<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 {

    int solve(int start, int end, string& s, vector<vector<int>>& dp) {

        if(start == end)
            return 1;

        if(start > end)
            return 0;

        if(dp[start][end] != -1)
            return dp[start][end];

        int ans;

        if(s[start] == s[end])
            ans = 2 + solve(start+1, end-1, s, dp);
        else{

            ans = max(solve(start+1, end, s, dp), solve(start, end-1, s, dp));
        }

        return dp[start][end] = ans;
    }
public:
    int longestPalindromeSubseq(string s) {

        int n = s.length();

        vector<int> curr (n+1, 0);
        vector<int> next (n+1, 0);

        for(int start = n-1; start >= 0; start--){

            curr[start] = 1;

            for(int end = start+1; end < n; end++) {

                int ans;
                if(s[start] == s[end]){
                    ans = 2 + next[end-1];
                }
                else{
                    ans = max(next[end], curr[end-1]);
                }

                curr[end] = ans;
            }
            next = curr;
        }
        
        return next[n-1];
    }
};
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