Solve problem 102

python/e102.py

@@ -0,0 +1,51 @@
+from math import acos, sqrt, pi, atan
+import matplotlib.pyplot as plt
+
+
+def triangle(euler_text_line):
+    ps = list(map(int, euler_text_line.split(",")))
+    ps = [(ps[0], ps[1]), (ps[2], ps[3]), (ps[4], ps[5])]
+    return ps
+
+
+def angle_x(x, y):
+    if x > 0 and y == 0:
+        return 0
+    elif x < 0 and y == 0:
+        return pi
+    elif x == 0 and y > 0:
+        return pi / 2
+    elif x == 0 and y < 0:
+        return 3 / 2 * pi
+    elif x > 0 and y > 0:
+        return atan(y / x)
+    elif x < 0 and y > 0:
+        return pi - atan(y / abs(x))
+    elif x < 0 and y < 0:
+        return pi + atan(abs(y) / abs(x))
+    elif x > 0 and y < 0:
+        return 2 * pi - atan(abs(y) / x)
+    else:
+        raise Exception("Unhandled case")
+
+
+def contains_origin(triangle):
+    a, b, c = triangle
+    angles = sorted([angle_x(*a), angle_x(*b), angle_x(*c)])
+    a = angles[1] - angles[0]
+    b = angles[2] - angles[1]
+    c = angles[0] + 2 * pi - angles[2]
+    return not (a + b < pi or b + c < pi or c + a < pi)
+
+
+def euler_102():
+    with open("../txt/e102.txt", "r") as f:
+        triangles = list(map(triangle, f.readlines()))
+    return len([1 for t in triangles if contains_origin(t)])
+
+
+if __name__ == "__main__":
+    solution = euler_102()
+    print("e102.py: " + str(solution))
+    assert(solution == 228)
+