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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")

>>> min_distance_bottom_up("intention", "")

>>> min_distance_bottom_up("", "")

"""

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 ***************")

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