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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.word1 = ""

self.word2 = ""

self.dp = []

def __min_dist_top_down_dp(self, m: int, n: int) -> int:

if m == -1:

return n + 1

elif n == -1:

return m + 1

elif self.dp[m][n] > -1:

return self.dp[m][n]

else:

if self.word1[m] == self.word2[n]:

self.dp[m][n] = self.__min_dist_top_down_dp(m - 1, n - 1)

else:

insert = self.__min_dist_top_down_dp(m, n - 1)

delete = self.__min_dist_top_down_dp(m - 1, n)

replace = self.__min_dist_top_down_dp(m - 1, n - 1)

self.dp[m][n] = 1 + min(insert, delete, replace)

return self.dp[m][n]

def min_dist_top_down(self, word1: str, word2: str) -> int:

"""

>>> EditDistance().min_dist_top_down("intention", "execution")

5

>>> EditDistance().min_dist_top_down("intention", "")

9

>>> EditDistance().min_dist_top_down("", "")

0

"""

self.word1 = word1

self.word2 = word2

self.dp = [[-1 for _ in range(len(word2))] for _ in range(len(word1))]

return self.__min_dist_top_down_dp(len(word1) - 1, len(word2) - 1)

def min_dist_bottom_up(self, word1: str, word2: str) -> int:

"""

>>> EditDistance().min_dist_bottom_up("intention", "execution")

5

>>> EditDistance().min_dist_bottom_up("intention", "")

9

>>> EditDistance().min_dist_bottom_up("", "")

0

"""

self.word1 = word1

self.word2 = word2

m = len(word1)

n = len(word2)

self.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

self.dp[i][j] = j

elif j == 0: # second string is empty

self.dp[i][j] = i

elif word1[i - 1] == word2[j - 1]: # last characters are equal

self.dp[i][j] = self.dp[i - 1][j - 1]

else:

insert = self.dp[i][j - 1]

delete = self.dp[i - 1][j]

replace = self.dp[i - 1][j - 1]

self.dp[i][j] = 1 + min(insert, delete, replace)

return self.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(f"The minimum edit distance is: {solver.min_dist_top_down(S1, S2)}")

print(f"The minimum edit distance is: {solver.min_dist_bottom_up(S1, S2)}")

print()

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