<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 {

    int func(int prev, int i , string s, int k, int n )
    {
        if(i>=n){
            return 0;
        }
        int l1= func(prev,i+1,s,k,n);
        int l2=0;
        if(prev==0|| abs(int(s[i]-96-prev)) <=k)
        {
            l2= 1+func(int(s[i])-96,i+1,s,k,n);
        }
        return max(l1,l2);
    }
public:
    int longestIdealString(string s, int k) {
        int n= s.length();
        // return func(0,0,s,k,n);

        vector<vector<int>> dp(n+1, vector<int> (27,0));
        int maxno= INT_MIN;

        for(int i=n-1;i>=0;i--)
        {
            for(int prev=26;prev>=0;prev--)
            {
                int l1= dp[i+1][prev];
                int l2=0;
                if(prev==0|| abs(int(s[i]-96-prev)) <=k)
                {
                    l2= 1+dp[i+1][int(s[i])-96];
                }
                dp[i][prev]=  max(l1,l2);
                maxno= max(maxno, dp[i][prev]);
            }
        }
        return maxno;
        
    }
};
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