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git-subtree-dir: universe
git-subtree-mainline: 15110e6de9
git-subtree-split: 8ad51b24dd
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William Carroll 2020-01-29 14:29:25 +00:00
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universe/data_structures_and_algorithms/rectangular-love.py Normal file
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import unittest
################################################################################
# Solution
################################################################################
# bottom :: Rectangle -> Int
def bottom(x):
return x.get('bottom_y')
# top :: Rectangle -> Int
def top(x):
return bottom(x) + x.get('height')
# left :: Rectangle -> Int
def left(x):
return x.get('left_x')
# right :: Rectangle -> Int
def right(x):
return left(x) + x.get('width')
# sort_highest :: Rectangle -> Rectangle -> (Rectangle, Rectangle)
def sort_highest(x, y):
if top(x) >= top(y):
return x, y
else:
return y, x
# sort_leftmost :: Rectangle -> Rectangle -> (Rectangle, Rectangle)
def sort_leftmost(x, y):
if left(x) <= left(y):
return x, y
else:
return y, x
# rectify :: Int -> Int -> Int -> Int -> Rectify
def rectify(top=None, bottom=None, left=None, right=None):
assert top >= bottom
assert left <= right
return {
'left_x': left,
'bottom_y': bottom,
'width': right - left,
'height': top - bottom,
}
# empty_rect :: Rectangle
def empty_rect():
return {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
# find_rectangular_overlap :: Rectangle -> Rectangle -> Maybe(Rectangle)
def find_rectangular_overlap(x, y):
ha, hb = sort_highest(x, y)
la, lb = sort_leftmost(x, y)
if bottom(hb) <= top(hb) <= bottom(ha) <= top(ha):
return empty_rect()
if left(la) <= right(la) <= left(lb) <= right(lb):
return empty_rect()
# We should have an intersection here.
verts = [bottom(ha), top(ha), bottom(hb), top(hb)]
verts.sort()
horzs = [left(la), right(la), left(lb), right(lb)]
horzs.sort()
return rectify(top=verts[2],
bottom=verts[1],
left=horzs[1],
right=horzs[2])
################################################################################
# Tests
################################################################################
class Test(unittest.TestCase):
def test_overlap_along_both_axes(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 6,
'height': 3,
}
rect2 = {
'left_x': 5,
'bottom_y': 2,
'width': 3,
'height': 6,
}
expected = {
'left_x': 5,
'bottom_y': 2,
'width': 2,
'height': 2,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_one_rectangle_inside_another(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 6,
'height': 6,
}
rect2 = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_both_rectangles_the_same(self):
rect1 = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
rect2 = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
expected = {
'left_x': 2,
'bottom_y': 2,
'width': 4,
'height': 4,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_on_horizontal_edge(self):
rect1 = {
'left_x': 1,
'bottom_y': 2,
'width': 3,
'height': 4,
}
rect2 = {
'left_x': 2,
'bottom_y': 6,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_on_vertical_edge(self):
rect1 = {
'left_x': 1,
'bottom_y': 2,
'width': 3,
'height': 4,
}
rect2 = {
'left_x': 4,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_touch_at_a_corner(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 2,
'height': 2,
}
rect2 = {
'left_x': 3,
'bottom_y': 3,
'width': 2,
'height': 2,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
def test_no_overlap(self):
rect1 = {
'left_x': 1,
'bottom_y': 1,
'width': 2,
'height': 2,
}
rect2 = {
'left_x': 4,
'bottom_y': 6,
'width': 3,
'height': 6,
}
expected = {
'left_x': None,
'bottom_y': None,
'width': None,
'height': None,
}
actual = find_rectangular_overlap(rect1, rect2)
self.assertEqual(actual, expected)
unittest.main(verbosity=2)