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- import collections
- import itertools
- import re
-
-
- def part1(H):
- """
- 2 variables, 2 equations
-
- px1 + vx1 * t1 == px2 + vx2 * t2
- py1 + vy1 * t1 == py2 + vy2 * t2
-
- t1 = (px2 - px1) / vx1 + (vx2 / vx1) * t2
- t1 = (py2 - py1) / vy1 + (vy2 / vy1) * t2
-
- (px2 - px1) / vx1 - (py2 - py1) / vy1 = (vy2 / vy1 - vx2 / vx1) * t2
- t2 = c1 / c2
- c1 = (px2 - px1) / vx1 - (py2 - py1) / vy1
- c2 = (vy2 / vy1 - vx2 / vx1)
- """
- n = 0
- lo, hi = (7, 27) if len(H) < 100 else (2e14, 4e14)
- for aa, bb in itertools.combinations(H, 2):
- px1, py1, pz1, vx1, vy1, vz1 = aa
- px2, py2, pz2, vx2, vy2, vz2 = bb
-
- c1 = (px2 - px1) / vx1 - (py2 - py1) / vy1
- c2 = (vy2 / vy1 - vx2 / vx1)
- if c2 == 0: continue
- t2 = (c1 / c2)
- t1 = (px2 - px1) / vx1 + (vx2 / vx1) * t2
- if t1 <= 0 or t2 <= 0: continue
- if not lo < px1 + vx1 * t1 < hi: continue
- if not lo < py1 + vy1 * t1 < hi: continue
- if not lo < px2 + vx2 * t2 < hi: continue
- if not lo < py2 + vy2 * t2 < hi: continue
- n += 1
- return n
-
-
- def part2(H):
- """
- 6 + t variables, 3 * t equations
- """
- try:
- import z3
- except:
- return 'Need z3-solver'
- Q = {k: z3.Real(k) for k in 'px py pz vx vy vz t0 t1 t2'.split()}
- solver = z3.Solver()
- solver.add(H[0].px + H[0].vx * Q['t0'] == Q['px'] + Q['vx'] * Q['t0'])
- solver.add(H[0].py + H[0].vy * Q['t0'] == Q['py'] + Q['vy'] * Q['t0'])
- solver.add(H[0].pz + H[0].vz * Q['t0'] == Q['pz'] + Q['vz'] * Q['t0'])
- solver.add(H[1].px + H[1].vx * Q['t1'] == Q['px'] + Q['vx'] * Q['t1'])
- solver.add(H[1].py + H[1].vy * Q['t1'] == Q['py'] + Q['vy'] * Q['t1'])
- solver.add(H[1].pz + H[1].vz * Q['t1'] == Q['pz'] + Q['vz'] * Q['t1'])
- solver.add(H[2].px + H[2].vx * Q['t2'] == Q['px'] + Q['vx'] * Q['t2'])
- solver.add(H[2].py + H[2].vy * Q['t2'] == Q['py'] + Q['vy'] * Q['t2'])
- solver.add(H[2].pz + H[2].vz * Q['t2'] == Q['pz'] + Q['vz'] * Q['t2'])
- solver.check()
- model = solver.model()
- return model.eval(Q['px'] + Q['py'] + Q['pz'])
-
-
- text = open(0).read()
- Hail = collections.namedtuple('Hail', 'px py pz vx vy vz')
- H = [Hail(*[int(n) for n in re.findall(r'-?\d+', line)]) for line in text.splitlines()]
- print(part1(H))
- print(part2(H))
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