thecoded.prof
CMU Coding Bootcamp
1from math import sqrt
2
3
4def almostEqual(x, y):
5 return abs(x - y) < 10**-9
6
7
8def distance(a: tuple[float, float], b: tuple[float, float]) -> float:
9 """Calculate the distance between two points using the Euclidean distance formula."""
10 return sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)
11
12
13def triangleArea(a: float, b: float, c: float) -> float:
14 """Use herons formula: `sp = (a+b+c)/2` & `sqrt(sp(sp-a)(sp-b)(sp-c))` to calculate the area of a triangle using it's side lengths."""
15 semiperimeter = 0.5 * (a + b + c)
16 return sqrt(
17 semiperimeter * (semiperimeter - a) * (semiperimeter - b) * (semiperimeter - c)
18 )
19
20
21def intersect(m1: float, b1: float, m2: float, b2: float) -> tuple[float, float]:
22 """Calculate the intersection point of two lines."""
23 x = (b2 - b1) / (m1 - m2)
24 y = m1 * x + b1
25 return x, y
26
27
28def areaWithinThreeLines(
29 m1: float, b1: float, m2: float, b2: float, m3: float, b3: float
30) -> float | None:
31 """Calculate the area of a triangle formed by three lines."""
32 if m1 == m2 or m2 == m3 or m3 == m1:
33 return None
34 a = intersect(m1, b1, m2, b2)
35 b = intersect(m2, b2, m3, b3)
36 c = intersect(m3, b3, m1, b1)
37 return triangleArea(distance(a, b), distance(b, c), distance(c, a))
38
39
40print("Testing areaWithinThreeLines()...", end="")
41assert almostEqual(areaWithinThreeLines(0, 7, 1, 0, -1, 2), 36)
42assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 2), 25)
43assert almostEqual(areaWithinThreeLines(0, -9.75, -6, 2.25, 1, -4.75), 21)
44assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 25), 272.25)
45assert almostEqual(areaWithinThreeLines(1, 2, 3, 4, 5, 6), 0)
46
47# The first two lines are parallel:
48assert areaWithinThreeLines(1, 2, 1, 4, 0, 7) == None
49
50# Here, the second and third lines are parallel
51assert areaWithinThreeLines(5, 2, 1, 4, 1, 6) == None
52print("Passed!")