Longest Palindrome in a String formed by concatenating its prefix and suffix
Last Updated :
26 Dec, 2022
Given a string str consisting of lowercase English letters, the task is to find the longest palindromic string T which satisfies the following condition:
- T = p + m + s where p and s are the prefix and the suffix of the given string str respectively and the string m is either the prefix or suffix of the string str after removing both p and s from it.
- The string formed by the concatenation of p and s is a palindrome itself.
- Either of the strings p and s can be an empty string.
Examples:
Input: str = "abcdfdcecba"
Output: abcdfdcba
Explanation:
Here, p = "abc"
s = "cba"
m = "dfd"
p + s = "abccba" which is a palindrome and m = "dfd" is the prefix after removing the prefix and suffix from the string str. Therefore, T = "abcdfdcba".
Input: str = "geeksforgeeks"
Output: g
Explanation:
Here, p = ""
s = "g"
m = ""
p + s = "" which is a palindrome and m = "g" is the prefix after removing the prefix and suffix from the string str. Therefore, T = "g".
Approach: The idea for this problem is to divide the answer into three parts, such that there will be a part of suffix and prefix of the given string which forms palindrome together which will form the beginning and the ending of the answer string. Now, after removing these prefix and suffix from the given string, we can find the maximum length suffix or prefix string (which we may call midPalindrome) which is palindromic.
Therefore, the answer string will be given by:
answer = prefix + midPalindrome + suffix
The following steps can be followed to compute the answer to the problem:
- Find the length up to which the suffix and prefix of str form a palindrome together.
- Remove the suffix and prefix substrings that already form a palindrome from str and store them in separate strings.
- Check all prefix and suffix substrings in the remaining string str and find the longest of such strings.
- Finally, combine all three parts of the answer and return it.
Below is the implementation of the above approach:
C++
// C++ program to find the longest
// palindrome in a string formed by
// concatenating its prefix and suffix
#include <bits/stdc++.h>
using namespace std;
// Function to check whether
// the string is a palindrome
bool isPalindrome(string r)
{
string p = r;
// Reverse the string to
// compare with the
// original string
reverse(p.begin(), p.end());
// Check if both are same
return (r == p);
}
// Function to find the longest
// palindrome in a string formed by
// concatenating its prefix and suffix
string PrefixSuffixPalindrome(string str)
{
// Length of the string
int n = str.size(), len = 0;
// Finding the length upto which
// the suffix and prefix forms a
// palindrome together
for (int i = 0; i < n / 2; i++) {
if (str[i] != str[n - i - 1]) {
len = i;
break;
}
}
// Check whether the string
// has prefix and suffix substrings
// which are palindromes.
string prefix = "", suffix = "";
string midPal = "";
// Removing the suffix and prefix
// substrings which already forms
// a palindrome and storing them
// in separate strings
prefix = str.substr(0, len);
suffix = str.substr(n - len);
str = str.substr(len, n - 2 * len);
// Check all prefix substrings
// in the remaining string str
for (int i = 1; i <= str.size(); i++) {
string y = str.substr(0, i);
// Check if the prefix substring
// is a palindrome
if (isPalindrome(y)) {
// If the prefix substring
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.size() < y.size()) {
midPal = y;
}
}
}
// Check all the suffix substrings
// in the remaining string str
for (int i = 1; i <= str.size(); i++) {
string y = str.substr(str.size() - i);
// Check if the suffix substring
// is a palindrome
if (isPalindrome(y)) {
// If the suffix substring
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.size() < y.size()) {
midPal = y;
}
}
}
// Combining all the three parts
// of the answer
string answer = prefix + midPal + suffix;
return answer;
}
// Driver code
int main()
{
string str = "abcdfdcecba";
cout << PrefixSuffixPalindrome(str) << "\n";
return 0;
}
// Java program to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
import java.util.*;
class GFG{
// Function to check whether
// the String is a palindrome
static boolean isPalindrome(String r)
{
String p = r;
// Reverse the String to
// compare with the
// original String
p = reverse(p);
// Check if both are same
return (r.equals(p));
}
// Function to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
static String PrefixSuffixPalindrome(String str)
{
// Length of the String
int n = str.length(), len = 0;
// Finding the length upto which
// the suffix and prefix forms a
// palindrome together
for (int i = 0; i < n / 2; i++) {
if (str.charAt(i) != str.charAt(n - i - 1)) {
len = i;
break;
}
}
// Check whether the String
// has prefix and suffix subStrings
// which are palindromes.
String prefix = "", suffix = "";
String midPal = "";
// Removing the suffix and prefix
// subStrings which already forms
// a palindrome and storing them
// in separate Strings
prefix = str.substring(0, len);
suffix = str.substring(n - len);
str = str.substring(len, (n - 2 * len) + len);
// Check all prefix subStrings
// in the remaining String str
for (int i = 1; i <= str.length(); i++) {
String y = str.substring(0, i);
// Check if the prefix subString
// is a palindrome
if (isPalindrome(y)) {
// If the prefix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.length() < y.length()) {
midPal = y;
}
}
}
// Check all the suffix subStrings
// in the remaining String str
for (int i = 1; i <= str.length(); i++) {
String y = str.substring(str.length() - i);
// Check if the suffix subString
// is a palindrome
if (isPalindrome(y)) {
// If the suffix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.length() < y.length()) {
midPal = y;
}
}
}
// Combining all the parts
// of the answer
String answer = prefix + midPal + suffix;
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 = "abcdfdcecba";
System.out.print(PrefixSuffixPalindrome(str));
}
}
// This code is contributed by 29AjayKumar
# Python3 program to find the longest
# palindrome in a string formed by
# concatenating its prefix and suffix
# Function to check whether
# the string is a palindrome
def isPalindrome(r):
p = r
# Reverse the string to
# compare with the
# original string
p = "".join(reversed(p))
# Check if both are same
return (r == p)
# Function to find the longest
# palindrome in a string formed by
# concatenating its prefix and suffix
def PrefixSuffixPalindrome(st):
# Length of the string
n = len(st)
length = 0
# Finding the length upto which
# the suffix and prefix forms a
# palindrome together
for i in range( n // 2):
if (st[i] != st[n - i - 1]):
length = i
break
# Check whether the string
# has prefix and suffix substrings
# which are palindromes.
prefix = ""
suffix = ""
midPal = ""
# Removing the suffix and prefix
# substrings which already forms
# a palindrome and storing them
# in separate strings
prefix = st[:length]
suffix = st[n - length:]
st = st[length: n - 2 * length+length]
# Check all prefix substrings
# in the remaining string str
for i in range(1,len(st)+1):
y = st[0: i]
# Check if the prefix substring
# is a palindrome
if (isPalindrome(y)):
# If the prefix substring
# is a palindrome then check
# if it is of maximum length
# so far
if (len(midPal) < len(y)):
midPal = y
# Check all the suffix substrings
# in the remaining string str
for i in range(1,len(st)+1):
y = st[len(st)-i]
# Check if the suffix substring
# is a palindrome
if (isPalindrome(y)):
# If the suffix substring
# is a palindrome then check
# if it is of maximum length
# so far
if (len(midPal) < len(y)):
midPal = y
# Combining all the parts
# of the answer
answer = prefix + midPal + suffix
return answer
# Driver code
if __name__ == "__main__":
st = "abcdfdcecba";
print(PrefixSuffixPalindrome(st))
# This code is contributed by chitranayal
// C# program to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
using System;
class GFG{
// Function to check whether
// the String is a palindrome
static bool isPalindrome(String r)
{
String p = r;
// Reverse the String to
// compare with the
// original String
p = reverse(p);
// Check if both are same
return (r.Equals(p));
}
// Function to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
static String PrefixSuffixPalindrome(String str)
{
// Length of the String
int n = str.Length, len = 0;
// Finding the length upto which
// the suffix and prefix forms a
// palindrome together
for (int i = 0; i < n / 2; i++) {
if (str[i] != str[n - i - 1]) {
len = i;
break;
}
}
// Check whether the String
// has prefix and suffix subStrings
// which are palindromes.
String prefix = "", suffix = "";
String midPal = "";
// Removing the suffix and prefix
// subStrings which already forms
// a palindrome and storing them
// in separate Strings
prefix = str.Substring(0, len);
suffix = str.Substring(n - len);
str = str.Substring(len, (n - 2 * len) + len);
// Check all prefix subStrings
// in the remaining String str
for (int i = 1; i <= str.Length; i++) {
String y = str.Substring(0, i);
// Check if the prefix subString
// is a palindrome
if (isPalindrome(y)) {
// If the prefix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.Length < y.Length) {
midPal = y;
}
}
}
// Check all the suffix subStrings
// in the remaining String str
for (int i = 1; i <= str.Length; i++) {
String y = str.Substring(str.Length - i);
// Check if the suffix subString
// is a palindrome
if (isPalindrome(y)) {
// If the suffix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.Length < y.Length) {
midPal = y;
}
}
}
// Combining all the parts
// of the answer
String answer = prefix + midPal + suffix;
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 = "abcdfdcecba";
Console.Write(PrefixSuffixPalindrome(str));
}
}
// This code is contributed by 29AjayKumar
<script>
// Javascript program to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
// Function to check whether
// the String is a palindrome
function isPalindrome(r)
{
let p = r;
// Reverse the String to
// compare with the
// original String
p = reverse(p);
// Check if both are same
return (r == (p));
}
// Function to find the longest
// palindrome in a String formed by
// concatenating its prefix and suffix
function PrefixSuffixPalindrome(str)
{
// Length of the String
let n = str.length, len = 0;
// Finding the length upto which
// the suffix and prefix forms a
// palindrome together
for (let i = 0; i < n / 2; i++) {
if (str[i] != str[n - i - 1]) {
len = i;
break;
}
}
// Check whether the String
// has prefix and suffix subStrings
// which are palindromes.
let prefix = "", suffix = "";
let midPal = "";
// Removing the suffix and prefix
// subStrings which already forms
// a palindrome and storing them
// in separate Strings
prefix = str.substring(0, len);
suffix = str.substring(n - len);
str = str.substring(len, (n - 2 * len) + len);
// Check all prefix subStrings
// in the remaining String str
for (let i = 1; i <= str.length; i++) {
let y = str.substring(0, i);
// Check if the prefix subString
// is a palindrome
if (isPalindrome(y)) {
// If the prefix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.length < y.length) {
midPal = y;
}
}
}
// Check all the suffix subStrings
// in the remaining String str
for (let i = 1; i <= str.length; i++) {
let y = str.substring(str.length - i);
// Check if the suffix subString
// is a palindrome
if (isPalindrome(y)) {
// If the suffix subString
// is a palindrome then check
// if it is of maximum length
// so far
if (midPal.length < y.length) {
midPal = y;
}
}
}
// Combining all the parts
// of the answer
let answer = prefix + midPal + suffix;
return answer;
}
function reverse(input)
{
let a = input.split("");
let l, r = a.length - 1;
for (l = 0; l < r; l++, r--) {
let temp = a[l];
a[l] = a[r];
a[r] = temp;
}
return (a).join("");
}
// Driver code
let str = "abcdfdcecba";
document.write(PrefixSuffixPalindrome(str));
// This code is contributed by avanitrachhadiya2155
</script>
Time Complexity: O(n2)
Auxiliary Space: O(n), where n is the length of the given string.
Similar Reads
Basics & Prerequisites
Data Structures
Array Data StructureIn this article, we introduce array, implementation in different popular languages, its basic operations and commonly seen problems / interview questions. An array stores items (in case of C/C++ and Java Primitive Arrays) or their references (in case of Python, JS, Java Non-Primitive) at contiguous
3 min read
String in Data StructureA string is a sequence of characters. The following facts make string an interesting data structure.Small set of elements. Unlike normal array, strings typically have smaller set of items. For example, lowercase English alphabet has only 26 characters. ASCII has only 256 characters.Strings are immut
2 min read
Hashing in Data StructureHashing is a technique used in data structures that efficiently stores and retrieves data in a way that allows for quick access. Hashing involves mapping data to a specific index in a hash table (an array of items) using a hash function. It enables fast retrieval of information based on its key. The
2 min read
Linked List Data StructureA linked list is a fundamental data structure in computer science. It mainly allows efficient insertion and deletion operations compared to arrays. Like arrays, it is also used to implement other data structures like stack, queue and deque. Here’s the comparison of Linked List vs Arrays Linked List:
2 min read
Stack Data StructureA Stack is a linear data structure that follows a particular order in which the operations are performed. The order may be LIFO(Last In First Out) or FILO(First In Last Out). LIFO implies that the element that is inserted last, comes out first and FILO implies that the element that is inserted first
2 min read
Queue Data StructureA Queue Data Structure is a fundamental concept in computer science used for storing and managing data in a specific order. It follows the principle of "First in, First out" (FIFO), where the first element added to the queue is the first one to be removed. It is used as a buffer in computer systems
2 min read
Tree Data StructureTree Data Structure is a non-linear data structure in which a collection of elements known as nodes are connected to each other via edges such that there exists exactly one path between any two nodes. Types of TreeBinary Tree : Every node has at most two childrenTernary Tree : Every node has at most
4 min read
Graph Data StructureGraph Data Structure is a collection of nodes connected by edges. It's used to represent relationships between different entities. If you are looking for topic-wise list of problems on different topics like DFS, BFS, Topological Sort, Shortest Path, etc., please refer to Graph Algorithms. Basics of
3 min read
Trie Data StructureThe Trie data structure is a tree-like structure used for storing a dynamic set of strings. It allows for efficient retrieval and storage of keys, making it highly effective in handling large datasets. Trie supports operations such as insertion, search, deletion of keys, and prefix searches. In this
15+ min read
Algorithms
Searching AlgorithmsSearching algorithms are essential tools in computer science used to locate specific items within a collection of data. In this tutorial, we are mainly going to focus upon searching in an array. When we search an item in an array, there are two most common algorithms used based on the type of input
2 min read
Sorting AlgorithmsA Sorting Algorithm is used to rearrange a given array or list of elements in an order. For example, a given array [10, 20, 5, 2] becomes [2, 5, 10, 20] after sorting in increasing order and becomes [20, 10, 5, 2] after sorting in decreasing order. There exist different sorting algorithms for differ
3 min read
Introduction to RecursionThe process in which a function calls itself directly or indirectly is called recursion and the corresponding function is called a recursive function. A recursive algorithm takes one step toward solution and then recursively call itself to further move. The algorithm stops once we reach the solution
14 min read
Greedy AlgorithmsGreedy algorithms are a class of algorithms that make locally optimal choices at each step with the hope of finding a global optimum solution. At every step of the algorithm, we make a choice that looks the best at the moment. To make the choice, we sometimes sort the array so that we can always get
3 min read
Graph AlgorithmsGraph is a non-linear data structure like tree data structure. The limitation of tree is, it can only represent hierarchical data. For situations where nodes or vertices are randomly connected with each other other, we use Graph. Example situations where we use graph data structure are, a social net
3 min read
Dynamic Programming or DPDynamic Programming is an algorithmic technique with the following properties.It is mainly an optimization over plain recursion. Wherever we see a recursive solution that has repeated calls for the same inputs, we can optimize it using Dynamic Programming. The idea is to simply store the results of
3 min read
Bitwise AlgorithmsBitwise algorithms in Data Structures and Algorithms (DSA) involve manipulating individual bits of binary representations of numbers to perform operations efficiently. These algorithms utilize bitwise operators like AND, OR, XOR, NOT, Left Shift, and Right Shift.BasicsIntroduction to Bitwise Algorit
4 min read
Advanced
Segment TreeSegment Tree is a data structure that allows efficient querying and updating of intervals or segments of an array. It is particularly useful for problems involving range queries, such as finding the sum, minimum, maximum, or any other operation over a specific range of elements in an array. The tree
3 min read
Pattern SearchingPattern searching algorithms are essential tools in computer science and data processing. These algorithms are designed to efficiently find a particular pattern within a larger set of data. Patten SearchingImportant Pattern Searching Algorithms:Naive String Matching : A Simple Algorithm that works i
2 min read
GeometryGeometry is a branch of mathematics that studies the properties, measurements, and relationships of points, lines, angles, surfaces, and solids. From basic lines and angles to complex structures, it helps us understand the world around us.Geometry for Students and BeginnersThis section covers key br
2 min read
Interview Preparation
Practice Problem