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from math import sqrt, ceil, floor
from utils import parse_day
from collections import defaultdict
tx_min, tx_max, ty_min, ty_max = \
map(int, parse_day(17, r'.* x=(-?\d+)..(-?\d+), y=(-?\d+)..(-?\d+)'))
vx_min = int(sqrt(tx_min * 2) - 1)
vx_max = tx_max
vy_min = ty_min
vy_max = abs(ty_min) - 1
def sum_n(n):
return n * (n + 1) // 2
print(sum_n(vy_max))
def time_at_pos(v, d):
"""d = -t(t - 2v - 1) / 2 solved for t"""
middle = sqrt((2 * v + 1) ** 2 - 8 * d)
return (-middle + 2 * v + 1) / 2, (middle + 2 * v + 1) / 2
def time_at_xpos(v, d):
if d > sum_n(v): return float('inf')
return time_at_pos(v, d)[0]
def y_times(vy0):
start = ceil(time_at_pos(vy0, ty_max)[1])
end = floor(time_at_pos(vy0, ty_min)[1])
return start, end
def x_times(vx0):
start = time_at_xpos(vx0, tx_min)
end = time_at_xpos(vx0, tx_max)
return start, end
times = defaultdict(set)
for vy0 in range(vy_min, vy_max + 1):
tmin, tmax = y_times(vy0)
for t in range(tmin, tmax + 1):
times[t].add(vy0)
points = set()
for vx0 in range(vx_min, vx_max + 1):
tmin, tmax = x_times(vx0)
for t, vy0set in times.items():
if tmin <= t <= tmax:
for vy0 in vy0set:
points.add((vx0, vy0))
print(len(points))
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