# Longest Palindromic Substring | Set 2

Given a string, find the longest substring which is palindrome. For example, if the given string is “forgeeksskeegfor”, the output should be “geeksskeeg”.

## Recommended: Please solve it on “PRACTICE ” first, before moving on to the solution.

We have discussed dynamic programming solution in the previous post. The time complexity of the Dynamic Programming based solution is O(n^2) and it requires O(n^2) extra space. We can find the longest palindrome substring in (n^2) time with O(1) extra space. The idea is to generate all even length and odd length palindromes and keep track of the longest palindrome seen so far.

Step to generate odd length palindrome:
Fix a centre and expand in both directions for longer palindromes.

Step to generate even length palindrome
Fix two centre ( low and high ) and expand in both directions for longer palindromes.

 `// A O(n^2) time and O(1) space program to  ` `// find the longest palindromic substring  ` `#include ` `using` `namespace` `std; ` ` `  `// A utility function to print a substring str[low..high]  ` `void` `printSubStr(``char``* str, ``int` `low, ``int` `high)  ` `{  ` `    ``for``( ``int` `i = low; i <= high; ++i )  ` `        ``cout << str[i];  ` `}  ` ` `  `// This function prints the longest palindrome substring (LPS)  ` `// of str[]. It also returns the length of the longest palindrome  ` `int` `longestPalSubstr(``char` `*str)  ` `{  ` `    ``int` `maxLength = 1; ``// The result (length of LPS)  ` ` `  `    ``int` `start = 0;  ` `    ``int` `len = ``strlen``(str);  ` ` `  `    ``int` `low, high;  ` ` `  `    ``// One by one consider every character as center point of  ` `    ``// even and length palindromes  ` `    ``for` `(``int` `i = 1; i < len; ++i)  ` `    ``{  ` `        ``// Find the longest even length palindrome  ` `        ``// with center points as i-1 and i.  ` `        ``low = i - 1;  ` `        ``high = i;  ` `        ``while` `(low >= 0 && high < len && str[low] == str[high])  ` `        ``{  ` `            ``if` `(high - low + 1 > maxLength)  ` `            ``{  ` `                ``start = low;  ` `                ``maxLength = high - low + 1;  ` `            ``}  ` `            ``--low;  ` `            ``++high;  ` `        ``}  ` ` `  `        ``// Find the longest odd length palindrome with center  ` `        ``// point as i  ` `        ``low = i - 1;  ` `        ``high = i + 1;  ` `        ``while` `(low >= 0 && high < len && str[low] == str[high])  ` `        ``{  ` `            ``if` `(high - low + 1 > maxLength)  ` `            ``{  ` `                ``start = low;  ` `                ``maxLength = high - low + 1;  ` `            ``}  ` `            ``--low;  ` `            ``++high;  ` `        ``}  ` `    ``}  ` ` `  `    ``cout<<``"Longest palindrome substring is: "``;  ` `    ``printSubStr(str, start, start + maxLength - 1);  ` ` `  `    ``return` `maxLength;  ` `}  ` ` `  `// Driver program to test above functions  ` `int` `main()  ` `{  ` `    ``char` `str[] = ``"forgeeksskeegfor"``;  ` `    ``cout<<``"\nLength is: "``<

 `// A O(n^2) time and O(1) space program to find the longest palindromic substring ` `#include ` `#include ` ` `  `// A utility function to print a substring str[low..high] ` `void` `printSubStr(``char``* str, ``int` `low, ``int` `high) ` `{ ` `    ``for``( ``int` `i = low; i <= high; ++i ) ` `        ``printf``(``"%c"``, str[i]); ` `} ` ` `  `// This function prints the longest palindrome substring (LPS) ` `// of str[]. It also returns the length of the longest palindrome ` `int` `longestPalSubstr(``char` `*str) ` `{ ` `    ``int` `maxLength = 1;  ``// The result (length of LPS) ` ` `  `    ``int` `start = 0; ` `    ``int` `len = ``strlen``(str); ` ` `  `    ``int` `low, high; ` ` `  `    ``// One by one consider every character as center point of  ` `    ``// even and length palindromes ` `    ``for` `(``int` `i = 1; i < len; ++i) ` `    ``{ ` `        ``// Find the longest even length palindrome with center points ` `        ``// as i-1 and i.   ` `        ``low = i - 1; ` `        ``high = i; ` `        ``while` `(low >= 0 && high < len && str[low] == str[high]) ` `        ``{ ` `            ``if` `(high - low + 1 > maxLength) ` `            ``{ ` `                ``start = low; ` `                ``maxLength = high - low + 1; ` `            ``} ` `            ``--low; ` `            ``++high; ` `        ``} ` ` `  `        ``// Find the longest odd length palindrome with center  ` `        ``// point as i ` `        ``low = i - 1; ` `        ``high = i + 1; ` `        ``while` `(low >= 0 && high < len && str[low] == str[high]) ` `        ``{ ` `            ``if` `(high - low + 1 > maxLength) ` `            ``{ ` `                ``start = low; ` `                ``maxLength = high - low + 1; ` `            ``} ` `            ``--low; ` `            ``++high; ` `        ``} ` `    ``} ` ` `  `    ``printf``(``"Longest palindrome substring is: "``); ` `    ``printSubStr(str, start, start + maxLength - 1); ` ` `  `    ``return` `maxLength; ` `} ` ` `  `// Driver program to test above functions ` `int` `main() ` `{ ` `    ``char` `str[] = ``"forgeeksskeegfor"``; ` `    ``printf``(``"\nLength is: %d"``, longestPalSubstr( str ) ); ` `    ``return` `0; ` `} `

 `// Java implementation of O(n^2) time and O(1) space method ` `// to find the longest palindromic substring ` `public` `class` `LongestPalinSubstring ` `{ ` `    ``// A utility function to print a substring str[low..high] ` `    ``static` `void` `printSubStr(String str, ``int` `low, ``int` `high) { ` `        ``System.out.println(str.substring(low, high + ``1``)); ` `    ``} ` ` `  `    ``// This function prints the longest palindrome substring  ` `    ``// (LPS) of str[]. It also returns the length of the   ` `    ``// longest palindrome  ` `    ``static` `int` `longestPalSubstr(String str) { ` `        ``int` `maxLength = ``1``; ``// The result (length of LPS) ` ` `  `        ``int` `start = ``0``; ` `        ``int` `len = str.length(); ` ` `  `        ``int` `low, high; ` ` `  `        ``// One by one consider every character as center ` `        ``// point of even and length palindromes ` `        ``for` `(``int` `i = ``1``; i < len; ++i)  ` `        ``{ ` `            ``// Find the longest even length palindrome with  ` `            ``// center points as i-1 and i. ` `            ``low = i - ``1``; ` `            ``high = i; ` `            ``while` `(low >= ``0` `&& high < len ` `                    ``&& str.charAt(low) == str.charAt(high)) { ` `                ``if` `(high - low + ``1` `> maxLength) { ` `                    ``start = low; ` `                    ``maxLength = high - low + ``1``; ` `                ``} ` `                ``--low; ` `                ``++high; ` `            ``} ` ` `  `            ``// Find the longest odd length palindrome with  ` `            ``// center point as i ` `            ``low = i - ``1``; ` `            ``high = i + ``1``; ` `            ``while` `(low >= ``0` `&& high < len ` `                    ``&& str.charAt(low) == str.charAt(high)) { ` `                ``if` `(high - low + ``1` `> maxLength) { ` `                    ``start = low; ` `                    ``maxLength = high - low + ``1``; ` `                ``} ` `                ``--low; ` `                ``++high; ` `            ``} ` `        ``} ` ` `  `        ``System.out.print(``"Longest palindrome substring is: "``); ` `        ``printSubStr(str, start, start + maxLength - ``1``); ` ` `  `        ``return` `maxLength; ` `    ``} ` ` `  `    ``// Driver program to test above function ` `    ``public` `static` `void` `main(String[] args) { ` `         `  `        ``String str = ``"forgeeksskeegfor"``; ` `        ``System.out.println(``"Length is: "` `+  ` `                           ``longestPalSubstr(str)); ` `    ``} ` ` `  `} ` `// This code is contributed by Sumit Ghosh `

 `# A O(n^2) time and O(1) space program to find the  ` `#longest palindromic substring ` ` `  `# This function prints the longest palindrome substring (LPS) ` `# of str[]. It also returns the length of the longest palindrome ` `def` `longestPalSubstr(string): ` `    ``maxLength ``=` `1` ` `  `    ``start ``=` `0` `    ``length ``=` `len``(string) ` ` `  `    ``low ``=` `0` `    ``high ``=` `0` ` `  `    ``# One by one consider every character as center point of  ` `    ``# even and length palindromes ` `    ``for` `i ``in` `xrange``(``1``, length): ` `        ``# Find the longest even length palindrome with center ` `    ``# points as i-1 and i. ` `        ``low ``=` `i ``-` `1` `        ``high ``=` `i ` `        ``while` `low >``=` `0` `and` `high < length ``and` `string[low] ``=``=` `string[high]: ` `            ``if` `high ``-` `low ``+` `1` `> maxLength: ` `                ``start ``=` `low ` `                ``maxLength ``=` `high ``-` `low ``+` `1` `            ``low ``-``=` `1` `            ``high ``+``=` `1` ` `  `        ``# Find the longest odd length palindrome with center  ` `        ``# point as i ` `        ``low ``=` `i ``-` `1` `        ``high ``=` `i ``+` `1` `        ``while` `low >``=` `0` `and` `high < length ``and` `string[low] ``=``=` `string[high]: ` `            ``if` `high ``-` `low ``+` `1` `> maxLength: ` `                ``start ``=` `low ` `                ``maxLength ``=` `high ``-` `low ``+` `1` `            ``low ``-``=` `1` `            ``high ``+``=` `1` ` `  `    ``print` `"Longest palindrome substring is:"``, ` `    ``print` `string[start:start ``+` `maxLength] ` ` `  `    ``return` `maxLength ` ` `  `# Driver program to test above functions ` `string ``=` `"forgeeksskeegfor"` `print` `"Length is: "` `+` `str``(longestPalSubstr(string)) ` ` `  `# This code is contributed by BHAVYA JAIN `

 `// C# implementation of O(n^2) time  ` `// and O(1) space method to find the ` `// longest palindromic substring  ` `using` `System; ` ` `  `class` `GFG ` `{ ` `// A utility function to print  ` `// a substring str[low..high]  ` `public` `static` `void` `printSubStr(``string` `str,   ` `                               ``int` `low, ``int` `high) ` `{ ` `    ``Console.WriteLine(str.Substring(low,  ` `                     ``(high + 1) - low)); ` `} ` ` `  `// This function prints the longest  ` `// palindrome substring (LPS) of str[].  ` `// It also returns the length of the  ` `// longest palindrome  ` `public` `static` `int` `longestPalSubstr(``string` `str) ` `{ ` `    ``int` `maxLength = 1; ``// The result (length of LPS) ` ` `  `    ``int` `start = 0; ` `    ``int` `len = str.Length; ` ` `  `    ``int` `low, high; ` ` `  `    ``// One by one consider every  ` `    ``// character as center point ` `    ``// of even and length palindromes  ` `    ``for` `(``int` `i = 1; i < len; ++i) ` `    ``{ ` `        ``// Find the longest even length  ` `        ``// palindrome with center points  ` `        ``// as i-1 and i.  ` `        ``low = i - 1; ` `        ``high = i; ` `        ``while` `(low >= 0 && high < len &&  ` `               ``str[low] == str[high]) ` `        ``{ ` `            ``if` `(high - low + 1 > maxLength) ` `            ``{ ` `                ``start = low; ` `                ``maxLength = high - low + 1; ` `            ``} ` `            ``--low; ` `            ``++high; ` `        ``} ` ` `  `        ``// Find the longest odd length  ` `        ``// palindrome with center point as i  ` `        ``low = i - 1; ` `        ``high = i + 1; ` `        ``while` `(low >= 0 && high < len &&  ` `               ``str[low] == str[high]) ` `        ``{ ` `            ``if` `(high - low + 1 > maxLength) ` `            ``{ ` `                ``start = low; ` `                ``maxLength = high - low + 1; ` `            ``} ` `            ``--low; ` `            ``++high; ` `        ``} ` `    ``} ` ` `  `    ``Console.Write(``"Longest palindrome substring is: "``); ` `    ``printSubStr(str, start, start + maxLength - 1); ` ` `  `    ``return` `maxLength; ` `} ` ` `  `// Driver Code ` `public` `static` `void` `Main(``string``[] args) ` `{ ` `    ``string` `str = ``"forgeeksskeegfor"``; ` `    ``Console.WriteLine(``"Length is: "` `+ ` `                       ``longestPalSubstr(str)); ` `} ` `} ` ` `  `// This code is contributed by Shrikant13 `

 `= 0 && ``\$high` `< ``\$len` `&& ``\$str``[``\$low``] == ``\$str``[``\$high``]) ` `        ``{ ` `            ``if` `(``\$high` `- ``\$low` `+ 1 > ``\$maxLength``) ` `            ``{ ` `                ``\$start` `= ``\$low``; ` `                ``\$maxLength` `= ``\$high` `- ``\$low` `+ 1; ` `            ``} ` `            ``--``\$low``; ` `            ``++``\$high``; ` `        ``} ` `  `  `        ``// Find the longest odd length palindrome with center  ` `        ``// point as i ` `        ``\$low` `= ``\$i` `- 1; ` `        ``\$high` `= ``\$i` `+ 1; ` `        ``while` `(``\$low` `>= 0 && ``\$high` `< ``\$len` `&& ``\$str``[``\$low``] == ``\$str``[``\$high``]) ` `        ``{ ` `            ``if` `(``\$high` `- ``\$low` `+ 1 > ``\$maxLength``) ` `            ``{ ` `                ``\$start` `= ``\$low``; ` `                ``\$maxLength` `= ``\$high` `- ``\$low` `+ 1; ` `            ``} ` `            ``--``\$low``; ` `            ``++``\$high``; ` `        ``} ` `    ``} ` `  `  `    ``echo` `"Longest palindrome substring is: "``; ` `    ``printSubStr(``\$str``, ``\$start``, ``\$start` `+ ``\$maxLength` `- 1); ` `  `  `    ``return` `\$maxLength``; ` `} ` `  `  `// Driver program to test above functions ` ` `  `\$str` `= ``"forgeeksskeegfor"``; ` `echo` `"\nLength is: "``. longestPalSubstr( ``\$str` `) ; ` `return` `0; ` `?> `

Output:

```Longest palindrome substring is: geeksskeeg
Length is: 10```

Time complexity: O ( n^2 ) where n is the length of input string.
Auxiliary Space: O ( 1 )

We will soon be adding more optimized method as separate post.

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

Improved By : shrikanth13, Ita_c, rathbhupendra

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