&quot;, &quot;teel&quot;, &quot;tele&quot;, and &quot;tlee&quot;.
</pre>

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

<pre>
<strong>Input:</strong> n = 10
<strong>Output:</strong> 83943898
<strong>Explanation:</strong> The number of strings with length 10 which can be rearranged to have &quot;leet&quot; as a substring is 526083947580. Hence the answer is 526083947580 % (10<sup>9</sup> + 7) = 83943898.
</pre>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
</ul>
Math; Dynamic Programming; Combinatorics
class Solution {
    private final int mod = (int) 1e9 + 7;
    private Long[][][][] f;

    public int stringCount(int n) {
        f = new Long[n + 1][2][3][2];
        return (int) dfs(n, 0, 0, 0);
    }

    private long dfs(int i, int l, int e, int t) {
        if (i == 0) {
            return l == 1 && e == 2 && t == 1 ? 1 : 0;
        }
        if (f[i][l][e][t] != null) {
            return f[i][l][e][t];
        }
        long a = dfs(i - 1, l, e, t) * 23 % mod;
        long b = dfs(i - 1, Math.min(1, l + 1), e, t);
        long c = dfs(i - 1, l, Math.min(2, e + 1), t);
        long d = dfs(i - 1, l, e, Math.min(1, t + 1));
        return f[i][l][e][t] = (a + b + c + d) % mod;
    }
}