JavaAlgorithms/DynamicProgramming/PalindromicPartitioning.java

package DynamicProgramming;

import java.util.Scanner;

/**
 * @file
 * @brief Implements [Palindrome
 * Partitioning](https://leetcode.com/problems/palindrome-partitioning-ii/)
 * algorithm, giving you the minimum number of partitions you need to make
 *
 * @details
 * palindrome partitioning uses dynamic programming and goes to all the possible
 * partitions to find the minimum you are given a string and you need to give
 * minimum number of partitions needed to divide it into a number of palindromes
 * [Palindrome Partitioning]
 * (https://www.geeksforgeeks.org/palindrome-partitioning-dp-17/) overall time
 * complexity O(n^2) For example: example 1:- String : "nitik" Output : 2 => "n
 * | iti | k" For example: example 2:- String : "ababbbabbababa" Output : 3 =>
 * "aba | b | bbabb | ababa"
 * @author [Syed] (https://github.com/roeticvampire)
 */
public class PalindromicPartitioning {
  
    public static int minimalpartitions(String word){
        int len=word.length();
        /* We Make two arrays to create a bottom-up solution.
           minCuts[i] = Minimum number of cuts needed for palindrome partitioning of substring word[0..i]
           isPalindrome[i][j] = true if substring str[i..j] is palindrome
           Base Condition: C[i] is 0 if P[0][i]= true
        */
           int[] minCuts = new int[len];
           boolean[][] isPalindrome = new boolean[len][len];
    
           int i, j, L; // different looping variables
    
           // Every substring of length 1 is a palindrome
           for (i = 0; i < len; i++) {
               isPalindrome[i][i] = true;
           }
    
           /* L is substring length. Build the solution in bottom up manner by considering all substrings of length starting from 2 to n. */
           for (L = 2; L <= len; L++) {
               // For substring of length L, set different possible starting indexes
               for (i = 0; i < len - L + 1; i++) {
                   j = i + L - 1; // Ending index
                   // If L is 2, then we just need to
                   // compare two characters. Else need to
                   // check two corner characters and value
                   // of P[i+1][j-1]
                   if (L == 2)
                       isPalindrome[i][j] = (word.charAt(i) == word.charAt(j));
                   else
                       {
                        if((word.charAt(i) == word.charAt(j)) && isPalindrome[i + 1][j - 1])
                        isPalindrome[i][j] =true;
                        else 
                        isPalindrome[i][j]=false;

                    }      
                }
           }
    
           //We find the minimum for each index
           for (i = 0; i < len; i++) {
               if (isPalindrome[0][i] == true) 
                   minCuts[i] = 0;
               else {
                   minCuts[i] = Integer.MAX_VALUE;
                   for (j = 0; j < i; j++) {
                       if (isPalindrome[j + 1][i] == true && 1 + minCuts[j] < minCuts[i])
                           minCuts[i] = 1 + minCuts[j];
                   }
               }
           }
    
           // Return the min cut value for complete
           // string. i.e., str[0..n-1]
           return minCuts[len - 1];
    }



  public static void main(String[] args) {
    Scanner input = new Scanner(System.in);
    String word;
    System.out.println("Enter the First String");
    word = input.nextLine();
    // ans stores the final minimal cut count needed for partitioning
    int ans = minimalpartitions(word);
    System.out.println(
        "The minimum cuts needed to partition \"" + word + "\" into palindromes is " + ans);
    input.close();
  }
}