<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 helper(int i, int j, string s1, string s2, vector<vector<int>>& dp)
    {
        if(i == 0 || j == 0) return 0;

        if(dp[i][j] != -1) return dp[i][j];

        if(s1[i-1] == s2[j-1]) return dp[i][j] = 1 + helper(i-1, j-1, s1, s2, dp);
        return dp[i][j] = max(helper(i, j-1, s1, s2, dp), helper(i-1, j, s1, s2, dp));
    }
    int lcs(string s1, string s2)
    {
        int n = s1.size();
        int m = s2.size();

        //return helper(n, m, s1, s2, dp);

        vector<int> dp(m+1, 0);
        for(int i=1;i<=n;i++)
        {
            vector<int> temp(m+1, 0);
            for(int j=1;j<=m;j++)
            {
                if(s1[i-1] == s2[j-1]) temp[j] = 1 + dp[j-1];
                else temp[j] = max(temp[j-1], dp[j]);
            }
            dp = temp;
        }

        return dp[m];
    }
    int longestPalindromeSubseq(string s) {
        string t = s;
        reverse(t.begin(), t.end());

        return lcs(s, t);
    }
};
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