understand algorithm which implement variant of levenshtein distance

script.py

# https://stackoverflow.com/q/41275345/
def dist(s1, s2):
    cur = list(range(len(s2) + 1))
    prev = [0] * (len(s2) + 1)
    print(f"{cur=}")
    print(f"{prev=}")
    input()
    for i in range(len(s1)):
        cur, prev = prev, cur
        cur[0] = i + 1
        print(f"--{i=} {cur[0]=}")
        print(f"--{cur=}")
        print(f"--{prev=}")
        input()
        for j in range(len(s2)):
            # deletion 1 operation
            # substitution 2 operation (deletion and insertion)
            sub = 0 if s1[i] == s2[j] else 2
            cur[j+1] = min(prev[j] + sub, cur[j] + 1, prev[j+1] + 1)
            print(f"----{s1=} {s2=}")
            print(f"----{s1[:i+1]=} {s2[:j+1]=}")
            print(f"----{j=} {s1[i]=} {s2[j]=}")
            print(f"----{prev[j]=} {sub=} {cur[j]=} {prev[j+1]=}")
            print(f"----{(prev[j] + sub)=} {(cur[j] + 1)=} {(prev[j+1] + 1)=}")
            print(f"----{cur[j+1]=}")
            print(f"----{cur=}")
            print(f"----{prev=}")
            input()

    return cur[-1]

cases=[
    # ('cat','bat'),
    # ('bat','cat'),
    ('broom', 'ballroom'),
    # ('boat','got'),
    # ('foo', 'bar'),
    # ('foobar', '')
]

for s1, s2 in cases:
    print(f"{s1=} {s2=}")
    print(f"{dist(s1, s2)=}")