## Python, dynamic_programming, edit_distance.py

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