/* --------------------------------------------------------
   This program is derived from Gotoh1f_lin_space.java 

      I used double type cost
   -------------------------------------------------------- */



import java.util.*;

public class Myers
{

   public static double CC[];   // Min cost (overall)
   public static double DD[];   // Min cost that ends in delete x_i

   public static double e, c, s, t;


   public static double g = 2;        // Gap opening cost
   public static double h = .5;       // Gap continuation cost

   public static double w( char a, char b )
   {
      if ( a == b )
         return 0;
      else
	 return 1;
   }




   public static double solveMinAlignCost(String x, String y )
   {
      int i, j;
      int m, n;

      m = x.length();
      n = y.length();


      CC[0] = 0;

      t = g;
      
      for (j = 1; j <= n ; j++)
      {
         CC[j] = t = t + h;         // C(0,j) = gap(j) = g + j*h
         DD[j] = t + g;             // D(0,j) = C(0,j) + g (def)
      }

      t = g;

      for (i = 1; i <= m; i++) 
      {

         s = CC[0];

         CC[0] = c = t = t + h;     // C(i,0) = gap(i) = g + i*h

         e = t + g;                 // I(i,0) = C(i,0) + g (def)

         for (j = 1; j <= n; j++)
	 {
             e = min2 ( e+h, c+g+h ); 

             DD[j] = min2 ( DD[j]+h, CC[j] + g + h );
                 // DD[1][j] = min2 ( DD[0][j]+h   , CC[0][j]+g+h );

	     c = min3 ( DD[j], e, s + w( x.charAt(i-1), y.charAt(j-1) ) );

	     s = CC[j];

	     CC[j] = c;
	         // CC[1][j] = min3 ( DD[1][j], II[1][j], 
		 //       CC[0][j-1] + w( x.charAt(i-1), y.charAt(j-1) )  );
         }
      }

      return CC[n];

   }

   public static double min2( double x, double y )
   {
      return ( x < y ? x : y );
   }

   public static double min3( double x, double y, double z )
   {
      double m = ( x < y ? x : y );

      return ( m < z ? m : z );
   }

   public static void main(String[] args)
   {

       Scanner in = new Scanner(System.in);

       String x;
       String y;
       int i, j;

       double minCost;

       System.out.print("x = ");
       x = in.next();
       System.out.print("y = ");
       y = in.next();

/*
       x = "AAAA";
       y = "AAA";
*/

       CC = new double[y.length()+1];    // Linear space !
       DD = new double[y.length()+1];

       minCost = solveMinAlignCost(x, y);

       System.out.println("x = " + x);
       System.out.println("y = " + y);
       System.out.println("Min. Align. Cost = " + minCost );

       System.out.println();
       System.out.println();

   }

}