diff --git a/python/e102.py b/python/e102.py new file mode 100644 index 0000000..25668cf --- /dev/null +++ b/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) + diff --git a/txt/e102.txt b/txt/e102.txt new file mode 100644 index 0000000..3f01a1a --- /dev/null +++ b/txt/e102.txt @@ -0,0 +1,1000 @@ +-340,495,-153,-910,835,-947 +-175,41,-421,-714,574,-645 +-547,712,-352,579,951,-786 +419,-864,-83,650,-399,171 +-429,-89,-357,-930,296,-29 +-734,-702,823,-745,-684,-62 +-971,762,925,-776,-663,-157 +162,570,628,485,-807,-896 +641,91,-65,700,887,759 +215,-496,46,-931,422,-30 +-119,359,668,-609,-358,-494 +440,929,968,214,760,-857 +-700,785,838,29,-216,411 +-770,-458,-325,-53,-505,633 +-752,-805,349,776,-799,687 +323,5,561,-36,919,-560 +-907,358,264,320,204,274 +-728,-466,350,969,292,-345 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