<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 solve(string &s, int i, int j){
        if(i>j) return 0;
        if(i == j) return 1;

        int ans = 0;
        if(s[i] == s[j]){
            ans = 2 + solve(s, i+1,j-1);
        }
        else{
            ans = max(solve(s, i+1, j), solve(s, i, j-1));
        }

        return ans;
    }

    int solveByMem(string &s, int i, int j, vector<vector<int>> &dp){
        if(i>j) return 0;
        if(i == j) return 1;

        if(dp[i][j]!=-1){
            return dp[i][j];
        }
        
        int ans = 0;
        if(s[i] == s[j]){
            ans = 2 + solveByMem(s, i+1,j-1, dp);
        }
        else{
            ans = max(solveByMem(s, i+1, j, dp), solveByMem(s, i, j-1, dp));
        }

        dp[i][j] = ans;
        return dp[i][j];
    }

    int longestPalindromeSubseq(string s) {
        int n = s.length();
        vector<vector<int>> dp(n+1, vector<int>(n+1, -1));
        int ans = solveByMem(s, 0, n-1, dp);
        return ans;
    }
};
74600