diff options
| -rw-r--r-- | 17.py | 42 |
1 files changed, 27 insertions, 15 deletions
@@ -1,5 +1,6 @@ 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+)')) @@ -15,23 +16,34 @@ def sum_n(n): print(sum_n(vy_max)) def time_at_pos(v, d): - """d = - (t + 1)(t - 2v) / 2 solved for t""" - return (sqrt((2 * v + 1) ** 2 - 8 * d) + 2 * v - 1) / 2 + 1 + """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 = time_at_pos(vy0, ty_max) - end = time_at_pos(vy0, ty_min) - return range(ceil(start), floor(end) + 1) + start = ceil(time_at_pos(vy0, ty_max)[1]) + end = floor(time_at_pos(vy0, ty_min)[1]) + return start, end -def x_at(vx0, t): - assert(t >= 0) - return sum_n(vx0) - sum_n(max(vx0 - t, 0)) +def x_times(vx0): + start = time_at_xpos(vx0, tx_min) + end = time_at_xpos(vx0, tx_max) + return start, end -count = 0 +times = defaultdict(set) for vy0 in range(vy_min, vy_max + 1): - for vx0 in range(vx_min, vx_max + 1): - for t in y_times(vy0): - if tx_min <= x_at(vx0, t) <= tx_max: - count += 1 - break -print(count) + 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)) |