from typing import List


def levenshtein_distance(s1: str, s2: str) -> int:
    """Return the Levenshtein distance between two strings,
    using the Wagner-Fischer iterative algorithm.

    This function is based on code from https://github.com/toastdriven/pylev:

    Copyright (c) 2012, Daniel Lindsley
    All rights reserved.

    Redistribution and use in source and binary forms, with or without
    modification, are permitted provided that the following conditions are met:

        * Redistributions of source code must retain the above copyright
        notice, this list of conditions and the following disclaimer.
        * Redistributions in binary form must reproduce the above copyright
        notice, this list of conditions and the following disclaimer in the
        documentation and/or other materials provided with the distribution.
        * Neither the name of the pylev nor the
        names of its contributors may be used to endorse or promote products
        derived from this software without specific prior written permission.

    THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
    ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
    WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
    DISCLAIMED. IN NO EVENT SHALL pylev BE LIABLE FOR ANY
    DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
    (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
    LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
    ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
    (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
    SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
    """
    if s1 == s2:
        return 0

    len_1 = len(s1)
    len_2 = len(s2)

    if len_1 == 0:
        return len_2
    if len_2 == 0:
        return len_1

    if len_1 > len_2:
        s2, s1 = s1, s2
        len_2, len_1 = len_1, len_2

    d0: List[int] = [i for i in range(len_2 + 1)]
    d1: List[int] = [j for j in range(len_2 + 1)]

    cost: int
    x_cost: int
    y_cost: int

    for i in range(len_1):
        d1[0] = i + 1
        for j in range(len_2):
            cost = d0[j]

            if s1[i] != s2[j]:
                # Substitution
                cost += 1

                # Insertion
                x_cost = d1[j] + 1
                if x_cost < cost:
                    cost = x_cost

                # Deletion
                y_cost = d0[j + 1] + 1
                if y_cost < cost:
                    cost = y_cost

            d1[j + 1] = cost

        d0, d1 = d1, d0

    return d0[-1]