manachers_algorithm.cpp

//Manacher Algorithm
/*To find the longest palindromic substring from a string, we can use Manacher’s Algorithm. By selecting each character, we will try to find if there any palindrome using left and right pointer. There is another array to store information, from that information we can easily find how long the palindrome is. For each character, the array will store information. After traversing the whole string, we can find the longest palindromic subsequence from the created array.

The time complexity of this algorithm is O(n).*/
/*Enter String: levelup
Longest palindrome is: level*/

#include<iostream>
using namespace std;

int min(int a, int b) {
   return (a<b)?a:b;
}

string longestPalindrome(string mainString) {
   int n = mainString.size();
   if(n == 0)
      return "";
   n = 2*n + 1; //count the next position
   int longPal[n]; //array to store longest palindrome length
   longPal[0] = 0; longPal[1] = 1;
   int centerIndex = 1;
   int rightIndex = 2;
   int right = 0, left;
   int maxPalLength = 0, maxCenterIndex = 0;
   int start = -1, end = -1, diff = -1;

   for (right = 2; right < n; right++) {
      left  = 2*centerIndex-right; //calculate left position using center and right
      longPal[right] = 0;
      diff = rightIndex - right;

      if(diff > 0)
         longPal[right] = min(longPal[left], diff);
      while ( ((right + longPal[right]) < n && (right - longPal[right]) > 0) &&
         ( ((right + longPal[right] + 1) % 2 == 0) ||
         (mainString[(right + longPal[right] + 1)/2] == mainString[(right - longPal[right] - 1)/2] ))) {
         longPal[right]++;
      }

      if(longPal[right] > maxPalLength) {    //max palindrome length
         maxPalLength = longPal[right];
         axCenterIndex = right;
      }

      if (right + longPal[right] > rightIndex) {
         centerIndex = right;
         rightIndex = right + longPal[right];
      }
   }

   start = (maxCenterIndex - maxPalLength)/2;
   end = start + maxPalLength - 1;
   string palindrome;

   for(int i=start; i<=end; i++)
      palindrome += mainString[i];
      return palindrome;
}

int main(int argc, char *argv[]) {
   string mainString, palindrome;
   cout << "Enter String:";
   cin >> mainString;
   palindrome = longestPalindrome(mainString);
   cout << "Longest palindrome is: " << palindrome << endl;
}