feat: oct 1 level 3

python/oct1/level3/areaWithinThreeLines.py

···
+from math import sqrt
+
+
+def almostEqual(x, y):
+    return abs(x - y) < 10**-9
+
+
+def distance(a: tuple[float, float], b: tuple[float, float]) -> float:
+    """Calculate the distance between two points using the Euclidean distance formula."""
+    return sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2)
+
+
+def triangleArea(a: float, b: float, c: float) -> float:
+    """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."""
+    semiperimeter = 0.5 * (a + b + c)
+    return sqrt(
+        semiperimeter * (semiperimeter - a) * (semiperimeter - b) * (semiperimeter - c)
+    )
+
+
+def intersect(m1: float, b1: float, m2: float, b2: float) -> tuple[float, float]:
+    """Calculate the intersection point of two lines."""
+    x = (b2 - b1) / (m1 - m2)
+    y = m1 * x + b1
+    return x, y
+
+
+def areaWithinThreeLines(
+    m1: float, b1: float, m2: float, b2: float, m3: float, b3: float
+) -> float | None:
+    """Calculate the area of a triangle formed by three lines."""
+    if m1 == m2 or m2 == m3 or m3 == m1:
+        return None
+    a = intersect(m1, b1, m2, b2)
+    b = intersect(m2, b2, m3, b3)
+    c = intersect(m3, b3, m1, b1)
+    return triangleArea(distance(a, b), distance(b, c), distance(c, a))
+
+
+print("Testing areaWithinThreeLines()...", end="")
+assert almostEqual(areaWithinThreeLines(0, 7, 1, 0, -1, 2), 36)
+assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 2), 25)
+assert almostEqual(areaWithinThreeLines(0, -9.75, -6, 2.25, 1, -4.75), 21)
+assert almostEqual(areaWithinThreeLines(1, -5, 0, -2, 2, 25), 272.25)
+assert almostEqual(areaWithinThreeLines(1, 2, 3, 4, 5, 6), 0)
+
+# The first two lines are parallel:
+assert areaWithinThreeLines(1, 2, 1, 4, 0, 7) == None
+
+# Here, the second and third lines are parallel
+assert areaWithinThreeLines(5, 2, 1, 4, 1, 6) == None
+print("Passed!")

python/oct1/level3/dayOfWeek.py

···
+def dayOfWeek(month: int, day: int, year: int) -> int:
+    """Return the day of the week for a given date."""
+    m = month if month > 2 else month + 12
+    y = year - 1 if month <= 2 else year
+    n = (day + 2 * m + (3 * (m + 1)) // 5 + y + y // 4 - y // 100 + y // 400 + 2) % 7
+    return n if n != 0 else 7
+
+
+print("Testing dayOfWeek()...")
+# On 6/15/1215, the Magna Carta was signed on a Monday!
+assert dayOfWeek(6, 15, 1215) == 2
+# On 3/11/1952, the author Douglas Adams was born on a Tuesday!
+assert dayOfWeek(3, 11, 1952) == 3
+# on 4/12/1961, Yuri Gagarin became the first man in space, on a Wednesday!
+assert dayOfWeek(4, 12, 1961) == 4
+# On 7/4/1776, the Declaration of Independence was signed on a Thursday!
+assert dayOfWeek(7, 4, 1776) == 5
+# on 1/2/1920, Isaac Asimov was born on a Friday!
+assert dayOfWeek(1, 2, 1920) == 6
+# on 10/11/1975, Saturday Night Live debuted on a Saturday (of course)!
+assert dayOfWeek(10, 11, 1975) == 7
+# On 2/5/2006, the Steelers won Super Bowl XL on a Sunday!
+assert dayOfWeek(2, 5, 2006) == 1
+print("Passed!")