"""
Author  : Turfa Auliarachman
Date    : October 12, 2016

This is a pure Python implementation of Dynamic Programming solution to the edit distance problem.

The problem is :
Given two strings A and B. Find the minimum number of operations to string B such that A = B. The permitted operations are removal,  insertion, and substitution.
"""
from __future__ import print_function


class EditDistance:
    """
    Use :
    solver              = EditDistance()
    editDistanceResult  = solver.solve(firstString, secondString)
    """

    def __init__(self):
        self.__prepare__()

    def __prepare__(self, N = 0, M = 0):
        self.dp = [[-1 for y in range(0,M)] for x in range(0,N)]

    def __solveDP(self, x, y):
        if (x==-1):
            return y+1
        elif (y==-1):
            return x+1
        elif (self.dp[x][y]>-1):
            return self.dp[x][y]
        else:
            if (self.A[x]==self.B[y]):
                self.dp[x][y] = self.__solveDP(x-1,y-1)
            else:
                self.dp[x][y] = 1+min(self.__solveDP(x,y-1), self.__solveDP(x-1,y), self.__solveDP(x-1,y-1))

            return self.dp[x][y]

    def solve(self, A, B):
        if isinstance(A,bytes):
            A = A.decode('ascii')

        if isinstance(B,bytes):
            B = B.decode('ascii')

        self.A = str(A)
        self.B = str(B)

        self.__prepare__(len(A), len(B))

        return self.__solveDP(len(A)-1, len(B)-1)

if __name__ == '__main__':
        try:
            raw_input          # Python 2
        except NameError:
            raw_input = input  # Python 3

        solver = EditDistance()

        print("****************** Testing Edit Distance DP Algorithm ******************")
        print()

        print("Enter the first string: ", end="")
        S1 = raw_input().strip()

        print("Enter the second string: ", end="")
        S2 = raw_input().strip()

        print()
        print("The minimum Edit Distance is: %d" % (solver.solve(S1, S2)))
        print()
        print("*************** End of Testing Edit Distance DP Algorithm ***************")