<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:
#     def longestPalindromeSubseq(self, s: str) -> int:
#         n = len(s)

#         s2 = s[::-1]

#         m = len(s2)

#         @cache
#         def dfs(i, j):
#             if i < 0 or j < 0:
#                 return 0

#             if s[i] == s2[j]:
#                 return dfs(i-1, j-1) + 1

#             return max(dfs(i-1, j), dfs(i, j-1))

#         return dfs(n-1, m-1)

# class Solution:
#     def longestPalindromeSubseq(self, s: str) -> int:

#         n = len(s)

#         @cache
#         def dfs(i, j):

#             if i > j: return 0
#             if i == j: return 1

#             if s[i] == s[j]:
#                 return dfs(i+1, j-1) + 2

#             return max(dfs(i+1, j-1), dfs(i+1, j), dfs(i, j-1))

#         return dfs(0, n-1)

# class Solution:
#     def longestPalindromeSubseq(self, s: str) -> int:

#         n = len(s)

#         @cache
#         def dfs(i, j):

#             if i > j: return 0
#             if i == j: return 1

#             if s[i] == s[j]:
#                 return dfs(i+1, j-1) + 2

#             return max(dfs(i+1, j), dfs(i, j-1))

#         return dfs(0, n-1)

class Solution:
    def longestPalindromeSubseq(self, s: str) -> int:

        n = len(s)
        dp = [[0] * (n+1) for _ in range(n+1)]

        # for i in range(n):
        #     for j in range(n):
        #         if i == j:
        #             dp[i][j] = 1

        for i in range(n-1, -1, -1):
            for j in range(n):
                if i > j:
                    dp[i][j] = 0
                
                elif i == j:
                    dp[i][j] = 1

                elif s[i] == s[j]:
                    dp[i][j] = dp[i+1][j-1] + 2

                else:
                    dp[i][j] = max(dp[i+1][j], dp[i][j-1])
                

        f = [[0] * n for _ in range(n)]
        for i in range(n-1, -1, -1):
            f[i][i] = 1
            for j in range(i+1, n):
                if s[i] == s[j]:
                    f[i][j] = f[i+1][j-1] + 2
                else:
                    f[i][j] = max(f[i+1][j], f[i][j-1])

        # print(dp)
        # print(f)
        return dp[0][n-1]
46481