Longest Palindromic Substring
Last Updated :
10 Mar, 2025
Given a string s, the task is to find the longest substring which is a palindrome. If there are multiple answers, then return the first appearing substring.
Examples:
Input: s = "forgeeksskeegfor"
Output: "geeksskeeg"
Explanation: There are several possible palindromic substrings like "kssk", "ss", "eeksskee" etc. But the substring "geeksskeeg" is the longest among all.
Input: s = "Geeks"
Output: "ee"
Input: s = "abc"
Output: "a"
Input: s = ""
Output: ""
[Naive Approach] Generating all sub-strings - O(n^3) time and O(1) space
The idea is to generate all substrings.
- For each substring, check if it is palindrome or not.
- If substring is Palindrome, then update the result on the basis of longest palindromic substring found till now.
C++
#include <bits/stdc++.h>
using namespace std;
// Function to check if a substring
// s[low..high] is a palindrome
bool checkPal(string &s, int low, int high) {
while (low < high) {
if (s[low] != s[high])
return false;
low++;
high--;
}
return true;
}
// function to find the longest palindrome substring
string longestPalindrome(string& s) {
// Get length of input string
int n = s.size();
// All substrings of length 1 are palindromes
int maxLen = 1, start = 0;
// Nested loop to mark start and end index
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
// Check if the current substring is
// a palindrome
if (checkPal(s, i, j) && (j - i + 1) > maxLen) {
start = i;
maxLen = j - i + 1;
}
}
}
return s.substr(start, maxLen);
}
int main() {
string s = "forgeeksskeegfor";
cout << longestPalindrome(s) << endl;
return 0;
}
Java
// Java program to find the longest
// palindromic substring.
import java.util.*;
class GfG {
// Function to check if a substring
// s[low..high] is a palindrome
static boolean checkPal(String s, int low, int high) {
while (low < high) {
if (s.charAt(low) != s.charAt(high))
return false;
low++;
high--;
}
return true;
}
// Function to find the longest palindrome substring
static String longestPalindrome(String s) {
// Get length of input string
int n = s.length();
// All substrings of length 1 are palindromes
int maxLen = 1, start = 0;
// Nested loop to mark start and end index
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
// Check if the current substring is
// a palindrome
if (checkPal(s, i, j) && (j - i + 1) > maxLen) {
start = i;
maxLen = j - i + 1;
}
}
}
return s.substring(start, start + maxLen);
}
public static void main(String[] args) {
String s = "forgeeksskeegfor";
System.out.println(longestPalindrome(s));
}
}
Python
# Python program to find the longest
# palindromic substring.
# Function to check if a substring
# s[low..high] is a palindrome
def checkPal(str, low, high):
while low < high:
if str[low] != str[high]:
return False
low += 1
high -= 1
return True
# Function to find the longest palindrome substring
def longestPalindrome(s):
# Get length of input string
n = len(s)
# All substrings of length 1 are palindromes
maxLen = 1
start = 0
# Nested loop to mark start and end index
for i in range(n):
for j in range(i, n):
# Check if the current substring is
# a palindrome
if checkPal(s, i, j) and (j - i + 1) > maxLen:
start = i
maxLen = j - i + 1
return s[start:start + maxLen]
if __name__ == "__main__":
s = "forgeeksskeegfor"
print(longestPalindrome(s))
C#
// C# program to find the longest
// palindromic substring.
using System;
class GfG {
// Function to check if a substring
// s[low..high] is a palindrome
static bool checkPal(string s, int low, int high) {
while (low < high) {
if (s[low] != s[high])
return false;
low++;
high--;
}
return true;
}
// Function to find the longest palindrome substring
static string longestPalindrome(string s) {
// Get length of input string
int n = s.Length;
// All substrings of length 1 are palindromes
int maxLen = 1, start = 0;
// Nested loop to mark start and end index
for (int i = 0; i < n; i++) {
for (int j = i; j < n; j++) {
// Check if the current substring is
// a palindrome
if (checkPal(s, i, j) && (j - i + 1) > maxLen) {
start = i;
maxLen = j - i + 1;
}
}
}
return s.Substring(start, maxLen);
}
static void Main(string[] args) {
string s = "forgeeksskeegfor";
Console.WriteLine(longestPalindrome(s));
}
}
JavaScript
// JavaScript program to find the longest
// palindromic substring.
// Function to check if a substring
// s[low..high] is a palindrome
function checkPal(s, low, high) {
while (low < high) {
if (s[low] !== s[high])
return false;
low++;
high--;
}
return true;
}
// Function to find the longest palindrome substring
function longestPalindrome(s) {
// Get length of input string
const n = s.length;
// All substrings of length 1 are palindromes
let maxLen = 1, start = 0;
// Nested loop to mark start and end index
for (let i = 0; i < n; i++) {
for (let j = i; j < n; j++) {
// Check if the current substring is
// a palindrome
if (checkPal(s, i, j) && (j - i + 1) > maxLen) {
start = i;
maxLen = j - i + 1;
}
}
}
return s.substring(start, start + maxLen);
}
// Driver Code
const s = "forgeeksskeegfor";
console.log(longestPalindrome(s));
[Better Approach - 1] Using Dynamic Programming - O(n^2) time and O(n^2) space
The idea is to use Dynamic Programming to store the status of smaller substrings and use these results to check if a longer substring forms a palindrome.
- The main idea behind the approach is that if we know the status (i.e., palindrome or not) of the substring ranging [i, j], we can find the status of the substring ranging [i-1, j+1] by only matching the character str[i-1] and str[j+1].
- If the substring from i to j is not a palindrome, then the substring from i-1 to j+1 will also not be a palindrome. Otherwise, it will be a palindrome only if str[i-1] and str[j+1] are the same.
- Base on this fact, we can create a 2D table (say table[][] which stores status of substring str[i . . . j] ), and check for substrings with length from 1 to N. For each length find all the substrings starting from each character i and find if it is a palindrom or not using the above idea. The longest length for which a palindrome formed will be the required asnwer.
Note: Refer to Longest Palindromic Substring using Dynamic Programming for detailed approach and code.
[Better Approach - 2] Using Expansion from center - O(n^2) time and O(1) space
The idea is to traverse each character in the string and treat it as a potential center of a palindrome, trying to expand around it in both directions while checking if the expanded substring remains a palindrome.
- For each position, we check for both odd-length palindromes (where the current character is the center) and even-length palindromes (where the current character and the next character together form the center).
- As we expand outward from each center, we keep track of the start position and length of the longest palindrome found so far, updating these values whenever we find a longer valid palindrome.
Step-by-step approach:
- Use two pointers, low and hi, for the left and right end of the current palindromic substring being found.
- Then checks if the characters at s[low] and s[hi] are the same.
- If they are, it expands the substring to the left and right by decrementing low and incrementing hi.
- It continues this process until the characters at s[low] and s[hi] are unequal or until the indices are in bounds.
- If the length of the current palindromic substring becomes greater than the maximum length, it updates the maximum length.
C++
// C++ program to find the longest
// palindromic substring.
#include <bits/stdc++.h>
using namespace std;
// Function to find the longest palindrome substring
string longestPalindrome(string &s) {
int n = s.length();
if (n == 0) return "";
int start = 0, maxLen = 1;
// Traverse the input string
for (int i = 0; i < n; i++) {
// THIS RUNS TWO TIMES
// for both odd and even length
// palindromes. j = 0 means odd
// and j = 1 means even length
for (int j = 0; j <= 1; j++) {
int low = i;
int high = i + j;
// Expand substring while it is a palindrome
// and in bounds
while (low >= 0 && high < n && s[low] == s[high]) {
int currLen = high - low + 1;
if (currLen > maxLen) {
start = low;
maxLen = currLen;
}
low--;
high++;
}
}
}
return s.substr(start, maxLen);
}
int main() {
string s = "forgeeksskeegfor";
cout << longestPalindrome(s) << endl;
return 0;
}
Java
// Java program to find the longest
// palindromic substring.
class GfG {
// Function to find the longest palindrome substring
static String longestPalindrome(String s) {
int n = s.length();
if (n == 0) return "";
int start = 0, maxLen = 1;
// Traverse the input string
for (int i = 0; i < n; i++) {
// THIS RUNS TWO TIMES
// for both odd and even length
// palindromes. j = 0 means odd
// and j = 1 means even length
for (int j = 0; j <= 1; j++) {
int low = i;
int high = i + j;
// Expand substring while it is a palindrome
// and in bounds
while (low >= 0 && high < n && s.charAt(low) == s.charAt(high)) {
int currLen = high - low + 1;
if (currLen > maxLen) {
start = low;
maxLen = currLen;
}
low--;
high++;
}
}
}
return s.substring(start, start + maxLen);
}
public static void main(String[] args) {
String s = "forgeeksskeegfor";
System.out.println(longestPalindrome(s));
}
}
Python
# Python program to find the longest
# palindromic substring.
# Function to find the
# longest palindrome substring
def longestPalindrome(s):
n = len(s)
if n == 0:
return ""
start, maxLen = 0, 1
# Traverse the input string
for i in range(n):
# THIS RUNS TWO TIMES
# for both odd and even length
# palindromes. j = 0 means odd
# and j = 1 means even length
for j in range(2):
low, high = i, i + j
# Expand substring while it is a palindrome
# and in bounds
while low >= 0 and high < n and s[low] == s[high]:
currLen = high - low + 1
if currLen > maxLen:
start = low
maxLen = currLen
low -= 1
high += 1
return s[start:start + maxLen]
if __name__ == "__main__":
s = "forgeeksskeegfor"
print(longestPalindrome(s))
C#
// C# program to find the longest
// palindromic substring.
using System;
class GfG {
// Function to find the longest palindrome substring
static string longestPalindrome(string s) {
int n = s.Length;
if (n == 0) return "";
int start = 0, maxLen = 1;
// Traverse the input string
for (int i = 0; i < n; i++) {
// THIS RUNS TWO TIMES
// for both odd and even length
// palindromes. j = 0 means odd
// and j = 1 means even length
for (int j = 0; j <= 1; j++) {
int low = i;
int high = i + j;
// Expand substring while it is a palindrome
// and in bounds
while (low >= 0 && high < n && s[low] == s[high]) {
int currLen = high - low + 1;
if (currLen > maxLen) {
start = low;
maxLen = currLen;
}
low--;
high++;
}
}
}
return s.Substring(start, maxLen);
}
static void Main(string[] args) {
string s = "forgeeksskeegfor";
Console.WriteLine(longestPalindrome(s));
}
}
JavaScript
// JavaScript program to find the longest
// palindromic substring.
// Function to find the longest palindrome substring
function longestPalindrome(s) {
const n = s.length;
if (n === 0) return "";
let start = 0, maxLen = 1;
// Traverse the input string
for (let i = 0; i < n; i++) {
// THIS RUNS TWO TIMES
// for both odd and even length
// palindromes. j = 0 means odd
// and j = 1 means even length
for (let j = 0; j <= 1; j++) {
let low = i;
let high = i + j;
// Expand substring while it is a palindrome
// and in bounds
while (low >= 0 && high < n && s[low] === s[high]) {
const currLen = high - low + 1;
if (currLen > maxLen) {
start = low;
maxLen = currLen;
}
low--;
high++;
}
}
}
return s.substring(start, start + maxLen);
}
// Driver Code
const s = "forgeeksskeegfor";
console.log(longestPalindrome(s));
[Expected Approach] Using Manacher’s Algorithm - O(n) time and O(n) space
We can solve this problem in linear time using Manacher’s Algorithm. Refer the below links for details:
Similar Reads
Palindrome String Coding Problems A string is called a palindrome if the reverse of the string is the same as the original one.Example: âmadamâ, âracecarâ, â12321â.Palindrome StringProperties of a Palindrome String:A palindrome string has some properties which are mentioned below:A palindrome string has a symmetric structure which m
2 min read
Palindrome String Given a string s, the task is to check if it is palindrome or not.Example:Input: s = "abba"Output: 1Explanation: s is a palindromeInput: s = "abc" Output: 0Explanation: s is not a palindromeUsing Two-Pointers - O(n) time and O(1) spaceThe idea is to keep two pointers, one at the beginning (left) and
13 min read
Check Palindrome by Different Language
Easy Problems on Palindrome
Sentence Palindrome Given a sentence s, the task is to check if it is a palindrome sentence or not. A palindrome sentence is a sequence of characters, such as a word, phrase, or series of symbols, that reads the same backward as forward after converting all uppercase letters to lowercase and removing all non-alphanumer
9 min read
Check if actual binary representation of a number is palindrome Given a non-negative integer n. The problem is to check if binary representation of n is palindrome or not. Note that the actual binary representation of the number is being considered for palindrome checking, no leading 0âs are being considered. Examples : Input : 9 Output : Yes (9)10 = (1001)2 Inp
6 min read
Print longest palindrome word in a sentence Given a string str, the task is to print longest palindrome word present in the string str.Examples: Input : Madam Arora teaches Malayalam Output: Malayalam Explanation: The string contains three palindrome words (i.e., Madam, Arora, Malayalam) but the length of Malayalam is greater than the other t
14 min read
Count palindrome words in a sentence Given a string str and the task is to count palindrome words present in the string str. Examples: Input : Madam Arora teaches malayalam Output : 3 The string contains three palindrome words (i.e., Madam, Arora, malayalam) so the count is three. Input : Nitin speaks malayalam Output : 2 The string co
5 min read
Check if characters of a given string can be rearranged to form a palindrome Given a string, Check if the characters of the given string can be rearranged to form a palindrome. For example characters of "geeksogeeks" can be rearranged to form a palindrome "geeksoskeeg", but characters of "geeksforgeeks" cannot be rearranged to form a palindrome. Recommended PracticeAnagram P
14 min read
Lexicographically first palindromic string Rearrange the characters of the given string to form a lexicographically first palindromic string. If no such string exists display message "no palindromic string". Examples: Input : malayalam Output : aalmymlaa Input : apple Output : no palindromic string Simple Approach: 1. Sort the string charact
13 min read