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try writing julia

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This commit is contained in:
Michael Zhang 2020-12-07 20:32:54 -06:00
parent b08be585bc
commit 162bc5102f
Signed by: michael
GPG key ID: BDA47A31A3C8EE6B
2 changed files with 32 additions and 25 deletions
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3
001.jl Normal file
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@ -0,0 +1,3 @@
f(c) = c % 3 == 0 || c % 5 == 0
println(sum(filter(f, 0:999)))

54
727.py
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@ -1,7 +1,7 @@
import sympy
import joblib import joblib
import tqdm import tqdm
import multiprocessing import multiprocessing
from math import *
def gcd(a, b): def gcd(a, b):
if b == 0: return a if b == 0: return a
@ -21,56 +21,59 @@ class Point:
def distance_to(self, other): def distance_to(self, other):
dx = other.x - self.x dx = other.x - self.x
dy = other.y - self.y dy = other.y - self.y
return sympy.sqrt(dx * dx + dy * dy) return sqrt(dx * dx + dy * dy)
def circumcenter(A: Point, B: Point, C: Point) -> Point: def circumcenter(A: Point, B: Point, C: Point) -> Point:
D = sympy.S(2) * (A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y)) D = 2.0 * (A.x * (B.y - C.y) + B.x * (C.y - A.y) + C.x * (A.y - B.y))
Ux = (A.magnitude() * (B.y - C.y) + B.magnitude() * (C.y - A.y) + C.magnitude() * (A.y - B.y)) / D Ux = (A.magnitude() * (B.y - C.y) + B.magnitude() * (C.y - A.y) + C.magnitude() * (A.y - B.y)) / D
Uy = (A.magnitude() * (C.x - B.x) + B.magnitude() * (A.x - C.x) + C.magnitude() * (B.x - A.x)) / D Uy = (A.magnitude() * (C.x - B.x) + B.magnitude() * (A.x - C.x) + C.magnitude() * (B.x - A.x)) / D
return Point(Ux, Uy) return Point(Ux, Uy)
def lerp(src: Point, dst: Point, dist: float) -> Point: def lerp(src: Point, dst: Point, dist: float) -> Point:
total = src.distance_to(dst) total = src.distance_to(dst)
ratio = sympy.Rational(dist, total) ratio = dist / total
dx = src.x + (dst.x - src.x) * ratio dx = src.x + (dst.x - src.x) * ratio
dy = src.y + (dst.y - src.y) * ratio dy = src.y + (dst.y - src.y) * ratio
return Point(dx, dy) return Point(dx, dy)
def heron(a, b, c): def heron(a, b, c):
a, b, c = sympy.S(a), sympy.S(b), sympy.S(c) p = (a + b + c) / 2.0
p = (a + b + c) / sympy.S(2) return sqrt(p * (p - a) * (p - b) * (p - c))
return sympy.sqrt(p * (p - a) * (p - b) * (p - c))
def inv_law_cosines(a, b, c): def inv_law_cosines(a, b, c):
# given a, b, c return C # given a, b, c return C
return sympy.acos((a * a + b * b - c * c) / (sympy.S(2) * a * b)) return acos((a * a + b * b - c * c) / (2.0 * a * b))
def compute_d(A: Point, B: Point, C: Point, r1: float, r2: float, r3: float) -> float: def compute_d(A: Point, B: Point, C: Point, r1: float, r2: float, r3: float) -> float:
r1, r2, r3 = sympy.S(r1), sympy.S(r2), sympy.S(r3)
ABmid = lerp(A, B, r1) ABmid = lerp(A, B, r1)
BCmid = lerp(B, C, r2) BCmid = lerp(B, C, r2)
CAmid = lerp(C, A, r3) CAmid = lerp(C, A, r3)
D = circumcenter(ABmid, BCmid, CAmid) D = circumcenter(ABmid, BCmid, CAmid)
result = r1 + r2 + r3 + sympy.S(2) * sympy.sqrt(r1 * r2 + r2 * r3 + r1 * r3) k1, k2, k3 = 1.0 / r1, 1.0 / r2, 1.0 / r3
e1 = k1 + k2 + k3 + 2.0 * sqrt(k1 * k2 + k2 * k3 + k1 * k3)
e2 = k1 + k2 + k3 - 2.0 * sqrt(k1 * k2 + k2 * k3 + k1 * k3)
result = 1.0 / max(e1, e2)
# re = sympy.symbols("re") # re = sympy.symbols("re")
# re = result
# t1 = heron(r1 + r3, r1 + re, r3 + re) # t1 = heron(r1 + r3, r1 + re, r3 + re)
# t2 = heron(r1 + r2, r1 + re, r2 + re) # t2 = heron(r1 + r2, r1 + re, r2 + re)
# t3 = heron(r2 + r3, r2 + re, r3 + re) # t3 = heron(r2 + r3, r2 + re, r3 + re)
# tfull = heron(r1 + r2, r1 + r3, r2 + r3) # tfull = heron(r1 + r2, r1 + r3, r2 + r3)
# print(t1 + t2 + t3, tfull, "=", tfull - t1 - t2 - t3)
# eq = sympy.Eq(t1 + t2 + t3, tfull) # eq = sympy.Eq(t1 + t2 + t3, tfull)
# result = sympy.solve(eq, re) # result = sympy.solve(eq, re)
# result = result[0].evalf() # result = result[0].evalf()
# print(f"radius of E is {result}") # print(f"radius of E is {result}")
EAB = inv_law_cosines(r1 + result, r1 + r2, r2 + result) EAB = inv_law_cosines(r1 + result, r1 + r2, r2 + result)
Ex = (r1 + result) * sympy.cos(EAB) Ex = (r1 + result) * cos(EAB)
Ey = (r1 + result) * sympy.sin(EAB) Ey = (r1 + result) * sin(EAB)
E = Point(Ex, Ey) E = Point(Ex, Ey)
# print(D, E) # print(r1, r2, r3, D, E)
return D.distance_to(E).evalf() return D.distance_to(E)
total = 0 total = 0
count = 0 count = 0
@ -88,22 +91,23 @@ def calc(x):
# B is at (c, 0), b = r1 + r3 # B is at (c, 0), b = r1 + r3
# c = r1 + r2 # c = r1 + r2
# C is at () # C is at ()
a = sympy.S(r2 + r3) a = r2 + r3
b = sympy.S(r1 + r3) b = r1 + r3
c = sympy.S(r1 + r2) c = r1 + r2
A = Point(sympy.S(0), sympy.S(0)) A = Point(0, 0)
B = Point(c, sympy.S(0)) B = Point(c, 0)
CAB = sympy.acos(sympy.Rational(b * b + c * c - a * a, 2.0 * b * c)) CAB = inv_law_cosines(b, c, a)
Cx = b * sympy.cos(CAB) Cx = b * cos(CAB)
Cy = b * sympy.sin(CAB) Cy = b * sin(CAB)
C = Point(Cx, Cy) C = Point(Cx, Cy)
d = compute_d(A, B, C, r1, r2, r3) d = compute_d(A, B, C, r1, r2, r3)
return d return d
print(f"d({r1}, {r2}, {r3}) = {d}") # return (f"d({r1}, {r2}, {r3}) = {d}")
total = len(list(create_loop())) total = len(list(create_loop()))
L = joblib.Parallel(n_jobs=multiprocessing.cpu_count())(joblib.delayed(calc)(tup) for tup in tqdm.tqdm(create_loop(), total=total)) L = joblib.Parallel(n_jobs=multiprocessing.cpu_count())(joblib.delayed(calc)(tup) for tup in tqdm.tqdm(create_loop(), total=total))
print(sum(L) / len(L)) # print(L)
print(round(sum(L) / len(L), 8))