def editDistance(source: str, target: str) -> int:
    n: int = len(source)
    m: int = len(target)

    if n < m:
        return editDistance(target, source)

    prev: list[int] = [*range(-~m)]

    for i in range(1, -~n):
        current : list[int] = [i] + [0] * m

        for j in range(1, -~m):
            if source[~-i] == target[~-j]:
                current[j] = prev[~-j]
            else:
                current[j] = 1 + min(prev[j], current[~-j], prev[~-j])
        
        prev = current

    return prev[m]