<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:
    // int f(int i, string& s, char prev, int& k, vector<vector<int>>& dp) {
    //     if (i < 0) return 0;

    //     int prevIdx = (prev == '{') ? 0 : (prev - 'a' + 1);
    //     if (dp[i][prevIdx] != -1) return dp[i][prevIdx];

    //     int take = 0, nottake = 0;
    //     if (prev == '{') {
    //         take = 1 + f(i - 1, s, s[i], k, dp);
    //         nottake = 0 + f(i - 1, s, prev, k, dp);
    //     } else {
    //         if (abs(s[i] - prev) <= k) {
    //             take = 1 + f(i - 1, s, s[i], k, dp);
    //         }
    //         nottake = 0 + f(i - 1, s, prev, k, dp);
    //     }
    //     return dp[i][prevIdx] = max(take, nottake);
    // }

    // int longestIdealString(string s, int k) {
    //     int n = s.length();
    //     vector<vector<int>> dp(n, vector<int>(27, -1)); 
    //     return f(n - 1, s, '{', k, dp);
    // }
    int longestIdealString(string s, int k) {
        int n = s.length();
        vector<vector<int>> dp(n+1,vector<int>(27,0)); 


        //Tabulation
        for(int idx=n-1; idx>=0; idx--){
            for(int prev=0; prev<=26; prev++){
                int take=0,nottake=0;
                nottake = dp[idx+1][prev];
                if(prev == 0 || abs(s[idx]-'a'+1 - prev) <= k){
                    take = 1+ dp[idx+1][s[idx]-'a'+ 1];
                }
                dp[idx][prev] = max(take , nottake);
            }
        }
        return dp[0][0];

    }
};

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