"""
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 first word index is overflow - delete all from the second word
        if index1 >= len_word1:
            return len_word2 - index2
        # if second word index is overflow - delete all from the first word
        if index2 >= len_word2:
            return len_word1 - index1
        diff = int(word1[index1] != word2[index2])  # current letters not identical
        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()