<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 {
    static const int mx=1001;
    int dp[mx][mx];
    pair<int,int> nxt[mx][mx];
    int solve(int i,int j,string &s)
    {
        if(i>j) return 0;
        if(i==j)    return dp[i][j]=1;
        else if(dp[i][j]!=-1)   return dp[i][j];
        if(s[i]==s[j]){
            nxt[i][j]={i+1,j-1};
            return 2+solve(i+1,j-1,s);
        }else{
            int val1,val2;
            val1=solve(i+1,j,s);
            val2=solve(i,j-1,s);
            if(val1>=val2){
                nxt[i][j]={i+1,j};
                return dp[i][j]=val1;
            }else{
                nxt[i][j]={i,j-1};
                return dp[i][j]=val2;
            }
        }
    }
public:
    int longestPalindromeSubseq(string s) {
        int n=s.size();
        s="$"+s;
        for(int i=1;i<=n;i++){
            for(int j=1;j<=n;j++)   dp[i][j]=-1;
        }

        return solve(1,n,s);
    }
}; 
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