mirror of
https://github.com/3b1b/manim.git
synced 2025-11-14 22:57:44 +00:00
HowToComputeNChooseK in eop/combinations
This commit is contained in:
Grant Sanderson
parent
76a420139d
commit
43d947657d
1 changed files with 398 additions and 25 deletions
|
|
@ -2161,13 +2161,12 @@ class ChooseThreeFromFive(InitialFiveChooseThreeExample, PiCreatureScene):
|
|||
],
|
||||
}
|
||||
def construct(self):
|
||||
self.force_skipping()
|
||||
|
||||
self.remove(self.people)
|
||||
self.show_binary_strings()
|
||||
self.add_people()
|
||||
self.choose_triplets()
|
||||
self.show_association_with_binary()
|
||||
self.show_association_with_binary(3)
|
||||
self.show_association_with_binary(5)
|
||||
self.order_doesnt_matter()
|
||||
self.that_phrase_is_confusing()
|
||||
self.pattern_is_unambiguous()
|
||||
|
|
@ -2203,19 +2202,8 @@ class ChooseThreeFromFive(InitialFiveChooseThreeExample, PiCreatureScene):
|
|||
def add_people(self):
|
||||
people = self.people
|
||||
|
||||
names = VGroup(*map(TextMobject, [
|
||||
"Ali", "Ben", "Cam", "Denis", "Evan"
|
||||
]))
|
||||
for name, pi in zip(names, people):
|
||||
name.scale(0.75)
|
||||
name.next_to(pi, UP, 2*SMALL_BUFF)
|
||||
group = VGroup(people, names)
|
||||
|
||||
lb, rb = braces = TexMobject("\\{ \\}")
|
||||
braces.scale(2)
|
||||
braces.stretch_to_fit_height(1.3*group.get_height())
|
||||
lb.next_to(group, LEFT, SMALL_BUFF)
|
||||
rb.next_to(group, RIGHT, SMALL_BUFF)
|
||||
names = self.get_names(people)
|
||||
braces = self.get_people_braces(people)
|
||||
|
||||
self.play(
|
||||
Write(braces),
|
||||
|
|
@ -2227,19 +2215,224 @@ class ChooseThreeFromFive(InitialFiveChooseThreeExample, PiCreatureScene):
|
|||
self.set_variables_as_attrs(names, braces)
|
||||
|
||||
def choose_triplets(self):
|
||||
pass
|
||||
movers = VGroup()
|
||||
movers.generate_target()
|
||||
max_name_width = max([n.get_width() for n in self.names])
|
||||
for name_triplet in it.combinations(self.names, 3):
|
||||
mover = VGroup(*name_triplet).copy()
|
||||
mover.generate_target()
|
||||
if hasattr(self, "stack"):
|
||||
mover.target.scale_to_fit_height(self.stack[0].get_height())
|
||||
for name in mover.target[:2]:
|
||||
name[-1].set_fill(opacity = 1)
|
||||
mover.target.arrange_submobjects(RIGHT, MED_SMALL_BUFF)
|
||||
movers.add(mover)
|
||||
movers.target.add(mover.target)
|
||||
movers.target.arrange_submobjects(
|
||||
DOWN, buff = SMALL_BUFF,
|
||||
aligned_edge = LEFT,
|
||||
)
|
||||
movers.target.next_to(self.people, DOWN, MED_LARGE_BUFF)
|
||||
if hasattr(self, "stack"):
|
||||
movers.target.align_to(self.stack, UP)
|
||||
|
||||
self.play(LaggedStart(
|
||||
MoveToTarget, movers,
|
||||
lag_ratio = 0.2,
|
||||
run_time = 4,
|
||||
))
|
||||
self.dither()
|
||||
|
||||
self.name_triplets = movers
|
||||
|
||||
def show_association_with_binary(self):
|
||||
pass
|
||||
def show_association_with_binary(self, index):
|
||||
people = self.people
|
||||
names = self.names
|
||||
for mob in people, names:
|
||||
mob.save_state()
|
||||
mob.generate_target()
|
||||
|
||||
line = self.stack[index].copy()
|
||||
triplet = self.name_triplets[index]
|
||||
triplet.save_state()
|
||||
line.generate_target()
|
||||
for bit, name in zip(line.target, self.names):
|
||||
bit.next_to(name, UP)
|
||||
|
||||
line_rect = SurroundingRectangle(line)
|
||||
full_line_rect = SurroundingRectangle(VGroup(line, triplet))
|
||||
people_rects = VGroup()
|
||||
for pi, name, obj in zip(people.target, names.target, line):
|
||||
if "1" in obj.get_tex_string():
|
||||
rect = SurroundingRectangle(VGroup(pi, name))
|
||||
people_rects.add(rect)
|
||||
pi.change_mode("hooray")
|
||||
else:
|
||||
pi.fade(0.5)
|
||||
name.fade(0.5)
|
||||
|
||||
self.play(ShowCreation(line_rect))
|
||||
self.play(MoveToTarget(line))
|
||||
self.play(
|
||||
LaggedStart(ShowCreation, people_rects),
|
||||
MoveToTarget(people),
|
||||
MoveToTarget(names),
|
||||
)
|
||||
self.dither()
|
||||
self.play(
|
||||
ReplacementTransform(line_rect, full_line_rect),
|
||||
triplet.highlight, YELLOW
|
||||
)
|
||||
self.dither(2)
|
||||
self.play(
|
||||
people.restore,
|
||||
names.restore,
|
||||
triplet.restore,
|
||||
FadeOut(line),
|
||||
FadeOut(full_line_rect),
|
||||
FadeOut(people_rects),
|
||||
)
|
||||
|
||||
def order_doesnt_matter(self):
|
||||
pass
|
||||
triplet = self.name_triplets[0].copy()
|
||||
triplet.set_fill(opacity = 1)
|
||||
triplet.next_to(
|
||||
self.name_triplets, RIGHT,
|
||||
buff = LARGE_BUFF,
|
||||
aligned_edge = UP,
|
||||
)
|
||||
updownarrow = TexMobject("\\Updownarrow")
|
||||
updownarrow.highlight(YELLOW)
|
||||
updownarrow.next_to(triplet, DOWN, SMALL_BUFF)
|
||||
permutations = VGroup()
|
||||
for indices in it.permutations(range(len(triplet))):
|
||||
perm = triplet.copy()
|
||||
resorter = VGroup(*[
|
||||
perm[i] for i in indices
|
||||
])
|
||||
resorter.arrange_submobjects(RIGHT, MED_SMALL_BUFF)
|
||||
resorter.next_to(updownarrow, DOWN)
|
||||
permutations.add(perm)
|
||||
|
||||
words = TextMobject("``Order doesn't matter''")
|
||||
words.scale(0.75)
|
||||
words.highlight(BLUE)
|
||||
words.next_to(permutations, DOWN)
|
||||
|
||||
self.play(ReplacementTransform(
|
||||
self.name_triplets[0].copy(), triplet
|
||||
))
|
||||
curr_perm = permutations[0]
|
||||
self.play(
|
||||
ReplacementTransform(triplet.copy(), curr_perm),
|
||||
Write(updownarrow)
|
||||
)
|
||||
for i in range(8):
|
||||
new_perm = permutations[i%(len(permutations)-1)+1]
|
||||
anims = [
|
||||
Transform(
|
||||
curr_perm, new_perm,
|
||||
path_arc = np.pi,
|
||||
)
|
||||
]
|
||||
if i == 1:
|
||||
self.dither()
|
||||
if i == 4:
|
||||
anims.append(Write(words, run_time = 1))
|
||||
self.play(*anims)
|
||||
self.play(*map(FadeOut, [triplet, curr_perm, updownarrow]))
|
||||
|
||||
self.order_doesnt_matter_words = words
|
||||
|
||||
def that_phrase_is_confusing(self):
|
||||
pass
|
||||
odm_words = self.order_doesnt_matter_words
|
||||
odm_words_outline = VGroup()
|
||||
for letter in odm_words:
|
||||
mob = VMobject()
|
||||
mob.points = letter.points
|
||||
odm_words_outline.add(mob)
|
||||
odm_words_outline.set_fill(opacity = 0)
|
||||
odm_words_outline.set_stroke(YELLOW, 1)
|
||||
|
||||
line = self.stack[0].copy()
|
||||
|
||||
self.play(
|
||||
LaggedStart(
|
||||
ShowCreationThenDestruction, odm_words_outline,
|
||||
lag_ratio = 0.2,
|
||||
run_time = 1,
|
||||
),
|
||||
LaggedStart(
|
||||
ApplyMethod, self.people,
|
||||
lambda pi : (pi.change, "confused", odm_words,)
|
||||
)
|
||||
)
|
||||
self.play(line.next_to, odm_words, UP)
|
||||
for x in range(6):
|
||||
line.generate_target()
|
||||
resorter = VGroup(*line.target)
|
||||
resorter.sort_submobjects(lambda p : random.random())
|
||||
resorter.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
|
||||
resorter.move_to(line)
|
||||
self.play(MoveToTarget(line, path_arc = np.pi))
|
||||
self.dither()
|
||||
|
||||
line.sort_submobjects(lambda p : p[0])
|
||||
words = VGroup(*map(TextMobject, ["First", "Second", "Fifth"]))
|
||||
words.highlight(YELLOW)
|
||||
words.scale(0.75)
|
||||
word_arrow_groups = VGroup()
|
||||
for i, word in zip([0, 1, 4], words):
|
||||
arrow = Vector(0.5*DOWN)
|
||||
arrow.highlight(YELLOW)
|
||||
arrow.next_to(line[i], UP, SMALL_BUFF)
|
||||
word.next_to(arrow, UP, SMALL_BUFF)
|
||||
word_arrow_groups.add(VGroup(word, arrow))
|
||||
|
||||
for x in range(2):
|
||||
for i in range(len(word_arrow_groups)+1):
|
||||
anims = []
|
||||
if i > 0:
|
||||
anims.append(FadeOut(word_arrow_groups[i-1]))
|
||||
if i < len(word_arrow_groups):
|
||||
anims.append(FadeIn(word_arrow_groups[i]))
|
||||
self.play(*anims)
|
||||
self.dither()
|
||||
word_arrow_groups.submobjects = [
|
||||
word_arrow_groups[j]
|
||||
for j in 1, 2, 0
|
||||
]
|
||||
self.play(*map(FadeOut, [line, odm_words]))
|
||||
|
||||
def pattern_is_unambiguous(self):
|
||||
pass
|
||||
all_ones = VGroup()
|
||||
for line in self.stack:
|
||||
ones = VGroup(*filter(
|
||||
lambda m : "1" in m.get_tex_string(),
|
||||
line
|
||||
)).copy()
|
||||
ones.highlight(YELLOW)
|
||||
all_ones.add(ones)
|
||||
|
||||
self.play(
|
||||
LaggedStart(
|
||||
FadeIn, all_ones,
|
||||
lag_ratio = 0.2,
|
||||
run_time = 3,
|
||||
rate_func = there_and_back
|
||||
),
|
||||
LaggedStart(
|
||||
ApplyMethod, self.people,
|
||||
lambda pi : (pi.change, "happy", ones),
|
||||
)
|
||||
)
|
||||
self.dither()
|
||||
for trip in it.combinations(self.people, 3):
|
||||
rects = VGroup(*map(SurroundingRectangle, trip))
|
||||
self.add(rects)
|
||||
self.dither(0.3)
|
||||
self.remove(rects)
|
||||
self.dither()
|
||||
|
||||
###
|
||||
|
||||
|
|
@ -2249,12 +2442,192 @@ class ChooseThreeFromFive(InitialFiveChooseThreeExample, PiCreatureScene):
|
|||
for color in self.people_colors
|
||||
])
|
||||
people.arrange_submobjects(RIGHT)
|
||||
people.shift(SPACE_WIDTH*LEFT/2)
|
||||
people.to_edge(UP, buff = LARGE_BUFF)
|
||||
people.shift(3*LEFT)
|
||||
people.to_edge(UP, buff = 1.25)
|
||||
self.people = people
|
||||
return people
|
||||
|
||||
|
||||
def get_names(self, people):
|
||||
names = VGroup(*[
|
||||
TextMobject(name + ",")
|
||||
for name in "Ali", "Ben", "Cam", "Denis", "Evan"
|
||||
])
|
||||
for name, pi in zip(names, people):
|
||||
name[-1].set_fill(opacity = 0)
|
||||
name.scale(0.75)
|
||||
name.next_to(pi, UP, 2*SMALL_BUFF)
|
||||
pi.name = name
|
||||
return names
|
||||
|
||||
def get_people_braces(self, people):
|
||||
group = VGroup(people, *[pi.name for pi in people])
|
||||
lb, rb = braces = TexMobject("\\{ \\}")
|
||||
braces.scale(2)
|
||||
braces.stretch_to_fit_height(1.3*group.get_height())
|
||||
lb.next_to(group, LEFT, SMALL_BUFF)
|
||||
rb.next_to(group, RIGHT, SMALL_BUFF)
|
||||
return braces
|
||||
|
||||
class SubsetProbabilityExample(ChooseThreeFromFive):
|
||||
CONFIG = {
|
||||
"random_seed" : 1,
|
||||
}
|
||||
def construct(self):
|
||||
self.setup_people()
|
||||
self.ask_question()
|
||||
self.show_all_triplets()
|
||||
self.circle_those_with_ali()
|
||||
|
||||
def setup_people(self):
|
||||
people = self.people
|
||||
names = self.get_names(people)
|
||||
braces = self.get_people_braces(people)
|
||||
group = VGroup(people, names, braces)
|
||||
|
||||
self.play(group.shift, -group.get_center()[0]*RIGHT)
|
||||
self.dither()
|
||||
|
||||
self.set_variables_as_attrs(names, braces)
|
||||
|
||||
def ask_question(self):
|
||||
pi_name_groups = VGroup(*[
|
||||
VGroup(pi, pi.name)
|
||||
for pi in self.people
|
||||
])
|
||||
|
||||
words = TextMobject(
|
||||
"Choose 3 people randomly.\\\\",
|
||||
"Probability", "Ali", "is one of them?"
|
||||
)
|
||||
words.highlight_by_tex("Ali", self.people[0].get_color())
|
||||
words.next_to(pi_name_groups, DOWN, 2*LARGE_BUFF)
|
||||
|
||||
checkmark = TexMobject("\\checkmark").highlight(GREEN)
|
||||
cross = TexMobject("\\times").highlight(RED)
|
||||
for mob in checkmark, cross:
|
||||
mob.scale(2)
|
||||
mob.next_to(self.braces, DOWN, aligned_edge = LEFT)
|
||||
mob.shift(MED_SMALL_BUFF*LEFT)
|
||||
|
||||
ali = pi_name_groups[0]
|
||||
|
||||
self.play(FadeIn(words))
|
||||
for x in range(4):
|
||||
group = VGroup(*random.sample(pi_name_groups, 3))
|
||||
group.save_state()
|
||||
group.generate_target()
|
||||
group.target.shift(LARGE_BUFF*DOWN)
|
||||
for pi, name in group.target:
|
||||
pi.change("hooray", checkmark)
|
||||
if ali in group:
|
||||
symbol = checkmark
|
||||
rect = SurroundingRectangle(
|
||||
group.target[group.submobjects.index(ali)]
|
||||
)
|
||||
rect.set_stroke(GREEN)
|
||||
else:
|
||||
symbol = cross
|
||||
rect = VGroup()
|
||||
|
||||
run_time = 1
|
||||
self.play(
|
||||
MoveToTarget(group),
|
||||
FadeIn(symbol),
|
||||
ShowCreation(rect),
|
||||
run_time = run_time,
|
||||
)
|
||||
self.dither(0.5)
|
||||
self.play(
|
||||
group.restore,
|
||||
FadeOut(symbol),
|
||||
FadeOut(rect),
|
||||
run_time = run_time,
|
||||
)
|
||||
|
||||
self.question = words
|
||||
self.set_variables_as_attrs(pi_name_groups)
|
||||
|
||||
def show_all_triplets(self):
|
||||
self.play(
|
||||
self.question.scale, 0.75,
|
||||
self.question.to_corner, UP+RIGHT,
|
||||
VGroup(self.people, self.names, self.braces).to_edge, LEFT,
|
||||
)
|
||||
self.choose_triplets()
|
||||
|
||||
brace = Brace(self.name_triplets, RIGHT)
|
||||
total_count = brace.get_tex(
|
||||
"{5 \\choose 3}", "=", "10",
|
||||
buff = MED_LARGE_BUFF
|
||||
)
|
||||
total_count.highlight(BLUE)
|
||||
self.play(
|
||||
GrowFromCenter(brace),
|
||||
Write(total_count),
|
||||
)
|
||||
self.dither()
|
||||
|
||||
self.set_variables_as_attrs(brace, total_count)
|
||||
|
||||
def circle_those_with_ali(self):
|
||||
name_triplets = self.name_triplets
|
||||
five_choose_three, equals, ten = self.total_count
|
||||
names = self.names
|
||||
|
||||
with_ali = VGroup(*name_triplets[:6])
|
||||
alis = VGroup(*[group[0] for group in with_ali])
|
||||
rect = SurroundingRectangle(with_ali)
|
||||
|
||||
frac_lines = VGroup()
|
||||
for vect in LEFT, RIGHT:
|
||||
frac_line = TexMobject("\\quad \\over \\quad")
|
||||
if vect is LEFT:
|
||||
frac_line.stretch(1.5, 0)
|
||||
frac_line.next_to(equals, vect)
|
||||
frac_lines.add(frac_line)
|
||||
four_choose_two = TexMobject("4 \\choose 2")
|
||||
four_choose_two.next_to(frac_lines[0], UP, SMALL_BUFF)
|
||||
six = TexMobject("6")
|
||||
six.next_to(frac_lines[1], UP, SMALL_BUFF)
|
||||
|
||||
self.play(
|
||||
ShowCreation(rect),
|
||||
alis.highlight, YELLOW
|
||||
)
|
||||
for pair in it.combinations(names[1:], 2):
|
||||
arrows = VGroup()
|
||||
for pi in pair:
|
||||
arrow = Vector(0.5*DOWN, color = YELLOW)
|
||||
arrow.next_to(pi, UP)
|
||||
arrows.add(arrow)
|
||||
self.add(arrows)
|
||||
self.dither(0.5)
|
||||
self.remove(arrows)
|
||||
self.add(arrows)
|
||||
self.dither()
|
||||
self.play(
|
||||
FadeIn(frac_lines),
|
||||
five_choose_three.next_to, frac_lines[0], DOWN, SMALL_BUFF,
|
||||
ten.next_to, frac_lines[1], DOWN, SMALL_BUFF,
|
||||
Write(four_choose_two)
|
||||
)
|
||||
self.dither()
|
||||
self.play(ReplacementTransform(
|
||||
four_choose_two.copy(), six
|
||||
))
|
||||
self.play(FadeOut(arrows))
|
||||
|
||||
for x in range(20):
|
||||
name_rect = SurroundingRectangle(random.choice(name_triplets))
|
||||
name_rect.highlight(BLUE)
|
||||
name_rect.set_fill(BLUE, opacity = 0.25)
|
||||
self.play(Animation(name_rect, run_time = 0))
|
||||
self.dither(0.25)
|
||||
self.remove(name_rect)
|
||||
|
||||
class HowToComputeNChooseK(ChooseThreeFromFive):
|
||||
def construct(self):
|
||||
pass
|
||||
|
||||
|
||||
|
||||
|
|
|
|||
Loading…
Add table
Reference in a new issue