def levenshtein_dist(s1: str, s2: str) -> int:
    if len(s1) < len(s2):
        return levenshtein_dist(s2, s1)

    # len(s1) >= len(s2)
    if len(s2) == 0:
        return len(s1)

    previous_row = range(len(s2) + 1)
    for i, c1 in enumerate(s1):
        current_row = [i + 1]
        for j, c2 in enumerate(s2):
            # j+1 instead of j since previous_row and current_row are one character longer
            insertions = previous_row[j + 1] + 1
            deletions = current_row[j] + 1  # than s2
            substitutions = previous_row[j] + (c1 != c2)
            current_row.append(min(insertions, deletions, substitutions))
        previous_row = current_row

    return previous_row[-1]