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BuildFiveFromFour of eop/combinations
This commit is contained in:
Grant Sanderson
parent
e95acbdce7
commit
0e7fbe73b8
1 changed files with 338 additions and 4 deletions
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@ -36,6 +36,8 @@ def get_stack(
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obj1, obj2, n, k,
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fixed_start = None,
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fixed_end = None,
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obj_to_obj_buff = SMALL_BUFF,
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vertical_buff = MED_SMALL_BUFF,
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):
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stack = VGroup()
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for indices in it.combinations(range(n), k):
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@ -47,9 +49,9 @@ def get_stack(
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term.add_to_back(fixed_start.copy())
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if fixed_end:
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term.add(fixed_end.copy())
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term.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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term.arrange_submobjects(RIGHT, buff = obj_to_obj_buff)
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stack.add(term)
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stack.arrange_submobjects(DOWN)
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stack.arrange_submobjects(DOWN, buff = vertical_buff)
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return stack
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def get_stacks(obj1, obj2, n, **kwargs):
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@ -802,12 +804,13 @@ class ProbabilityOfThreeWomenInGroupOfFive(Scene):
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])
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return lineup
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def get_lineup(self, *mobjects):
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def get_lineup(self, *mobjects, **kwargs):
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buff = kwargs.get("buff", MED_SMALL_BUFF)
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lines = VGroup(*[
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Line(ORIGIN, self.item_line_width*RIGHT)
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for mob in mobjects
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])
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lines.arrange_submobjects(RIGHT)
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lines.arrange_submobjects(RIGHT, buff = buff)
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items = VGroup()
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for line, mob in zip(lines, mobjects):
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item = VectorizedPoint() if mob is None else mob.copy()
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@ -824,6 +827,337 @@ class RememberThisSensation(TeacherStudentsScene):
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self.change_student_modes("confused", "pondering", "erm")
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self.dither(2)
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class GroupsOf6(Scene):
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def construct(self):
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title = TexMobject("2^6 =", "64", "\\text{ Possibilities}")
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title.to_edge(UP, buff = MED_SMALL_BUFF)
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title.highlight_by_tex("64", YELLOW)
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man, woman = Male(), Female()
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stacks = get_stacks(man, woman, 6, vertical_buff = SMALL_BUFF)
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stacks.scale_to_fit_height(6.25)
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stacks.to_edge(DOWN, buff = MED_SMALL_BUFF)
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women_groups = VGroup()
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for stack in stacks:
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for lineup in stack:
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group = VGroup()
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for item in lineup:
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if "female" in item.get_tex_string():
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group.add(item)
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women_groups.add(group)
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numbers = VGroup()
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for stack in stacks:
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number = TexMobject(str(len(stack)))
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number.next_to(stack, UP, SMALL_BUFF)
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numbers.add(number)
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self.add(title)
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self.play(LaggedStart(
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LaggedStart, stacks,
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lambda s : (FadeIn, s),
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run_time = 3,
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))
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self.play(Write(numbers, run_time = 3))
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self.dither()
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self.play(LaggedStart(
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ApplyMethod, women_groups,
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lambda m : (m.highlight, PINK),
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lag_ratio = 0.1,
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rate_func = wiggle,
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run_time = 6,
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))
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class GroupsOf7(Scene):
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def construct(self):
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stack = get_stack(Male(), Female(), 7, 3)
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question = TextMobject(
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"How many groups \\\\ of 7 with 3 ", "$\\female$", "?"
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)
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question.highlight_by_tex("female", MAROON_B)
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question.shift(1.5*UP)
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self.add(question)
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for n, item in enumerate(stack):
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item.center()
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number = TexMobject(str(n))
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number.next_to(ORIGIN, DOWN, LARGE_BUFF)
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self.add(item, number)
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self.dither(0.2)
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self.remove(item, number)
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self.add(item, number)
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self.dither(2)
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class BuildFiveFromFour(ProbabilityOfThreeWomenInGroupOfFive):
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def construct(self):
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self.show_all_configurations_of_four()
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self.organize_into_stacks()
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self.walk_through_stacks()
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self.split_into_two_possibilities()
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self.combine_stacks()
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def show_all_configurations_of_four(self):
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man, woman = Male(), Female()
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n = 4
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vects = [
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1.5*UP,
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0.5*UP,
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3.5*RIGHT,
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1.5*RIGHT,
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]
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lineup_groups = VGroup()
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for k in range(n+1):
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lineup_group = VGroup()
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for tup in it.product(*[[man, woman]]*k):
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lineup = self.get_lineup(*list(tup) + (n-k)*[None])
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lineup.scale(1.4*(0.9)**k)
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lineup.move_to(0.5*DOWN)
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for mob, vect in zip(tup, vects):
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if mob is woman:
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lineup.shift(vect)
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else:
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lineup.shift(-vect)
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lineup_group.add(lineup)
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lineup_groups.add(lineup_group)
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n_possibilities = TexMobject(
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"2 \\cdot", "2 \\cdot", "2 \\cdot", "2",
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"\\text{ Possibilities}"
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)
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n_possibilities.to_edge(UP)
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twos = VGroup(*n_possibilities[-2::-1])
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two_anims = [
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ReplacementTransform(
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VectorizedPoint(twos[0].get_center()),
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twos[0]
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)
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] + [
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ReplacementTransform(t1.copy(), t2)
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for t1, t2 in zip(twos, twos[1:])
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]
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curr_lineup_group = lineup_groups[0]
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self.play(
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ShowCreation(curr_lineup_group[0]),
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)
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for i, lineup_group in enumerate(lineup_groups[1:]):
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anims = [ReplacementTransform(curr_lineup_group, lineup_group)]
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anims += two_anims[:i+1]
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if i == 0:
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anims.append(FadeIn(n_possibilities[-1]))
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self.remove(twos)
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self.play(*anims)
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self.dither()
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curr_lineup_group = lineup_group
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self.lineups = curr_lineup_group
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eq_16 = TexMobject("=", "16")
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eq_16.move_to(twos.get_right())
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eq_16.highlight_by_tex("16", YELLOW)
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self.play(
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n_possibilities[-1].next_to, eq_16, RIGHT,
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twos.next_to, eq_16, LEFT,
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FadeIn(eq_16),
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)
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self.dither()
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n_possibilities.add(eq_16)
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self.n_possibilities = n_possibilities
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def organize_into_stacks(self):
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lineups = self.lineups
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stacks = VGroup(*[VGroup() for x in range(5)])
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for lineup in lineups:
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women = filter(
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lambda m : "female" in m.get_tex_string(),
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lineup.items
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)
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stacks[len(women)].add(lineup)
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stacks.generate_target()
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stacks.target.scale(0.75)
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for stack in stacks.target:
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stack.arrange_submobjects(DOWN, buff = SMALL_BUFF)
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stacks.target.arrange_submobjects(
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RIGHT, buff = MED_LARGE_BUFF, aligned_edge = DOWN
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)
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stacks.target.to_edge(DOWN, buff = MED_SMALL_BUFF)
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self.play(MoveToTarget(
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stacks,
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run_time = 2,
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path_arc = np.pi/2
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))
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self.dither()
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self.stacks = stacks
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def walk_through_stacks(self):
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stacks = self.stacks
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numbers = VGroup()
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for stack in stacks:
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rect = SurroundingRectangle(stack)
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rect.set_stroke(WHITE, 2)
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self.play(ShowCreation(rect))
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for n, lineup in enumerate(stack):
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lineup_copy = lineup.copy()
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lineup_copy.highlight(YELLOW)
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number = TexMobject(str(n+1))
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number.next_to(stack, UP)
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self.add(lineup_copy, number)
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self.dither(0.25)
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self.remove(lineup_copy, number)
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self.add(number)
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numbers.add(number)
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self.play(FadeOut(rect))
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self.dither()
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stacks.numbers = numbers
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def split_into_two_possibilities(self):
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bottom_stacks = self.stacks
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top_stacks = bottom_stacks.deepcopy()
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top_group = VGroup(top_stacks, top_stacks.numbers)
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h_line = DashedLine(SPACE_WIDTH*LEFT, SPACE_WIDTH*RIGHT)
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#Initial split
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self.play(
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FadeOut(self.n_possibilities),
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top_group.to_edge, UP, MED_SMALL_BUFF,
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)
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self.play(ShowCreation(h_line))
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#Add extra slot
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for stacks, sym in (top_stacks, Female()), (bottom_stacks, Male()):
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sym.set_fill(opacity = 0)
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new_stacks = VGroup()
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to_fade_in = VGroup()
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for stack in stacks:
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new_stack = VGroup()
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for lineup in stack:
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new_lineup = self.get_lineup(*[
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Female() if "female" in item.get_tex_string() else Male()
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for item in lineup.items
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] + [sym], buff = SMALL_BUFF)
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new_lineup.replace(lineup, dim_to_match = 1)
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new_stack.add(new_lineup)
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for group in lineup.items, lineup.lines:
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point = VectorizedPoint(group[-1].get_center())
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group.add(point)
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to_fade_in.add(lineup.items[-1])
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new_stacks.add(new_stack)
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new_stacks.arrange_submobjects(
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RIGHT, buff = MED_LARGE_BUFF, aligned_edge = DOWN
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)
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new_stacks.move_to(stacks, DOWN)
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stacks.target = new_stacks
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stacks.to_fade_in = to_fade_in
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stacks.numbers.generate_target()
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for number, stack in zip(stacks.numbers.target, new_stacks):
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number.next_to(stack, UP)
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for stacks in top_stacks, bottom_stacks:
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self.play(
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MoveToTarget(stacks),
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MoveToTarget(stacks.numbers)
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)
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self.dither()
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#Fill extra slot
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add_man = TextMobject("Add", "$\\male$")
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add_man.highlight_by_tex("male", BLUE)
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add_woman = TextMobject("Add", "$\\female$")
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add_woman.highlight_by_tex("female", MAROON_B)
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add_man.next_to(ORIGIN, DOWN).to_edge(LEFT)
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add_woman.to_corner(UP+LEFT)
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for stacks, words in (bottom_stacks, add_man), (top_stacks, add_woman):
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to_fade_in = stacks.to_fade_in
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to_fade_in.set_fill(opacity = 1)
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to_fade_in.save_state()
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Transform(to_fade_in, VGroup(words[-1])).update(1)
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self.play(Write(words, run_time = 1))
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self.play(to_fade_in.restore)
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self.dither()
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#Perform shift
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dist = top_stacks[1].get_center()[0] - top_stacks[0].get_center()[0]
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self.play(
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top_stacks.shift, dist*RIGHT/2,
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top_stacks.numbers.shift, dist*RIGHT/2,
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bottom_stacks.shift, dist*LEFT/2,
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bottom_stacks.numbers.shift, dist*LEFT/2,
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)
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self.dither()
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self.play(*map(FadeOut, [add_man, add_woman, h_line]))
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self.set_variables_as_attrs(top_stacks, bottom_stacks)
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def combine_stacks(self):
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top_stacks = self.top_stacks
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bottom_stacks = self.bottom_stacks
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rects = VGroup()
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for stacks, color in (top_stacks, MAROON_C), (bottom_stacks, BLUE_D):
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for stack in stacks:
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rect = SurroundingRectangle(stack)
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rect.set_stroke(color, 2)
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rects.add(rect)
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stack.add(rect)
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new_numbers = VGroup()
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self.play(LaggedStart(ShowCreation, rects, run_time = 1))
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for i, top_stack in enumerate(top_stacks[:-1]):
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bottom_stack = bottom_stacks[i+1]
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top_number = top_stacks.numbers[i]
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bottom_number = bottom_stacks.numbers[i+1]
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movers = top_stack, top_number, bottom_number
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for mob in movers:
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mob.generate_target()
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top_stack.target.move_to(bottom_stack.get_top(), DOWN)
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plus = TexMobject("+")
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expr = VGroup(top_number.target, plus, bottom_number.target)
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expr.arrange_submobjects(RIGHT, buff = SMALL_BUFF)
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expr.next_to(top_stack.target.get_top(), UP)
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new_number = TexMobject(str(
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len(top_stack) + len(bottom_stack) - 2
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))
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new_number.next_to(expr, UP)
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new_numbers.add(new_number)
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self.play(
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Write(plus),
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*map(MoveToTarget, movers)
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)
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self.play(
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VGroup(top_stacks[-1], top_stacks.numbers[-1]).align_to,
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bottom_stacks, DOWN
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)
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self.dither()
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new_numbers.add_to_back(bottom_stacks.numbers[0].copy())
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new_numbers.add(top_stacks.numbers[-1].copy())
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new_numbers.highlight(PINK)
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self.play(Write(new_numbers, run_time = 3))
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self.dither()
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