Create Longest_Palindromic_Substring.java

Author: 17tanya

DynamicProgramming/Longest_Palindromic_Substring.java

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+//LeetCode 5. Longest Palindromic Susbtring
+//Question - https://leetcode.com/problems/longest-palindromic-substring/
+
+class Solution {
+    public String longestPalindrome(String s) {
+        int n = s.length();
+        if(n == 0) return s;
+        
+        //isPalin[i][j] indicates if the substring s(i...j) is a palindrome or not
+        boolean isPalin[][] = new boolean[n][n];
+        /*
+        A string is a palindrome if - 
+            1. Length of string is 0 or 1
+            2. If length of string is 2 then s[i] == s[j]
+            3. If length of string is greater than or equal to 3, check
+                3.1. if s[i] == s[j]
+                3.2. if dp[i+1][j-1] is true, ie. s[i+1...j-1] is a palindrome or not
+        
+        For the 3rd condition it can be seen that for a problem s[i...j] the subproblem is s[i+1...j-1]
+        To solve the problem, subproblem must be pre-computed.
+        So, the outer loop starts in a reverse way, ie. from n...0 (i+1 for each i)
+        The inner loop starts from i and moves up to n, ie. i...n
+        
+        Using a nested loop we are considering all substrings.
+        */
+        String res = null;
+        
+        for(int i = n - 1 ; i >= 0 ; i--){
+            for(int j = i ; j < n ; j++){
+                //condition (2) and (3)
+                isPalin[i][j] = (s.charAt(i) == s.charAt(j)) && ((j - i + 1 < 3) || isPalin[i+1][j-1]);
+                
+                //storing the longest palindromic substring
+                if(isPalin[i][j] && (res == null || j - i + 1 > res.length())){
+                    res = s.substring(i, j+1);
+                }
+            }    
+        }
+        
+        return res;
+    }
+}