create Longest Palindromic Subsequence

Author: MayankUjawane

Dynamic Programming/26) Longest Palindromic Subsequence.md

@@ -0,0 +1,40 @@
+# Longest Palindromic Subsequence
+Question -> [Longest Palindromic Subsequence](https://leetcode.com/problems/longest-palindromic-subsequence/)   
+
+> **Logic**    
+> We will be finding the longest common subsequence between string s and reverse of string s and this will give us Longest Palindromic Subsequence.       
+
+### Tabulation
+```java
+class Solution {
+    public int longestPalindromeSubseq(String s) {
+        StringBuilder sb = new StringBuilder(s);
+        String rev = sb.reverse().toString();
+        return lcs(s, rev);
+    }
+    private int lcs(String s, String t) {
+        int n = s.length();
+        int[][] dp = new int[n+1][n+1];
+        // base case 
+        for(int i=0; i<=n; i++) {
+            dp[i][0] = 0;
+            dp[0][i] = 0;
+        }
+        for(int i=1; i<=n; i++) {
+            for(int j=1; j<=n; j++) {
+                if(s.charAt(i-1) == t.charAt(j-1)) {
+                    dp[i][j] = 1 + dp[i-1][j-1];
+                } else {
+                    dp[i][j] = Math.max(dp[i-1][j],dp[i][j-1]);
+                }
+            }
+        }
+        return dp[n][n];
+    }
+}
+```
+> `Time Complexity` : **O(N\*N)**            
+> `Space Complexity` : **O(N\*N)**
+---
+Video Explanations -> [Longest Palindromic Subsequence](https://youtu.be/6i_T5kkfv4A?list=PLgUwDviBIf0qUlt5H_kiKYaNSqJ81PMMY)   
+<hr>