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| -rw-r--r-- | 24.py | 84 |
1 files changed, 84 insertions, 0 deletions
@@ -0,0 +1,84 @@ +from dataclasses import dataclass +from functools import cache +from itertools import combinations +from sys import stdin + +from z3 import z3 + + +@dataclass(frozen=True, slots=True) +class Vec: + x: float + y: float + z: float + + def __str__(self) -> str: + return f"{self.x}, {self.y}, {self.z}" + + +@dataclass(frozen=True, slots=True) +class Hailstone: + pos: Vec + vel: Vec + + @property + @cache + def m(self) -> float: + return self.vel.y / self.vel.x + + @property + @cache + def c(self) -> float: + return self.pos.y - self.pos.x / self.vel.x * self.vel.y + + def __str__(self) -> str: + return f"{self.pos} @ {self.vel}" + + +inp: list[Hailstone] = list() +for line in stdin: + pos, vel = line.rstrip("\n").split(" @ ") + pos = Vec(*map(float, pos.split(", "))) + vel = Vec(*map(float, vel.split(", "))) + inp.append(Hailstone(pos, vel)) + + +def intersection(a: Hailstone, b: Hailstone) -> tuple[float, float] | None: + numer = b.c - a.c + denom = a.m - b.m + if denom == 0: + return None + xi = numer / denom + return xi, xi * a.m + a.c + + +lbound = 200000000000000 +ubound = 400000000000000 + +p1 = 0 +for a, b in combinations(inp, 2): + inter = intersection(a, b) + if inter is None: + continue + ix, iy = inter + a_dist = (ix - a.pos.x) / a.vel.x + b_dist = (ix - b.pos.x) / b.vel.x + if ( + a_dist >= 0 + and b_dist >= 0 + and lbound <= ix <= ubound + and lbound <= iy <= ubound + ): + p1 += 1 +print(p1) + +a, b, c, x, y, z = (z3.Int(c) for c in "abcxyz") +s = z3.Solver() +for i, m in enumerate("tuvw"): + m = z3.Int(m) + h = inp[i] + s.add(h.pos.x + h.vel.x * m == x + a * m) + s.add(h.pos.y + h.vel.y * m == y + b * m) + s.add(h.pos.z + h.vel.z * m == z + c * m) +s.check() +print(s.model().eval(x + y + z)) |