<p>You are given a string <code>s</code> consisting of lowercase letters and an integer <code>k</code>. We call a string <code>t</code> <strong>ideal</strong> if the following conditions are satisfied:</p>

<ul>
	<li><code>t</code> is a <strong>subsequence</strong> of the string <code>s</code>.</li>
	<li>The absolute difference in the alphabet order of every two <strong>adjacent</strong> letters in <code>t</code> is less than or equal to <code>k</code>.</li>
</ul>

<p>Return <em>the length of the <strong>longest</strong> ideal string</em>.</p>

<p>A <strong>subsequence</strong> is a string that can be derived from another string by deleting some or no characters without changing the order of the remaining characters.</p>

<p><strong>Note</strong> that the alphabet order is not cyclic. For example, the absolute difference in the alphabet order of <code>&#39;a&#39;</code> and <code>&#39;z&#39;</code> is <code>25</code>, not <code>1</code>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;acfgbd&quot;, k = 2
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest ideal string is &quot;acbd&quot;. The length of this string is 4, so 4 is returned.
Note that &quot;acfgbd&quot; is not ideal because &#39;c&#39; and &#39;f&#39; have a difference of 3 in alphabet order.</pre>

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

<pre>
<strong>Input:</strong> s = &quot;abcd&quot;, k = 3
<strong>Output:</strong> 4
<strong>Explanation:</strong> The longest ideal string is &quot;abcd&quot;. The length of this string is 4, so 4 is returned.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>0 &lt;= k &lt;= 25</code></li>
	<li><code>s</code> consists of lowercase English letters.</li>
</ul>

class Solution {
public:
    string s;
    int k;
    vector<int> cache;

    int longestIdealString(string s, int k) {
        this->s = s;
        this->k = k;
        
        cache = vector<int>(s.size(), -1e9);
        int ans = 0;
        for (int i = 0; i < s.size(); i++) {
            if (cache[i]  == -1e9) 
                cache[i] = solve(i, cache);
            ans = max(ans, cache[i]);
        }

        return ans;
    }

    int solve(int idx, vector<int>& cache) {
        if (idx == 0) return 1;
        
        int ans = 1;
        int count = 0;
        int count2 = 0;
        vector<bool> mp(26, false);
        for (int i = idx - 1; i >= 0; i--) {
            if (mp[(int)(s[i] - 'a')] == false) {
                count++;
                mp[(int)(s[i] - 'a')] = true;
                if (abs(s[i] - s[idx]) <= k) {
                    count2++;
                    if (cache[i] == -1e9) cache[i] = solve(i, cache);
                    ans = max(ans, 1 + cache[i]);
                }
            }

            if (count >= 26) break;
            if (count2 > k) break;
        }

        return ans;
    }
};
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