<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 dp[1001][1001];
    int solve(int i, int j, string& s1, string& s2){

        if(i==s1.length() || j == s2.length()){
            return 0;
        }
        if(dp[i][j] != -1){
            return dp[i][j];
        }

        if(s1[i] == s2[j]){
            return dp[i][j] = 1 + solve(i+1, j+1, s1, s2);
        }

        int take1 = solve(i, j+1, s1, s2);
        int take2 = solve(i+1, j, s1, s2);

        return dp[i][j] = max(take1, take2);
    }
    int longestPalindromeSubseq(string s) {
        memset(dp, -1, sizeof(dp));
        int n = s.length();
        string s2 = "";

        for(int i=n-1; i>=0; i--){
            s2 += s[i];
        }

        return solve(0, 0, s, s2);
    }
};
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