Longest Palindromic Substring

Try it on GfG Practice

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.

#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 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 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# 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 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));

geeksskeeg

[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++ 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 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 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# 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 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));

geeksskeeg

[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:

• Manacher’s Algorithm - Part 1
• Manacher’s Algorithm - Part 2
• Manacher’s Algorithm - Part 3

kartik

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