a

001.py

@@ -0,0 +1 @@
+print(sum(filter(lambda c: c % 3 == 0 or c % 5 == 0, range(1000))))

727.py

@@ -0,0 +1,108 @@
+import sympy
+import joblib
+import tqdm
+
+def gcd(a, b):
+    if b == 0: return a
+    return gcd(b, a % b)
+
+class Point:
+    def __init__(self, x, y):
+        self.x = x
+        self.y = y
+
+    def __str__(self):
+        return f"({self.x}, {self.y})"
+
+    def magnitude(self):
+        return self.x * self.x + self.y * self.y
+
+    def distance_to(self, other):
+        dx = other.x - self.x
+        dy = other.y - self.y
+        return sympy.sqrt(dx * dx + dy * dy)
+
+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))
+    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
+    return Point(Ux, Uy)
+
+def lerp(src: Point, dst: Point, dist: float) -> Point:
+    total = src.distance_to(dst)
+    ratio = sympy.Rational(dist, total)
+    dx = src.x + (dst.x - src.x) * ratio
+    dy = src.y + (dst.y - src.y) * ratio
+    return Point(dx, dy)
+
+def heron(a, b, c):
+    a, b, c = sympy.S(a), sympy.S(b), sympy.S(c)
+    p = (a + b + c) / sympy.S(2)
+    return sympy.sqrt(p * (p - a) * (p - b) * (p - c))
+
+def inv_law_cosines(a, b, c):
+    # given a, b, c return C
+    return sympy.acos((a * a + b * b - c * c) / (sympy.S(2) * a * b))
+
+
+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)
+    BCmid = lerp(B, C, r2)
+    CAmid = lerp(C, A, r3)
+    D = circumcenter(ABmid, BCmid, CAmid)
+
+    re = sympy.symbols("re")
+    t1 = heron(r1 + r3, r1 + re, r3 + re)
+    t2 = heron(r1 + r2, r1 + re, r2 + re)
+    t3 = heron(r2 + r3, r2 + re, r3 + re)
+    tfull = heron(r1 + r2, r1 + r3, r2 + r3)
+    eq = sympy.Eq(t1 + t2 + t3, tfull)
+    result = sympy.solve(eq, re)
+    result = result[0].evalf()
+    # print(f"radius of E is {result}")
+
+    EAB = inv_law_cosines(r1 + result, r1 + r2, r2 + result)
+    Ex = (r1 + result) * sympy.cos(EAB)
+    Ey = (r1 + result) * sympy.sin(EAB)
+    E = Point(Ex, Ey)
+
+    # print(D, E)
+    return D.distance_to(E).evalf()
+
+total = 0
+count = 0
+def create_loop():
+    for r1 in range(1, 101 - 2):
+        for r2 in range(r1 + 1, 101 - 1):
+            for r3 in range(r2 + 1, 101):
+                if gcd(gcd(r1, r2), r3) != 1: continue
+                yield (r1, r2, r3)
+
+def calc(x):
+    r1, r2, r3 = x
+    # build a triangle out of the side lengths
+    # A is at (0, 0), a = r2 + r3
+    # B is at (c, 0), b = r1 + r3
+    # c = r1 + r2
+    # C is at ()
+    a = sympy.S(r2 + r3)
+    b = sympy.S(r1 + r3)
+    c = sympy.S(r1 + r2)
+
+    A = Point(sympy.S(0), sympy.S(0))
+    B = Point(c, sympy.S(0))
+    
+    CAB = sympy.acos(sympy.Rational(b * b + c * c - a * a, 2.0 * b * c))
+    Cx = b * sympy.cos(CAB)
+    Cy = b * sympy.sin(CAB)
+    C = Point(Cx, Cy)
+
+    d = compute_d(A, B, C, r1, r2, r3)
+    return d
+    print(f"d({r1}, {r2}, {r3}) = {d}")
+
+total = len(list(create_loop()))
+L = joblib.Parallel(n_jobs=8)(joblib.delayed(calc)(tup) for tup in tqdm.tqdm(create_loop(), total=total))
+print(sum(L) / len(L))