`dp[i][j]`

: the longest palindromic subsequence's length of substring(i, j)

`State transition`

:

`dp[i][j] = dp[i+1][j-1] + 2`

if s.charAt(i) == s.charAt(j)

otherwise, `dp[i][j] = Math.max(dp[i+1][j], dp[i][j-1])`

`Initialization`

: `dp[i][i] = 1`

```
public class Solution {
public int longestPalindromeSubseq(String s) {
int[][] dp = new int[s.length()][s.length()];
for (int i = s.length() - 1; i >= 0; i--) {
dp[i][i] = 1;
for (int j = i+1; j < s.length(); j++) {
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];
}
}
```

Top bottom recursive method with memoization

```
public class Solution {
public int longestPalindromeSubseq(String s) {
return helper(s, 0, s.length() - 1, new Integer[s.length()][s.length()]);
}
private int helper(String s, int i, int j, Integer[][] memo) {
if (memo[i][j] != null) {
return memo[i][j];
}
if (i > j) return 0;
if (i == j) return 1;
if (s.charAt(i) == s.charAt(j)) {
memo[i][j] = helper(s, i + 1, j - 1, memo) + 2;
} else {
memo[i][j] = Math.max(helper(s, i + 1, j, memo), helper(s, i, j - 1, memo));
}
return memo[i][j];
}
}
```