Longest palindromic string possible after removal of a substring Last Updated : 13 Aug, 2021 Comments Improve Suggest changes Like Article Like Report Given a string str, the task is to find the longest palindromic string that can be obtained from it after removing a substring. Examples: Input: str = "abcdefghiedcba" Output: "abcdeiedcba" Explanation: Removal of substring "fgh" leaves the remaining string palindromic Input: str = "abba" Output: "abba" Explanation: Removal of substring "" as the given string is already palindromic. Approach: Find the longest possible pair of substrings A and B from both ends of the given string which are reverse of each other.Remove them from the original string.Find the longest palindromic substrings from both ends of the remaining string using KMP and consider the substring which is longer.Add the strings A and B to beginning and end of this palindromic substring respectively to get the desired output. Below code is the implementation of the above approach: C++ // C++ Implementation of the // above approach #include <bits/stdc++.h> using namespace std; // Function to find the longest palindrome // from the start of the string using KMP match string findPalindrome(string C) { string S = C; reverse(S.begin(), S.end()); // Append S(reverse of C) to C C = C + "&" + S; int n = C.length(); int longestPalindrome[n]; longestPalindrome[0] = 0; int len = 0; int i = 1; // Use KMP algorithm while (i < n) { if (C[i] == C[len]) { len++; longestPalindrome[i] = len; i++; } else { if (len != 0) { len = longestPalindrome[len - 1]; } else { longestPalindrome[i] = 0; i++; } } } string ans = C.substr(0, longestPalindrome[n - 1]); return ans; } // Function to return longest palindromic // string possible from the given string // after removal of any substring string findAns(string s) { // Initialize three strings A, B AND F string A = ""; string B = ""; string F = ""; int i = 0; int j = s.length() - 1; int len = s.length(); // Loop to find longest substrings // from both ends which are // reverse of each other while (i < j && s[i] == s[j]) { i = i + 1; j = j - 1; } if (i > 0) { A = s.substr(0, i); B = s.substr(len - i, i); } // Proceed to third step of our approach if (len > 2 * i) { // Remove the substrings A and B string C = s.substr(i, s.length() - 2 * i); // Find the longest palindromic // substring from beginning of C string D = findPalindrome(C); // Find the longest palindromic // substring from end of C reverse(C.begin(), C.end()); string E = findPalindrome(C); // Store the maximum of D and E in F if (D.length() > E.length()) { F = D; } else { F = E; } } // Find the final answer string answer = A + F + B; return answer; } // Driver Code int main() { string str = "abcdefghiedcba"; cout << findAns(str) << endl; } Java // Java Implementation of the // above approach import java.util.*; class GFG{ // Function to find the longest palindrome // from the start of the String using KMP match static String findPalindrome(String C) { String S = C; S = reverse(S); // Append S(reverse of C) to C C = C + "&" + S; int n = C.length(); int []longestPalindrome = new int[n]; longestPalindrome[0] = 0; int len = 0; int i = 1; // Use KMP algorithm while (i < n) { if (C.charAt(i) == C.charAt(len)) { len++; longestPalindrome[i] = len; i++; } else { if (len != 0) { len = longestPalindrome[len - 1]; } else { longestPalindrome[i] = 0; i++; } } } String ans = C.substring(0, longestPalindrome[n - 1]); return ans; } // Function to return longest palindromic // String possible from the given String // after removal of any subString static String findAns(String s) { // Initialize three Strings A, B AND F String A = ""; String B = ""; String F = ""; int i = 0; int j = s.length() - 1; int len = s.length(); // Loop to find longest subStrings // from both ends which are // reverse of each other while (i < j && s.charAt(i) == s.charAt(j)) { i = i + 1; j = j - 1; } if (i > 0) { A = s.substring(0, i); B = s.substring(len - i, len); } // Proceed to third step of our approach if (len > 2 * i) { // Remove the subStrings A and B String C = s.substring(i, (s.length() - 2 * i) + i); // Find the longest palindromic // subString from beginning of C String D = findPalindrome(C); // Find the longest palindromic // subString from end of C C = reverse(C); String E = findPalindrome(C); // Store the maximum of D and E in F if (D.length() > E.length()) { F = D; } else { F = E; } } // Find the final answer String answer = A + F + B; return answer; } static String reverse(String input) { char[] a = input.toCharArray(); int l, r = a.length - 1; for (l = 0; l < r; l++, r--) { char temp = a[l]; a[l] = a[r]; a[r] = temp; } return String.valueOf(a); } // Driver Code public static void main(String[] args) { String str = "abcdefghiedcba"; System.out.print(findAns(str) +"\n"); } } // This code is contributed by PrinciRaj1992 Python3 # Python3 implementation of the # above approach # Function to find the longest # palindrome from the start of # the string using KMP match def findPalindrome(C): S = C[::-1] # Append S(reverse of C) to C C = C[:] + '&' + S n = len(C) longestPalindrome = [0 for i in range(n)] longestPalindrome[0] = 0 ll = 0 i = 1 # Use KMP algorithm while (i < n): if (C[i] == C[ll]): ll += 1 longestPalindrome[i] = ll i += 1 else: if (ll != 0): ll = longestPalindrome[ll - 1] else: longestPalindrome[i] = 0 i += 1 ans = C[0:longestPalindrome[n - 1]] return ans # Function to return longest palindromic # string possible from the given string # after removal of any substring def findAns(s): # Initialize three strings # A, B AND F A = "" B = "" F = "" i = 0 j = len(s) - 1 ll = len(s) # Loop to find longest substrings # from both ends which are # reverse of each other while (i < j and s[i] == s[j]): i = i + 1 j = j - 1 if (i > 0): A = s[0 : i] B = s[ll - i : ll] # Proceed to third step of our approach if (ll > 2 * i): # Remove the substrings A and B C = s[i : i + (len(s) - 2 * i)] # Find the longest palindromic # substring from beginning of C D = findPalindrome(C) # Find the longest palindromic # substring from end of C C = C[::-1] E = findPalindrome(C) # Store the maximum of D and E in F if (len(D) > len(E)): F = D else: F = E # Find the final answer answer = A + F + B return answer # Driver code if __name__=="__main__": str = "abcdefghiedcba" print(findAns(str)) # This code is contributed by rutvik_56 C# // C# Implementation of the // above approach using System; class GFG{ // Function to find the longest palindrome // from the start of the String using KMP match static String findPalindrome(String C) { String S = C; S = reverse(S); // Append S(reverse of C) to C C = C + "&" + S; int n = C.Length; int []longestPalindrome = new int[n]; longestPalindrome[0] = 0; int len = 0; int i = 1; // Use KMP algorithm while (i < n) { if (C[i] == C[len]) { len++; longestPalindrome[i] = len; i++; } else { if (len != 0) { len = longestPalindrome[len - 1]; } else { longestPalindrome[i] = 0; i++; } } } String ans = C.Substring(0, longestPalindrome[n - 1]); return ans; } // Function to return longest palindromic // String possible from the given String // after removal of any subString static String findAns(String s) { // Initialize three Strings A, B AND F String A = ""; String B = ""; String F = ""; int i = 0; int j = s.Length - 1; int len = s.Length; // Loop to find longest subStrings // from both ends which are // reverse of each other while (i < j && s[i] == s[j]) { i = i + 1; j = j - 1; } if (i > 0) { A = s.Substring(0, i); B = s.Substring(len - i, i); } // Proceed to third step of our approach if (len > 2 * i) { // Remove the subStrings A and B String C = s.Substring(i, (s.Length - 2 * i)); // Find the longest palindromic // subString from beginning of C String D = findPalindrome(C); // Find the longest palindromic // subString from end of C C = reverse(C); String E = findPalindrome(C); // Store the maximum of D and E in F if (D.Length > E.Length) { F = D; } else { F = E; } } // Find the readonly answer String answer = A + F + B; return answer; } static String reverse(String input) { char[] a = input.ToCharArray(); int l, r = a.Length - 1; for (l = 0; l < r; l++, r--) { char temp = a[l]; a[l] = a[r]; a[r] = temp; } return String.Join("",a); } // Driver Code public static void Main(String[] args) { String str = "abcdefghiedcba"; Console.Write(findAns(str) +"\n"); } } // This code is contributed by Rajput-Ji JavaScript <script> // JavaScript Implementation of the // above approach // Function to find the longest palindrome // from the start of the String using KMP match function findPalindrome(C) { var S = C; S = reverse(S); // Append S(reverse of C) to C C = C + "&" + S; var n = C.length; var longestPalindrome = new Array(n).fill(0); longestPalindrome[0] = 0; var len = 0; var i = 1; // Use KMP algorithm while (i < n) { if (C[i] === C[len]) { len++; longestPalindrome[i] = len; i++; } else { if (len !== 0) { len = longestPalindrome[len - 1]; } else { longestPalindrome[i] = 0; i++; } } } var ans = C.substring(0, longestPalindrome[n - 1]); return ans; } // Function to return longest palindromic // String possible from the given String // after removal of any subString function findAns(s) { // Initialize three Strings A, B AND F var A = ""; var B = ""; var F = ""; var i = 0; var j = s.length - 1; var len = s.length; // Loop to find longest subStrings // from both ends which are // reverse of each other while (i < j && s[i] === s[j]) { i = i + 1; j = j - 1; } if (i > 0) { A = s.substring(0, i); B = s.substring(len - i, len); } // Proceed to third step of our approach if (len > 2 * i) { // Remove the subStrings A and B var C = s.substring(i, i + (s.length - 2 * i)); // Find the longest palindromic // subString from beginning of C var D = findPalindrome(C); // Find the longest palindromic // subString from end of C C = reverse(C); var E = findPalindrome(C); // Store the maximum of D and E in F if (D.length > E.length) { F = D; } else { F = E; } } // Find the readonly answer var answer = A + F + B; return answer; } function reverse(input) { var a = input.split(""); var r = a.length - 1; for (var l = 0; l < r; l++, r--) { var temp = a[l]; a[l] = a[r]; a[r] = temp; } return a.join(""); } // Driver Code var str = "abcdefghiedcba"; document.write(findAns(str)); // This code is contributed by rdtank. </script> Output: abcdeiedcba Time complexity: O(N)Auxiliary Space: O(N) Comment More infoAdvertise with us Next Article Analysis of Algorithms A AmanGupta65 Follow Improve Article Tags : DSA Similar Reads Basics & PrerequisitesLogic Building ProblemsLogic building is about creating clear, step-by-step methods to solve problems using simple rules and principles. 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