109 lines
2.6 KiB
Python
109 lines
2.6 KiB
Python
class Vector:
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def __init__(self, x, y):
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self.x = x
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self.y = y
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def __add__(self, v2):
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return Vector(self.x + v2.x, self.y + v2.y)
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def __sub__(self, v2):
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return Vector(self.x - v2.x, self.y - v2.y)
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def __mul__(self, v2):
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if isinstance(v2, int):
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return Vector(self.x * v2, self.y * v2)
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else:
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return Vector(self.x * v2.x, self.y * v2.y)
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__rmul__ = __mul__
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def __str__(self):
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return "{" + str(self.x) + ", " + str(self.y) + "}"
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def __repr__(self):
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return "{" + str(self.x) + ", " + str(self.y) + "}"
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def mag(self):
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# Magnitude squared. For our scenario, this is
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# irrelvant, since sqrt is a monotonic function.
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# Caches magnitude, need to update manually.
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self.magnitude = self.x**2 + self.y**2
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return self
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def whole(self):
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# Gets reduced form of vector for parallel comparison.
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# Caches, need to update manually
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if self.x == 0 and self.y == 0:
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self.whole = (0,0)
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elif self.x == 0:
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self.whole = (0, sgn(self.y))
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elif self.y == 0:
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self.whole = (sgn(self.x), 0)
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else:
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d = gcd(abs(self.x), abs(self.y))
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self.whole = (self.x/d, self.y/d)
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return self
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def abs(a):
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return a if a > 0 else -a
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def sgn(a):
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return -1 if a < 0 else 1
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def gcd(a, b):
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while b > 0:
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a, b = b, a % b
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return a
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def gen_spiral(w):
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x = []
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i, j, dc = 0, 0, [0, -1]
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for z in range((2*w + 1)**2):
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x.append((i, j))
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if i == j or (i < 0 and i == -j) or (i > 0 and i == 1 - j):
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dc = [-dc[1], dc[0]]
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i, j = i+dc[0], j+dc[1]
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return x
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def solution(dim, pos_y, pos_g, dist):
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dim, pos_y, pos_g = Vector(*dim), Vector(*pos_y), Vector(*pos_g)
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# Vectors of all mirrors of you and guard.
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count = 0
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all_you_set, all_guard_set = set(), set()
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w = (dist / min([dim.x, dim.y])) + 1
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dist = dist**2
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spiral = gen_spiral(w)
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hits = set()
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off_y, off_g = (-2*pos_y + dim), (-2*pos_g + dim)
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for c in spiral:
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base = Vector(*c) * dim
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# Handle mirror reflections every other.
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decide = Vector(int(c[0] % 2 == 1), int(c[1] % 2 == 1))
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mir_y = (base + decide * off_y).mag().whole()
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mir_g = ((base + pos_g + decide * off_g) - pos_y).mag().whole()
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# Check that new vectors don't already exist.
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y_len, g_len = len(all_you_set), len(all_guard_set)
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all_you_set.add(mir_y.whole)
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all_guard_set.add(mir_g.whole)
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uniq_y = y_len != len(all_you_set)
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uniq_g = g_len != len(all_guard_set)
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# Since we spiral out, any guard vector in set of you vectors must
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# hit you first.
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if mir_g.whole in all_you_set: continue
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if mir_g.magnitude <= dist and uniq_g: count += 1
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return count
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