<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 tabu(string &s1, string &s2, int n){
        vector<vector<int>> dp(n+1, vector<int>(n+1, 0));
        for(int i=1; i<=n; i++){
            for(int j=1; j<=n; j++){
                if(s1[i-1] == s2[j-1]) dp[i][j] = 1+dp[i-1][j-1];
                else dp[i][j] = max(dp[i-1][j], dp[i][j-1]);
            }
        }
        return dp[n][n];
    }
    int space(string &s1, string &s2, int n){
        vector<int> prv(n+1, 0), cur(n+1, 0);
        for(int i=1; i<=n; i++){
            for(int j=1; j<=n; j++){
                if(s1[i-1] == s2[j-1]) cur[j] = 1 + prv[j-1];
                else cur[j] = max(prv[j], cur[j-1]);
            }
            prv = cur;
        }
        return prv[n];
    }
    int memo(string &s1, string &s2, int i, int j, vector<vector<int>> &dp){
        if(i<0 || j<0) return 0;
        if(dp[i][j] != -1) return dp[i][j];
        if(s1[i] == s2[j]) return dp[i][j] = 1 + memo(s1, s2, i-1, j-1, dp);
        return dp[i][j] = max(memo(s1, s2, i-1, j, dp), memo(s1, s2, i, j-1, dp));
    }
    int longestPalindromeSubseq(string s) {
        int n = s.size();
        string s2 = s; reverse(s2.begin(), s2.end());
        // vector<vector<int>> dp(n, vector<int> (n, -1));
        // return memo(s, s2, n-1, n-1, dp);
        // return tabu(s, s2, n);
        return space(s, s2, n);       
    }
};
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