"""
Author : Alexander Pantyukhin
Date : October 14, 2022
This is implementation Dynamic Programming up bottom approach
to find edit distance.
The aim is to demonstate up bottom approach for solving the task.
The implementation was tested on the
leetcode: https://leetcode.com/problems/edit-distance/
Levinstein distance
Dynamic Programming: up -> down.
"""
import functools
def min_distance_up_bottom(word1: str, word2: str) -> int:
"""
>>> min_distance_up_bottom("intention", "execution")
5
>>> min_distance_up_bottom("intention", "")
9
>>> min_distance_up_bottom("", "")
0
>>> min_distance_up_bottom("zooicoarchaeologist", "zoologist")
10
"""
len_word1 = len(word1)
len_word2 = len(word2)
@functools.cache
def min_distance(index1: int, index2: int) -> int:
if index1 >= len_word1:
return len_word2 - index2
if index2 >= len_word2:
return len_word1 - index1
diff = int(word1[index1] != word2[index2])
return min(
1 + min_distance(index1 + 1, index2),
1 + min_distance(index1, index2 + 1),
diff + min_distance(index1 + 1, index2 + 1),
)
return min_distance(0, 0)
if __name__ == "__main__":
import doctest
doctest.testmod()