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"""

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.

"""

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__":

solver = EditDistance()

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

print()

S1 = input("Enter the first string: ").strip()

S2 = input("Enter the second string: ").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 ***************")