"""
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)


def min_distance_bottom_up(word1: str, word2: str) -> int:
 """
 >>> min_distance_bottom_up("intention", "execution")
 5
 >>> min_distance_bottom_up("intention", "")
 9
 >>> min_distance_bottom_up("", "")
 0
 """
 m = len(word1)
 n = len(word2)
 dp = [[0 for _ in range(n+1) ] for _ in range(m+1)]
 for i in range(m+1):
 for j in range(n+1):
 
 if i == 0: #first string is empty
 dp[i][j] = j
 elif j == 0: #second string is empty 
 dp[i][j] = i 
 elif word1[i-1] == word2[j-1]: #last character of both substing is equal
 dp[i][j] = dp[i-1][j-1]
 else: 
 insert = dp[i][j-1]
 delete = dp[i-1][j]
 replace = dp[i-1][j-1]
 dp[i][j] = 1 + min(insert, delete, replace)
 return dp[m][n]

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