<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 {
    private:
int dp[1001][1001];
int m,n;
string s1,s2;

int rec(int i, int j){
    // pruning

    // basecase
    if(i == m || j == n){
        return 0;
    }

    // cache check
    if(dp[i][j] != -1){
        return dp[i][j];
    }

    // transition
    int ans = 0;
    if(s1[i] == s2[j]){
        ans = max(ans, 1+rec(i+1,j+1));
    }
    else {
        ans = max({ans, rec(i+1,j), rec(i,j+1)});
    }

    // save and return
    return dp[i][j] = ans;
}
public:
    int longestPalindromeSubseq(string s) {
        s1 = s;
        reverse(s.begin(),s.end());
        s2 = s;        
        n = s.size();
        m = n;

        memset(dp,-1,sizeof(dp));

        return rec(0,0);
    }
};
13600