wait for it

approach

for a race of length time, holding the button for i gives a distance of i * (time - i). num_ways counts the i that beat the record by trying them all.

part 1 multiplies the counts over every race. part 2 joins the digits of the times and of the distances into one big race and runs the same brute-force count on it, which is still quick enough.

the trick

the distance is i * (time - i), so just count the hold times that beat the record.

def num_ways(time, record):
    res = sum(1 for i in range(time+1) if (d := i * (time - i)) > record)
    return res

def part1(time, distance):
    res = 1
    for t, d in zip(time, distance):
        res *= num_ways(t, d)
    return res

def part2(time, distance):
    time = int("".join(map(str, time)))
    distance = int("".join(map(str, distance)))
    return num_ways(time, distance)