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## Problem

Given a string s, find the longest palindromic subsequence’s length in s.

A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.

Example 1:

Input: s = "bbbab"
Output: 4
Explanation: One possible longest palindromic subsequence is "bbbb".


Example 2:

Input: s = "cbbd"
Output: 2
Explanation: One possible longest palindromic subsequence is "bb".


Constraints:

• 1 <= s.length <= 1000
• s consists only of lowercase English letters.

## Code

dp[i, j]表示在 i 和 j 区间内最长的回文字符串

• 如果 i 和 j 的字符相同, 那么 i 和 j 之间的最长回文字符串就是[i+1, j-1] + 2
• 如果 i 和 j 的字符不同, 那么 i 和 j 之间的最长回文字符串就是 max([i+1, j],[i, j-1])

class Solution {
public int longestPalindromeSubseq(String s) {
int[][] dp = new int[s.length()][s.length()];

for (int len = 1; len <= s.length(); len++) {
for (int i = 0; i + len <= s.length(); i++) {
int j = i + len - 1;

if (i == j) {
dp[i][j] = 1;
continue;
}

if (s.charAt(i) == s.charAt(j)) {
dp[i][j] = dp[i + 1][j - 1] + 2;
} else {
dp[i][j] = Math.max(dp[i + 1][j], dp[i][j - 1]);
}
}
}

return dp[0][s.length() - 1];
}
}