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NineChooseFourExample of eop/combinations
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Grant Sanderson
parent
47ee3c71dd
commit
1471c4eef9
1 changed files with 184 additions and 23 deletions
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@ -2634,7 +2634,8 @@ class HowToComputeNChooseK(ChooseThreeFromFive):
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CONFIG = {
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"n" : 5,
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"k" : 3,
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"line_colors" : [GREEN, YELLOW]
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"line_colors" : [GREEN, YELLOW],
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"n_permutaitons_to_show" : 5,
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}
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def construct(self):
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self.setup_people()
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@ -2662,24 +2663,7 @@ class HowToComputeNChooseK(ChooseThreeFromFive):
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n, k = self.n, self.k
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names = self.names
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width = max([n.get_width() for n in self.names]) + 2*SMALL_BUFF
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lines = VGroup(*[
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Line(ORIGIN, width*RIGHT)
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for x in range(k)
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])
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lines.arrange_submobjects(RIGHT)
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lines.next_to(ORIGIN, DOWN, buff = LARGE_BUFF)
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place_words = VGroup(*[
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TexMobject("%d^\\text{%s}"%(i+1, s))
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for i, s in zip(
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range(k),
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it.chain(["st", "nd", "rd"], it.repeat("th"))
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)
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])
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for mob in place_words, lines:
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mob.gradient_highlight(*self.line_colors)
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for word, line in zip(place_words, lines):
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word.next_to(line, DOWN, SMALL_BUFF)
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lines, place_words = self.get_lines_and_place_words()
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for x in range(3):
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chosen_names = VGroup(*random.sample(names, k))
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@ -2761,7 +2745,8 @@ class HowToComputeNChooseK(ChooseThreeFromFive):
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chosen_names = self.chosen_names
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lines = self.lines
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for indices in list(it.permutations(range(3)))[1:]:
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n_perms = self.n_permutaitons_to_show + 1
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for indices in list(it.permutations(range(3)))[1:n_perms]:
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self.play(*[
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ApplyMethod(
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name.next_to, lines[i], UP, SMALL_BUFF,
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@ -2922,9 +2907,185 @@ class HowToComputeNChooseK(ChooseThreeFromFive):
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for count, line in zip(choice_counts, lines)
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])
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def get_lines_and_place_words(self):
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n, k = self.n, self.k
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width = max([n.get_width() for n in self.names]) + MED_SMALL_BUFF
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lines = VGroup(*[
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Line(ORIGIN, width*RIGHT)
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for x in range(k)
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])
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lines.arrange_submobjects(RIGHT)
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lines.next_to(ORIGIN, DOWN, buff = LARGE_BUFF)
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place_words = VGroup(*[
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TexMobject("%d^\\text{%s}"%(i+1, s))
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for i, s in zip(
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range(k),
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it.chain(["st", "nd", "rd"], it.repeat("th"))
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)
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])
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for mob in place_words, lines:
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mob.gradient_highlight(*self.line_colors)
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for word, line in zip(place_words, lines):
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word.next_to(line, DOWN, SMALL_BUFF)
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self.set_variables_as_attrs(lines, place_words)
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return lines, place_words
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class NineChooseFourExample(HowToComputeNChooseK):
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CONFIG = {
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"random_seed" : 2,
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"n" : 9,
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"k" : 4,
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"line_colors" : [RED, MAROON_B],
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"n_permutaitons_to_show" : 3,
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}
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def construct(self):
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self.setup_people()
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self.show_n_choose_k()
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self.show_n_choose_k_pattern()
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self.choose_k_people()
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self.count_how_to_choose_k()
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self.show_permutations()
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self.finish_computation()
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def setup_people(self):
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self.remove(self.people)
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self.people = TextMobject(" ".join([
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chr(ord('A') + i )
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for i in range(self.n)
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]))
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self.people.gradient_highlight(BLUE, YELLOW)
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self.names = self.people
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self.people.to_edge(UP, buff = LARGE_BUFF + MED_SMALL_BUFF)
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lb, rb = braces = TextMobject("\\{\\}")
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braces.scale(1.5)
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lb.next_to(self.people, LEFT, SMALL_BUFF)
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rb.next_to(self.people, RIGHT, SMALL_BUFF)
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self.people_group = VGroup(braces, self.people)
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self.people_braces = braces
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def show_n_choose_k(self):
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n, k = self.n, self.k
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n_choose_k = TexMobject("{%d \\choose %d}"%(n, k))
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n_choose_k.to_corner(UP + LEFT)
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self.play(FadeIn(n_choose_k))
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self.set_variables_as_attrs(n_choose_k)
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def show_n_choose_k_pattern(self):
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n, k = self.n, self.k
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stack = get_stack(
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TexMobject("1").highlight(PINK),
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TexMobject("0").highlight(BLUE),
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n, k
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)
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l = len(stack)
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n_stacks = 6
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columns = VGroup(*[
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VGroup(*stack[(i*l)/n_stacks:((i+1)*l)/n_stacks])
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for i in range(n_stacks)
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])
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columns.arrange_submobjects(
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RIGHT,
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aligned_edge = UP,
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buff = MED_LARGE_BUFF
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)
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columns.scale_to_fit_height(7)
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columns.to_corner(DOWN + RIGHT)
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for line in stack:
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self.play(FadeIn(line, run_time = 0.1))
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self.dither(2)
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self.play(FadeOut(
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stacks, submobject_mode = "lagged_start", run_time = 2
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))
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def choose_k_people(self):
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n, k = self.n, self.k
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people = self.people
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braces = self.people_braces
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n_items = TextMobject("%d items"%n)
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choose_k = TextMobject("choose %d"%k)
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n_items.next_to(people, UP, buff = MED_LARGE_BUFF)
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choose_k.next_to(people, DOWN, buff = LARGE_BUFF)
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chosen_subset = VGroup(*random.sample(people, k))
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self.play(
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Write(braces),
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LaggedStart(FadeIn, people, run_time = 1),
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FadeIn(n_items),
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)
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self.dither()
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self.play(
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FadeIn(choose_k),
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LaggedStart(
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ApplyMethod, chosen_subset,
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lambda m : (m.shift, MED_LARGE_BUFF*DOWN)
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)
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)
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self.dither()
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self.play(
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chosen_subset.shift, MED_LARGE_BUFF*UP,
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n_items.next_to, n_items.get_center(), LEFT,
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choose_k.next_to, n_items.get_center(), RIGHT,
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)
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def count_how_to_choose_k(self):
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lines, place_words = self.get_lines_and_place_words()
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self.play(
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LaggedStart(FadeIn, lines),
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LaggedStart(FadeIn, place_words),
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run_time = 1
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)
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self.count_possibilities()
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def show_permutations(self):
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self.show_permutations_of_ABC()
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self.count_permutations_of_ABC()
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def finish_computation(self):
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equals = TexMobject("=")
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fraction = self.fraction
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six = fraction[0][0][3]
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eight = fraction[0][0][1]
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two_three = VGroup(*fraction[2][0][1:3])
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four = fraction[2][0][0]
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rhs = TexMobject("= 9 \\cdot 2 \\cdot 7 = 126")
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self.play(
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self.names.restore,
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FadeOut(self.lines),
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FadeOut(self.place_words),
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self.n_choose_k.next_to, equals, LEFT,
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self.fraction.next_to, equals, RIGHT,
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FadeIn(equals),
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)
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self.dither()
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for mob in six, eight, two_three, four:
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mob.cross = Cross(mob)
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mob.cross.set_stroke("red", 5)
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two = TexMobject("2")
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two.highlight(eight.get_fill_color())
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two.next_to(eight, UP)
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rhs.next_to(fraction, RIGHT)
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self.play(
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ShowCreation(six.cross),
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ShowCreation(two_three.cross),
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)
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self.dither()
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self.play(
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ShowCreation(eight.cross),
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ShowCreation(four.cross),
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FadeIn(two)
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)
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self.dither()
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self.play(Write(rhs))
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self.dither()
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