**Longest Palindromic Subsequence - Amazon Top Interview Questions**

### Problem Statement :

Given a string s with all lower case characters, find the length of the longest palindromic subsequence in s. Constraints n ≤ 1,000 where n is the length of s Example 1 Input s = "rbaicneacrayr" Output 7 Explanation racecar is the longest palindromic subsequence of rbaicneacrayr Example 2 Input s = "binarysearch" Output 3 Explanation The longest palindromic subsequence here is aea. Example 3 Input s = "bbbbbbbbbb" Output 10 Explanation The whole string is a palindrome. Example 4 Input s = "a" Output 1

### Solution :

` ````
Solution in C++ :
int dp[3][1005];
int solve(string s) {
memset(dp[0], 0, sizeof(dp[0]));
for (int i = 0; i < s.size(); i++) {
dp[1][i] = 1;
}
for (int a = 2; a <= s.size(); a++) {
memset(dp[2], -1, sizeof(dp[2]));
for (int i = 0; i + a <= s.size(); i++) {
int j = i + a - 1;
if (s[i] == s[j]) dp[2][i] = max(dp[2][i], 2 + dp[0][i + 1]);
dp[2][i] = max(dp[2][i], max(dp[1][i], dp[1][i + 1]));
}
memcpy(dp[0], dp[1], sizeof(dp[0]));
memcpy(dp[1], dp[2], sizeof(dp[0]));
}
return dp[1][0];
}
```

` ````
Solution in Java :
import java.util.*;
class Solution {
public int solve(String s) {
int n = s.length();
if (n <= 1)
return n;
int[][] dp = new int[n][n];
int res = 1;
for (int i = 0; i < n; i++) dp[i][i] = 1;
for (int LENGTH = 2; LENGTH <= n; LENGTH++) {
for (int i = 0; i < n; i++) {
if (i + LENGTH - 1 >= n)
break;
int cand = Math.max(dp[i + 1][i + LENGTH - 1], dp[i][i + LENGTH - 2]);
if (s.charAt(i) == s.charAt(i + LENGTH - 1)) {
cand = Math.max(cand, 2 + dp[i + 1][i + LENGTH - 2]);
}
dp[i][i + LENGTH - 1] = cand;
}
}
return dp[0][n - 1];
}
}
```

` ````
Solution in Python :
class Solution:
def solve(self, s):
n = len(s)
@functools.lru_cache(None)
def dp(i, j):
if i == j:
return 1
elif i > j:
return 0
else:
if s[i] == s[j]:
return 2 + dp(i + 1, j - 1)
else:
return max(dp(i + 1, j), dp(i, j - 1))
return dp(0, n - 1)
```

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