Longest Palindromic Substring

Dynamic ProgrammingData StructureAlgorithms

In a given string, we have to find a substring, which is a palindrome and it is longest.

To get the longest palindromic substring, we have to solve many subproblems, some of the subproblems are overlapping. They are needed to be solved for multiple times. For that reason, the Dynamic programming is helpful. Using a table, we can store the result of the previous subproblems, and simply use them to generate further results.

Input and Output

Input:
A String. Say “thisispalapsiti”
Output:
The palindrome substring and the length of the palindrome.
Longest palindrome substring is: ispalapsi
Length is: 9

Algorithm

findLongPalSubstr(str)

Input − The main string.

Output − Longest palindromic substring and its length.

Begin
   n := length of the given string
   create a n x n table named palTab to store true or false value
   fill patTab with false values
   maxLen := 1

   for i := 0 to n-1, do
      patTab[i, i] = true       //as it is palindrome of length 1
   done

   start := 0
   for i := 0 to n-2, do
      if str[i] = str[i-1], then
         palTab[i, i+1] := true
         start := i
         maxLen := 2
   done

   for k := 3 to n, do
      for i := 0 to n-k, do
         j := i + k – 1
         if palTab[i+1, j-1] and str[i] = str[j], then
            palTab[i, j] := true
            if k > maxLen, then
               start := i
               maxLen := k
      done
   done
   display substring from start to maxLen from str, and return maxLen
 End

Example

#include<iostream>
using namespace std;

int findLongPalSubstr(string str) {
   int n = str.size();        // get length of input string
 
   bool palCheckTab[n][n];    //true when substring from i to j is palindrome
   
   for(int i = 0; i<n; i++)
      for(int j = 0; j<n; j++)
         palCheckTab[i][j] = false;      //initially set all values to false
 
   int maxLength = 1;
   
   for (int i = 0; i < n; ++i)
      palCheckTab[i][i] = true;       //as all substring of length 1 is palindrome
 
   int start = 0;
   for (int i = 0; i < n-1; ++i) {
      if (str[i] == str[i+1]) {      //for two character substring both characters are equal
         palCheckTab[i][i+1] = true;
         start = i;
         maxLength = 2;
      }
   }
 
   for (int k = 3; k <= n; ++k) {       //for substrings with length 3 to n
      for (int i = 0; i < n-k+1 ; ++i) {
         int j = i + k - 1;
         if (palCheckTab[i+1][j-1] && str[i] == str[j]) {    //if (i,j) and (i+1, j-1) are same, then check palindrome
            palCheckTab[i][j] = true;
            if (k > maxLength) {
               start = i;
               maxLength = k;
            }
         }
      }
   }
   cout << "Longest palindrome substring is: " << str.substr(start, maxLength) << endl;
   return maxLength; // return length
}
 
int main() {
   char str[] = "thisispalapsiti";
   cout << "Length is: "<< findLongPalSubstr(str);
}

Output

Longest palindrome substring is: ispalapsi
Length is: 9
raja
Published on 11-Jul-2018 07:53:53
Advertisements