<p>Given a string <code>s</code>, find <em>the longest palindromic <strong>subsequence</strong>&#39;s length in</em> <code>s</code>.</p>

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

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

<pre>
<strong>Input:</strong> s = &quot;bbbab&quot;
<strong>Output:</strong> 4
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bbbb&quot;.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;cbbd&quot;
<strong>Output:</strong> 2
<strong>Explanation:</strong> One possible longest palindromic subsequence is &quot;bb&quot;.
</pre>

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

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>s</code> consists only of lowercase English letters.</li>
</ul>

class Solution {
public:
    int n,m;
    int dp[1001][1001];
    int rec(int i,int j,string &text1,string &text2){
        // pruning
        if(i>=n || j>=m) return 0;
        // basecase

        // cache check
        if(dp[i][j]!=-1) return dp[i][j]; 
        // compute
        int ans = 0;
        if(text1[i]==text2[j]) ans = max(ans,1+rec(i+1,j+1,text1,text2));
        else ans = max(rec(i+1,j,text1,text2),rec(i,j+1,text1,text2));
        
        // save and return
        dp[i][j] = ans;
        return ans;
    }
    int longestPalindromeSubseq(string text2) {
        string text1 = text2;
        reverse(text2.begin(),text2.end());
        this->n = text1.size();
        this->m = text2.size();
        memset(dp,-1,sizeof(dp));
        int ans = rec(0,0,text1,text2);
        return ans;
    }
};
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