#### Edit Distance

```"""
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 ***************")
```  