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

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

        if(s[i] == s[j]){
            return dp[i][j] = 2 + solve(s, i+1, j-1, dp);
        }

        int nexti = solve(s, i+1, j, dp);
        int lastj = solve(s, i, j-1, dp);
        return dp[i][j] = max(nexti, lastj);
    }
    int longestPalindromeSubseq(string s) {
        int n = s.size();
        // vector<vector<int>> dp(n, vector<int>(n, -1));
        // return solve(s, 0, n-1, dp);

        // vector<vector<int>> dp(n, vector<int>(n, 0));
        // for(int i = n-1; i >= 0; i--){
        //     for(int j = 0; j < n; j++){
        //         if(i > j) continue;
        //         if(i == j) {
        //             dp[i][j] = 1;
        //             continue;
        //         }
        //         if(s[i] == s[j]){
        //             dp[i][j] = 2 + dp[i+1][j-1];
        //         }
        //         else{
        //             int nexti = dp[i+1][j];
        //             int lastj = dp[i][j-1];
        //             dp[i][j] = max(nexti, lastj);
        //         }
        //     }
        // }
        // return dp[0][n-1];

        vector<int> dp(n, 0);
        for(int i = n-1; i >= 0; i--){
            vector<int> temp(n, 0);
            for(int j = 0; j < n; j++){
                if(i > j) continue;
                if(i == j) {
                    temp[j] = 1;
                    continue;
                }
                if(s[i] == s[j]){
                    temp[j] = 2 + dp[j-1];
                }
                else{
                    int nexti = dp[j];
                    int lastj = temp[j-1];
                    temp[j] = max(nexti, lastj);
                }
            }
            dp = temp;
        }
        return dp[n-1];
    }
};
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