def construct(self):
fib_code = self.get_fib_code(0.75)
fib_code.to_edge(UP)
self.add(fib_code)
fc2 = self.get_fib_code(0.6)
fc2.to_edge(UR)
self.play(ReplacementTransform(fib_code, fc2))
fib_code = fc2
first_fib_arg = 4
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
int x = fib(%d);
}
""" % first_fib_arg,
line_offset=11,
code_scale=0.6,
)
main_frame = StackFrame(main_code,
'main()',
13, ['x'],
width=2.5,
text_scale=0.6)
main_code.highlight_lines(13)
VGroup(main_code,
main_frame).arrange(RIGHT, buff=LARGE_BUFF * 2).to_edge(DOWN)
tree_area_frame = Polygon(
np.array((-FRAME_X_RADIUS, FRAME_Y_RADIUS, 0)),
np.array((fib_code.get_corner(UL)[0], FRAME_Y_RADIUS, 0)),
np.array((fib_code.get_corner(DL)[0], main_code.get_top()[1], 0)),
np.array((-FRAME_X_RADIUS, main_code.get_top()[1], 0)),
mark_paths_closed=True,
close_new_points=True,
)
ready_desc = TextMobject(
"We'll compute $F_%d$\\\\and track \\textit{all} "
"our work as we go" % first_fib_arg)
ready_desc.move_to(tree_area_frame)
self.play(FadeIn(ready_desc))
self.wait(duration=2)
self.play(
fib_code.to_edge,
UP,
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
tree_text_scale = 1.0
tmp_leaf = TextMobject('$F_%d$' % 1).scale(tree_text_scale)
leaf_width = tmp_leaf.get_width()
level_spread_factors = [4, 1.9, 1.75]
level_spreads = [f * leaf_width for f in level_spread_factors]
tree = BinaryTree(
max_depth=first_fib_arg,
leaf_height=tmp_leaf.get_height(),
level_buff=LARGE_BUFF * 1.5,
level_spreads=level_spreads,
text_scale=tree_text_scale,
)
def update_for_return(current_node, val, run_ctx):
v = TextMobject(str(val))
# v = TextMobject(current_node.label.tex_string, '$=%d$' % val)
v.set_color(GREEN_SCREEN)
v.scale(tree_text_scale)
v.move_to(current_node.label)
self.play(ReplacementTransform(current_node.label, v))
self.wait(duration=run_ctx['update_node_delay'])
extra_anims = []
if current_node.parent:
sr = SurroundingRectangle(current_node.parent)
extra_anims.append(ReplacementTransform(tree.current_rect, sr))
tree.current_rect = sr
extra_anims.append(
ApplyMethod(current_node.parent.set_color, YELLOW))
else:
extra_anims.append(FadeOut(tree.current_rect))
return extra_anims
def call_fib(run_ctx, call_stack, current_node, n):
run_ctx['call_count'] += 1
call_ret_delay = 0.5
stack_frame = StackFrame(fib_code,
'fib(%d)' % n,
1, ['n', 'fn1', 'fn2'],
width=call_stack[0].width,
text_scale=call_stack[0].text_scale)
sr = SurroundingRectangle(current_node)
extra_anims = [current_node.set_color, YELLOW]
if tree.current_rect:
extra_anims.append(ReplacementTransform(tree.current_rect, sr))
else:
extra_anims.append(ShowCreation(sr))
tree.current_rect = sr
if current_node.parent:
extra_anims.append(
ApplyMethod(current_node.parent.set_color, ORANGE))
call_stack.animate_call(stack_frame, self, extra_anims=extra_anims)
self.play(
*stack_frame.get_update_line_anims(2),
stack_frame.update_slot,
'n',
n,
)
if n == 0:
self.play(*stack_frame.get_update_line_anims(3))
self.wait(duration=call_ret_delay)
extra_anims = []
if run_ctx['call_count'] == 5:
s1 = TextMobject("and we know $F_0=0$")
s1.move_to(tree_area_frame).shift(DOWN)
self.play(FadeIn(s1))
extra_anims.append(FadeOut(s1))
extra_anims.extend(update_for_return(current_node, 0, run_ctx))
call_stack.animate_return(self, extra_anims=extra_anims)
return 0
self.play(*stack_frame.get_update_line_anims(5))
if n == 1:
self.play(*stack_frame.get_update_line_anims(6))
self.wait(duration=call_ret_delay)
extra_anims = []
if run_ctx['call_count'] == 4:
s1 = TextMobject("we know $F_1=1$")
s1.move_to(tree_area_frame).shift(DOWN)
self.play(FadeIn(s1))
extra_anims.append(FadeOut(s1))
extra_anims.extend(update_for_return(current_node, 1, run_ctx))
call_stack.animate_return(self, extra_anims=extra_anims)
return 1
self.play(*stack_frame.get_update_line_anims(8))
self.wait(duration=call_ret_delay)
s1 = None
if run_ctx['call_count'] == 1:
s1 = TextMobject('we need $F_3$ and $F_2$')
s1.move_to(tree_area_frame)
self.play(FadeIn(s1))
self.wait()
elif run_ctx['call_count'] == 2:
s1 = TextMobject('and now we need $F_2$ and $F_1$')
s1.move_to(tree_area_frame).shift(DOWN)
self.play(FadeIn(s1))
self.wait()
left_node, ll = tree.add_left_node(current_node,
'$F_%d$' % (n - 1))
right_node, rl = tree.add_right_node(current_node,
'$F_%d$' % (n - 2))
left_node.set_color(BLUE)
right_node.set_color(BLUE)
self.add(ll, rl,
tree.current_rect) # Keep the rect on top of lines
self.play(*[FadeIn(o) for o in [left_node, ll, right_node, rl]])
if s1:
self.wait()
self.play(FadeOut(s1))
s1 = None
fn1 = call_fib(run_ctx, call_stack, left_node, n - 1)
if run_ctx['call_count'] == 4:
s1 = TextMobject("now do the other half")
s1.move_to(tree_area_frame).shift(DOWN)
self.play(FadeIn(s1))
elif run_ctx['call_count'] == 6:
t1 = TextMobject("Using a ``tree'' for this is \\textit{much} "
"more helpful!").scale(0.8)
t2 = TextMobject("Shows where we've ", "been", ", where we ",
"are", ",\\\\and where we're ", "going")
t2.scale(0.8)
t2.set_color_by_tex_to_color_map({
"been": GREEN_SCREEN,
"are": YELLOW,
"going": BLUE,
})
t1.move_to(tree_area_frame).shift(DOWN)
t2.next_to(t1, DOWN, buff=MED_SMALL_BUFF)
self.play(FadeIn(t1))
self.wait()
self.play(Write(t2))
self.wait()
run_ctx['final_desc'] = VGroup(t1, t2)
self.play(
*stack_frame.get_update_line_anims(9),
stack_frame.update_slot,
'fn1',
fn1,
)
if s1:
self.wait()
self.play(FadeOut(s1))
s1 = None
self.wait(duration=call_ret_delay)
fn2 = call_fib(run_ctx, call_stack, right_node, n - 2)
extra_anims = []
if run_ctx['call_count'] == 5:
s1 = TextMobject("add the two halves")
s1.move_to(tree_area_frame).shift(DOWN)
self.play(FadeIn(s1))
extra_anims.append(FadeOut(s1))
run_ctx['update_node_delay'] = 0.1
self.play(
*stack_frame.get_update_line_anims(10),
stack_frame.update_slot,
'fn2',
fn2,
)
self.wait(duration=call_ret_delay)
extra_anims.extend(
update_for_return(current_node, fn1 + fn2, run_ctx))
call_stack.animate_return(self, extra_anims=extra_anims)
return fn1 + fn2
root_node, _ = tree.add_left_node(None, '$F_%d$' % first_fib_arg)
root_node.move_to(tree_area_frame)
root_node.to_edge(UP)
self.play(ShowCreation(root_node))
self.wait()
self.play(FadeOut(ready_desc))
run_ctx = {
'call_count': 0,
'update_node_delay': 1.0,
}
result = call_fib(run_ctx, CallStack(main_frame, scroll_height=1),
root_node, first_fib_arg)
self.play(
*main_frame.get_update_line_anims(14),
main_frame.update_slot,
'x',
result,
)
self.wait(duration=2)
self.play(FadeOutAndShiftDown(main_code),
FadeOutAndShiftDown(main_frame))
self.wait()
t1 = TextMobject("It is common to see recursive algorithms "
"described with trees")
t2 = TextMobject("\\textit{Try drawing them out as you go!}")
t2.set_color(GREEN)
t2.to_edge(DOWN)
t1.next_to(t2, UP, buff=MED_LARGE_BUFF)
self.play(FadeInFromDown(t1))
self.wait(duration=1.5)
self.play(Write(t2))
self.wait(duration=5)
x = self.camera.get_mobjects_to_display(self.mobjects)
end_scale_group = VGroup(*x)
end_fade_group = VGroup()
self.animate_yt_end_screen(end_scale_group,
end_fade_group,
end_scale=0.6,
show_elements=False)
def construct(self):
fib_code = CodeBlock(
'Java',
r"""
public static int fib(int n) {
if (n == 0) {
return 0;
}
if (n == 1) {
return 1;
}
int fn1 = fib(n - 1);
int fn2 = fib(n - 2);
return fn1 + fn2;
}
""",
)
self.add(fib_code)
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
int x = fib(3);
}
""",
line_offset=11,
code_scale=0.6,
)
frame_width = 2.5
main_frame = StackFrame(main_code,
'main()',
13, ['x'],
width=frame_width)
main_code.highlight_lines(13)
VGroup(main_code,
main_frame).arrange(RIGHT, buff=LARGE_BUFF * 2).to_edge(DOWN)
self.play(
fib_code.to_edge,
UP,
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
def call_fib(run_ctx, n, call_stack):
run_ctx['call_count'] += 1
call_ret_delay = 0.5
stack_frame = StackFrame(fib_code,
'fib(%d)' % n,
1, ['n', 'fn1', 'fn2'],
width=frame_width)
call_stack.animate_call(stack_frame, self)
self.play(
*stack_frame.get_update_line_anims(2),
stack_frame.update_slot,
'n',
n,
)
if n == 0:
self.play(*stack_frame.get_update_line_anims(3))
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return 0
self.play(*stack_frame.get_update_line_anims(5))
if n == 1:
self.play(*stack_frame.get_update_line_anims(6))
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return 1
self.play(*stack_frame.get_update_line_anims(8))
self.wait(duration=call_ret_delay)
fn1 = call_fib(run_ctx, n - 1, call_stack)
self.play(
*stack_frame.get_update_line_anims(9),
stack_frame.update_slot,
'fn1',
fn1,
)
if run_ctx['call_count'] == 4:
t1 = TextMobject('\\textit{Whoa!!}')
t1.set_color(YELLOW).scale(1.2)
t1.next_to(fib_code, LEFT, buff=MED_LARGE_BUFF)
self.play(GrowFromCenter(t1))
t2 = TextMobject("\\textit{I'm lost...}")
t2.next_to(t1, DOWN, buff=LARGE_BUFF)
self.play(FadeInFromPoint(t2, t2.get_center()))
run_ctx['whoa_desc'] = VGroup(t1, t2)
self.wait(duration=call_ret_delay)
fn2 = call_fib(run_ctx, n - 2, call_stack)
self.play(
*stack_frame.get_update_line_anims(10),
stack_frame.update_slot,
'fn2',
fn2,
)
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return fn1 + fn2
run_ctx = {
'call_count': 0,
}
result = call_fib(run_ctx, 3, CallStack(main_frame))
self.play(
*main_frame.get_update_line_anims(14),
main_frame.update_slot,
'x',
result,
)
self.wait(duration=2)
hrm_desc = TextMobject(
"That worked, but it was really hard to follow!")
hrm_desc.next_to(fib_code, DOWN, buff=MED_LARGE_BUFF)
self.play(FadeOutAndShiftDown(main_frame),
FadeOutAndShiftDown(main_code),
FadeOut(run_ctx['whoa_desc']))
self.play(FadeInFromDown(hrm_desc))
self.wait(duration=2.5)
t1 = TextMobject("The call stack shows where we are at any moment")
t1.move_to(hrm_desc)
t2 = TextMobject("but we don't know where we've been...")
t2.next_to(t1, DOWN)
t3 = TextMobject("or where we're going...")
t3.next_to(t2, DOWN)
self.play(ReplacementTransform(hrm_desc, t1))
self.wait(duration=2)
self.play(FadeInFromDown(t2))
self.wait(duration=2)
self.play(FadeInFromDown(t3))
self.wait(duration=2)
t4 = TextMobject(
"Let's go again, but draw a new picture along the way")
t4.move_to(t1)
self.play(*[FadeOutAndShift(o, UP) for o in [t1, t2, t3]],
FadeInFromDown(t4))
self.wait(duration=2.5)
self.play(FadeOut(t4))
def construct(self):
code_scale = 0.75
ss_code = CodeBlock(
'Java',
r"""
public static double StrangeSqrt(double a) {
if (a < 0) {
double b = StrangeSqrt(a * -1);
return b;
}
return Math.sqrt(a);
}
""",
code_scale=code_scale,
)
t1 = TextMobject(
'Consider this somewhat strange square root function:')
t1.next_to(ss_code, UP, buff=LARGE_BUFF)
self.play(
FadeIn(t1),
ShowCreation(ss_code),
)
self.wait(duration=2.5)
t2 = TextMobject(
'It has a recursive call, meaning \\textit{it calls itself.}')
t2.next_to(ss_code, DOWN, buff=LARGE_BUFF)
# 012345 6 7 8901234567890 1 2345
# double b = StrangeSqrt(a * -1);
rl = ss_code.get_code().get_lines(3)
rc_highlight = SurroundingRectangle(rl[8:-1])
self.play(
FadeIn(t2),
FadeIn(rc_highlight),
)
self.wait(duration=3)
self.play(
FadeOut(t2),
FadeOut(rc_highlight),
)
# Run with a positive input
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
double n = StrangeSqrt(4);
}
""",
line_offset=7,
code_scale=code_scale - 0.1,
)
frame_width = 3.5
main_frame = StackFrame(main_code,
'main()',
9, ['n'],
width=frame_width)
main_code.highlight_lines(9)
VGroup(main_code, main_frame).arrange(RIGHT,
buff=LARGE_BUFF).to_edge(DOWN)
t3 = TextMobject("Let's see what it does with a positive input...")\
.next_to(ss_code, DOWN, buff=LARGE_BUFF)
self.play(
FadeOut(t1),
MaintainPositionRelativeTo(t1, ss_code),
ss_code.to_edge,
UP,
FadeIn(t3),
MaintainPositionRelativeTo(t3, ss_code),
)
self.wait()
self.play(
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
ss_frame = StackFrame(ss_code,
'StrangeSqrt(4)',
1, ['a', 'b'],
width=frame_width)
ss_frame.next_to(main_frame, UP, buff=SMALL_BUFF)
xi = main_code.pre_call(ss_code, 1)
self.play(
*main_code.get_control_transfer_counterclockwise(xi),
FadeInFrom(ss_frame, UP),
FadeOut(t3),
)
ss_code.post_control_transfer(xi, self)
self.wait()
self.play(
ss_code.highlight_lines,
2,
ss_frame.set_line,
2,
ss_frame.update_slot,
'a',
4,
)
self.wait()
self.play(
ss_code.highlight_lines,
6,
ss_frame.set_line,
6,
)
self.wait()
xi = ss_code.pre_return(main_code, 9)
self.play(
*ss_code.get_control_transfer_clockwise(xi),
Uncreate(ss_frame),
)
main_code.post_control_transfer(xi, self)
self.wait()
t1 = TextMobject('That seems pretty normal...').next_to(
ss_code, DOWN, buff=LARGE_BUFF)
self.play(
main_code.highlight_lines,
10,
main_frame.set_line,
10,
main_frame.update_slot,
'n',
2,
FadeIn(t1),
)
self.wait(duration=2)
t2 = TextMobject("Let's try it with a negative input...")\
.next_to(ss_code, DOWN, buff=LARGE_BUFF)
self.play(
FadeOutAndShiftDown(main_code),
FadeOutAndShiftDown(main_frame),
FadeOut(t1),
FadeIn(t2),
)
# Run with a negative input and see the recursion
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
double n = StrangeSqrt(-4);
}
""",
line_offset=7,
code_scale=code_scale - 0.1,
)
main_frame = StackFrame(main_code,
'main()',
9, ['n'],
width=frame_width)
main_code.highlight_lines(9)
VGroup(main_code, main_frame).arrange(RIGHT,
buff=LARGE_BUFF).to_edge(DOWN)
self.play(
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
ss_frame = StackFrame(ss_code,
'StrangeSqrt(-4)',
1, ['a', 'b'],
width=frame_width)
ss_frame.next_to(main_frame, UP, buff=SMALL_BUFF)
xi = main_code.pre_call(ss_code, 1)
self.play(
*main_code.get_control_transfer_counterclockwise(xi),
FadeInFrom(ss_frame, UP),
FadeOut(t2),
)
ss_code.post_control_transfer(xi, self)
self.wait()
self.play(
ss_code.highlight_lines,
2,
ss_frame.set_line,
2,
ss_frame.update_slot,
'a',
-4,
)
self.wait()
self.play(
ss_code.highlight_lines,
3,
ss_frame.set_line,
3,
)
self.wait()
self.play(Indicate(rl[8:-1]), )
ss2_frame = StackFrame(ss_code,
'StrangeSqrt(4)',
1, ['a', 'b'],
width=frame_width)
ss2_frame.next_to(ss_frame, UP, buff=SMALL_BUFF)
r1_call_site_rect = ss_code.get_current_highlight().copy().set_color(
WHITE)
self.play(
FadeInFrom(ss2_frame, UP),
ss_code.highlight_lines,
1,
FadeIn(r1_call_site_rect),
)
self.wait()
stack = VGroup(main_frame, ss_frame, ss2_frame)
t1 = TextMobject('Same function, but with\\\\a new frame on the stack')\
.next_to(stack, LEFT, buff=LARGE_BUFF).shift(UP * 0.5)
a = Arrow(t1.get_right(), ss2_frame.get_left(), stroke_width=3)
self.play(
FadeIn(t1),
GrowArrow(a),
)
self.wait(duration=2)
# Now we have a positive input again
self.play(
ss_code.highlight_lines,
2,
ss2_frame.set_line,
2,
ss2_frame.update_slot,
'a',
4,
)
self.wait()
self.play(
ss_code.highlight_lines,
6,
ss2_frame.set_line,
6,
FadeOut(t1),
FadeOut(a),
)
self.wait()
t1 = TextMobject('The stack tells us where to return,\\\\and with which values')\
.next_to(stack, LEFT, buff=LARGE_BUFF).shift(UP * 0.5)
a = Arrow(t1.get_right(), ss_frame.get_left(), stroke_width=3)
self.play(
FadeIn(t1),
GrowArrow(a),
)
self.wait(duration=2)
# Return back to line 3...
self.play(
FadeOut(r1_call_site_rect),
Uncreate(ss2_frame),
ss_code.highlight_lines,
3,
ss_frame.set_line,
3,
)
self.wait()
self.play(
ss_code.highlight_lines,
4,
ss_frame.set_line,
4,
ss_frame.update_slot,
'b',
2,
FadeOut(t1),
FadeOut(a),
)
self.wait()
xi = ss_code.pre_return(main_code, 9)
self.play(
*ss_code.get_control_transfer_clockwise(xi),
Uncreate(ss_frame),
)
main_code.post_control_transfer(xi, self)
self.wait()
self.play(
main_code.highlight_lines,
10,
main_frame.set_line,
10,
main_frame.update_slot,
'n',
2,
)
self.wait()
t1 = TextMobject(
'Thinking about the call stack can help you keep track of\\\\'
'what a recursive function is doing at any given moment.').next_to(
ss_code, DOWN, buff=LARGE_BUFF)
self.play(
FadeOutAndShiftDown(main_code),
FadeOutAndShiftDown(main_frame),
FadeIn(t1),
)
self.wait(duration=3)
t2 = TextMobject('Try writing down part of the stack as you go.')\
.next_to(t2, DOWN, buff=LARGE_BUFF)
self.play(FadeInFromDown(t2))
self.wait(duration=2)
self.play(
FadeOut(t1),
FadeOut(t2),
)
self.wait()
def construct(self):
t1 = TextMobject("Let's compute $x^n$").shift(UP)
self.play(FadeIn(t1))
self.wait()
t2 = TextMobject("i.e., $2^4=16$, or $4^3=64$, etc.")
t2.next_to(t1, DOWN, buff=LARGE_BUFF)
self.play(FadeInFromDown(t2))
self.wait(duration=2)
t3 = TextMobject('Recall that')
f1 = TexMobject('x^n=', 'x', '\\times', 'x \\times ... \\times x',
'x^{n-1}')
f2 = TexMobject('x^n=', 'x', '\\times', 'x^{n-1}')
f2.next_to(t3, RIGHT)
dg = VGroup(t3, f2).center().shift(
UP) # Place t3 so the final result is centered
f1.next_to(t3, RIGHT)
b1 = BraceLabel(f1[1:-1],
'$n$ times',
brace_direction=UP,
label_constructor=TextMobject)
g = VGroup(t3, f1[:-1], b1) # For display
self.play(
FadeOut(t1),
FadeOut(t2),
FadeInFromDown(g),
)
self.wait(duration=3)
b2 = BraceLabel(f1[3],
'$n-1$ times',
brace_direction=UP,
label_constructor=TextMobject)
self.play(ReplacementTransform(b1, b2), )
self.wait(duration=2)
self.play(
ReplacementTransform(f1[3], f2[3]),
FadeOut(b2),
)
self.wait(duration=2)
t4 = TextMobject("That's starting to feel a bit recursive!")
t4.next_to(dg, DOWN, buff=MED_LARGE_BUFF)
self.play(FadeIn(t4))
self.wait()
code_scale = 0.75
power_code = CodeBlock(
'Java',
r"""
public static int power(int x, int n) {
if (n == 0) {
return 1;
}
int t = power(x, n - 1);
return x * t;
}
""",
code_scale=code_scale,
)
self.play(
*[FadeOut(o) for o in [t3, t4, f1[:-1], f2[3]]],
FadeInFromDown(power_code),
)
self.wait()
b1 = BraceLabel(
power_code.get_code().get_lines((2, 4)),
'Remember $x^0=1$, because math!',
brace_direction=RIGHT,
label_constructor=TextMobject,
label_scale=0.75,
)
self.play(ShowCreation(b1))
self.wait(duration=2)
t1 = TextMobject("Let's step through it to see how it goes...")
t1.next_to(power_code, DOWN)
self.play(FadeIn(t1), )
self.wait()
# Start stepping through this and see it go.
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
int y = power(4, 3);
}
""",
line_offset=7,
code_scale=code_scale - 0.1,
)
frame_width = 3.5
main_frame = StackFrame(main_code,
'main()',
9, ['y'],
width=frame_width)
main_code.highlight_lines(9)
VGroup(main_code, main_frame).arrange(RIGHT,
buff=LARGE_BUFF).to_edge(DOWN)
self.play(
FadeOut(t1),
FadeOut(b1),
power_code.to_edge,
UP,
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
def call_power(x, n, call_stack):
stack_frame = StackFrame(power_code,
'power(%d, %d)' % (x, n),
1, ['x', 'n', 't'],
width=frame_width)
call_stack.animate_call(stack_frame, self)
self.play(*stack_frame.get_update_line_anims(2),
stack_frame.update_slot, 'x', x, stack_frame.update_slot,
'n', n)
if n == 0:
self.play(*stack_frame.get_update_line_anims(3))
self.wait()
call_stack.animate_return(self)
return 1
else:
self.play(*stack_frame.get_update_line_anims(5))
self.wait()
t = call_power(x, n - 1, call_stack)
self.play(
*stack_frame.get_update_line_anims(6),
stack_frame.update_slot,
't',
t,
)
self.wait()
call_stack[-1].code = power_code
call_stack.animate_return(self)
return x * t
result = call_power(4, 3, CallStack(main_frame))
self.play(*main_frame.get_update_line_anims(10),
main_frame.update_slot, 'y', result)
self.wait()
final_eq = TexMobject('4^3=', '64')
final_eq.next_to(power_code, DOWN, buff=LARGE_BUFF)
lhs = final_eq[0].copy().move_to(
main_code.get_code().get_lines(2)[12:15])
rhs = final_eq[1].copy().move_to(main_frame.slots()[0])
self.play(
ReplacementTransform(lhs, final_eq[0]),
ReplacementTransform(rhs, final_eq[1]),
)
self.wait(duration=2)
self.play(*[FadeOut(o) for o in [final_eq, main_frame, main_code]])
self.wait()
def construct(self):
# - Now, let's change this a bit and break it!
# - Now modify it (a <= 0) and call it with foo(0).
# - switch it out for the broken one, and highlight and note the change.
code_scale = 0.75
ss_good_code = CodeBlock(
'Java',
r"""
public static double StrangeSqrt(double a) {
if (a < 0) {
double b = StrangeSqrt(a * -1);
return b;
}
return Math.sqrt(a);
}
""",
code_scale=code_scale,
)
ss_good_code.to_edge(UP)
self.add(ss_good_code)
t1 = TextMobject(
"Let's break this code in a very small way and\\\\see what happens..."
)
t1.next_to(ss_good_code, DOWN, buff=LARGE_BUFF)
self.play(FadeIn(t1))
self.wait()
gl2 = ss_good_code.get_code().get_lines(2)
ghr = SurroundingRectangle(gl2[3:6])
self.play(ShowCreation(ghr))
self.wait()
ss_bad_code = CodeBlock(
'Java',
r"""
public static double StrangeSqrt(double a) {
if (a <= 0) {
double b = StrangeSqrt(a * -1);
return b;
}
return Math.sqrt(a);
}
""",
code_scale=code_scale,
)
ss_bad_code.to_edge(UP)
bl2 = ss_bad_code.get_code().get_lines(2)
bhr = SurroundingRectangle(bl2[3:7])
self.play(
ReplacementTransform(ss_good_code, ss_bad_code),
ReplacementTransform(ghr, bhr),
)
self.wait()
t2 = TextMobject(
"This small change will have a big effect on one case: 0\\\\"
"Let's run it and see.").next_to(ss_bad_code,
DOWN,
buff=LARGE_BUFF)
self.play(
FadeOut(t1),
FadeIn(t2),
)
self.wait(duration=3)
self.play(
FadeOut(t2),
FadeOut(bhr),
)
self.wait()
# - Start stepping through this and see the stack start to grow forever.
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
double n = StrangeSqrt(0);
}
""",
line_offset=7,
code_scale=code_scale - 0.1,
)
frame_width = 3.5
main_frame = StackFrame(main_code,
'main()',
9, ['n'],
width=frame_width)
main_code.highlight_lines(9)
VGroup(main_code, main_frame).arrange(RIGHT,
buff=LARGE_BUFF).to_edge(DOWN)
self.play(
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
ss_frame = StackFrame(ss_bad_code,
'StrangeSqrt(0)',
1, ['a', 'b'],
width=frame_width)
ss_frame.next_to(main_frame, UP, buff=SMALL_BUFF)
xi = main_code.pre_call(ss_bad_code, 1)
self.play(
*main_code.get_control_transfer_counterclockwise(xi),
FadeInFrom(ss_frame, UP),
)
ss_bad_code.post_control_transfer(xi, self)
self.wait()
self.play(ss_bad_code.highlight_lines, 2, ss_frame.set_line, 2,
ss_frame.update_slot, 'a', 0)
self.wait()
self.play(ss_bad_code.highlight_lines, 3, ss_frame.set_line, 3)
self.wait()
def call_ss_again(stack_group, previous_frame, extras=None):
wait_each_step = len(stack_group) < 3
runtime = 1.0 if len(stack_group) < 2 else 0.5 if len(
stack_group) < 6 else 0.20
extra_anims = []
if len(stack_group) > 2:
extra_anims.append(
ApplyMethod(
stack_group.shift,
DOWN * previous_frame.get_height() +
DOWN * SMALL_BUFF))
if extras:
extra_anims.extend(extras)
f = StackFrame(ss_bad_code,
'StrangeSqrt(0)',
1, ['a', 'b'],
width=frame_width)
f.next_to(previous_frame, UP, buff=SMALL_BUFF)
self.play(*extra_anims,
ss_bad_code.highlight_lines,
1,
f.set_line,
1,
FadeIn(f),
MaintainPositionRelativeTo(f, previous_frame),
run_time=runtime)
if wait_each_step:
self.wait()
self.play(ss_bad_code.highlight_lines,
2,
f.set_line,
2,
f.update_slot,
'a',
0,
run_time=runtime)
if wait_each_step:
self.wait()
self.play(ss_bad_code.highlight_lines,
3,
f.set_line,
3,
run_time=runtime)
if wait_each_step:
self.wait()
stack_group.add(f)
return f
sg = VGroup(main_frame, ss_frame)
curr_ss_frame = ss_frame
for i in range(3):
curr_ss_frame = call_ss_again(sg, curr_ss_frame)
# - When will this program end? Never?
t1 = TextMobject("Hrm... when is this going to end??").next_to(
main_code, UP, buff=LARGE_BUFF)
extra_text = [FadeIn(t1)]
for i in range(4):
curr_ss_frame = call_ss_again(sg, curr_ss_frame, extra_text)
extra_text = None
t2 = TextMobject("Never?").next_to(main_code, UP, buff=LARGE_BUFF)
extra_text = [FadeOut(t1), FadeIn(t2)]
for i in range(4):
curr_ss_frame = call_ss_again(sg, curr_ss_frame, extra_text)
extra_text = None
sg.save_state()
t3 = TextMobject("The stack is getting quite deep!").next_to(
main_code, UP, buff=LARGE_BUFF)
self.play(sg.scale, 0.20, {'about_edge': TOP}, FadeOut(t2), FadeIn(t3))
self.wait(duration=2)
self.play(sg.restore)
extra_text = [FadeOut(t3)]
for i in range(4):
curr_ss_frame = call_ss_again(sg, curr_ss_frame, extra_text)
extra_text = None
# - Well, the stack is finite, so eventually you get a SO.
# Use the Java SO exception and show it hit and stop.
so_frame = StackFrame(ss_bad_code,
'StrangeSqrt(0)',
1, ['a', 'b'],
width=frame_width)
so_frame.slots().set_color(ORANGE)
so_frame.header_line().set_color(ORANGE)
so_frame.background_rect().set_fill(color=[BLACK, RED])
so_frame.next_to(curr_ss_frame, UP, buff=SMALL_BUFF)
so_exception = TextMobject(
'\\texttt{Exception in thread "main"\\\\java.lang.StackOverflowError}',
).set_color(YELLOW).scale(0.75).next_to(main_code, UP, buff=LARGE_BUFF)
self.play(sg.shift,
DOWN * so_frame.get_height() + DOWN * SMALL_BUFF,
ss_bad_code.get_current_highlight().set_color, ORANGE,
FadeIn(so_frame),
MaintainPositionRelativeTo(so_frame, curr_ss_frame),
Write(so_exception))
sg.add(so_frame)
self.wait(duration=2)
ss_bad_code.generate_target()
so_exception.generate_target()
ss_bad_code.target.scale(0.75)
g = VGroup(so_exception.target,
ss_bad_code.target).arrange(RIGHT, buff=LARGE_BUFF)
g.to_edge(UP)
sg.generate_target()
sg.target.scale(0.15).next_to(g, DOWN).to_edge(RIGHT)
t1 = TextMobject(
"Space for the call stack is limited,\\\\so we can't make recursive calls forever!"
)
self.play(
*[MoveToTarget(t) for t in [so_exception, ss_bad_code, sg]],
FadeOutAndShiftDown(main_code),
FadeInFromDown(t1),
)
self.wait(duration=2)
t2 = TextMobject(
"This program made {\\raise.17ex\\hbox{$\\scriptstyle\\sim$}}15,000 calls before crashing."
)
t4 = TextMobject(
"\\textit{Java SE 13.0.1 on macOS Catalina 10.15.4}").scale(0.5)
t2.next_to(t1, DOWN, buff=MED_LARGE_BUFF)
t4.to_edge(DL)
self.play(
FadeIn(t2),
FadeInFromDown(t4),
)
self.wait(duration=4)
t5 = TextMobject('\\textit{Most common mistake with recursion.}')
t6 = TextMobject("You'll see this a lot. Everyone does!")
t6.next_to(t5, DOWN, buff=LARGE_BUFF)
self.play(
*[FadeOut(t) for t in [t1, t2, t4]],
*[FadeIn(t) for t in [t5, t6]],
)
self.wait(duration=3)
# Transition
t1 = TextMobject(
"Alright, let's look at a more interesting function...")
self.play(
*[FadeOut(o) for o in self.mobjects],
FadeIn(t1),
)
self.wait()
self.play(FadeOut(t1))
self.wait()
def construct(self):
code_scale = 0.7
power2_code = CodeBlock(
'Java',
r"""
public static int power2(int x, int n) {
if (n == 0) {
return 1;
}
int t = power2(x, n / 2);
if (n % 2 == 0) {
return t * t;
}
return t * t * x;
}
""",
code_scale=code_scale,
)
power2_code.to_edge(UP)
self.add(power2_code)
t1 = TextMobject(
"This version should call itself fewer than $n$ times")
t1.next_to(power2_code, DOWN, buff=LARGE_BUFF)
self.play(FadeInFromDown(t1))
self.wait(duration=2.5)
t2 = TextMobject(
'How many times do you think \\texttt{power2(2,30)} will call itself?',
tex_to_color_map={'30': YELLOW})
t2.next_to(t1, ORIGIN)
self.play(FadeOutAndShift(t1, UP), FadeInFromDown(t2))
self.wait(duration=2)
t3 = TextMobject("We know it'll be less than 30! Maybe 15?")
t3.next_to(t2, DOWN, buff=MED_LARGE_BUFF)
self.play(FadeInFromDown(t3))
self.wait(duration=2)
t4 = TextMobject("How about a lot less? Let's see...")
t4.next_to(t3, ORIGIN)
self.play(ReplacementTransform(t3, t4))
self.wait(duration=2)
self.play(*[FadeOut(o) for o in self.mobjects if o != power2_code])
# Start stepping through this and see it go.
main_code = CodeBlock(
'Java',
r"""
public static void main(String[] args) {
int y = power2(2, 30);
}
""",
line_offset=10,
code_scale=code_scale - 0.1,
)
frame_width = 3.5
main_frame = StackFrame(main_code,
'main()',
12, ['y'],
width=frame_width,
slot_char_width=8)
main_code.highlight_lines(12)
VGroup(main_code, main_frame).arrange(RIGHT,
buff=LARGE_BUFF).to_edge(DOWN)
self.play(
FadeInFromDown(main_frame),
FadeInFromDown(main_code),
)
self.wait()
def call_power2(x, n, call_stack, cc_num):
new_cc_num = TextMobject(str(len(call_stack) -
1)).move_to(cc_num).set_color(YELLOW)
update_cc_anims = [ReplacementTransform(cc_num, new_cc_num)]
call_ret_delay = 0.5
stack_frame = StackFrame(power2_code,
'power(%d, %d)' % (x, n),
1, ['x', 'n', 't'],
width=frame_width)
call_stack.animate_call(stack_frame,
self,
extra_anims=update_cc_anims)
self.play(
*stack_frame.get_update_line_anims(2),
stack_frame.update_slot,
'x',
x,
stack_frame.update_slot,
'n',
n,
)
if n == 0:
self.play(*stack_frame.get_update_line_anims(3))
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return 1
else:
self.play(*stack_frame.get_update_line_anims(5))
self.wait(duration=call_ret_delay)
t = call_power2(x, n // 2, call_stack, new_cc_num)
self.play(
*stack_frame.get_update_line_anims(6),
stack_frame.update_slot,
't',
t,
)
if n % 2 == 0:
self.play(*stack_frame.get_update_line_anims(7))
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return t * t
self.play(*stack_frame.get_update_line_anims(9))
self.wait(duration=call_ret_delay)
call_stack.animate_return(self)
return t * t * x
cc_label = TextMobject('Recursive Calls').scale(0.75)
cc_label.to_edge(UL).shift(DOWN)
call_counter = TextMobject('0').set_color(YELLOW).next_to(
cc_label, DOWN)
self.play(FadeIn(call_counter), FadeIn(cc_label))
result = call_power2(2, 30, CallStack(main_frame), call_counter)
self.play(
*main_frame.get_update_line_anims(13),
main_frame.update_slot,
'y',
result,
)
self.wait()
t1 = TextMobject(
'We got our answer in just 5 recursive calls!').set_color(YELLOW)
t1.next_to(power2_code, DOWN, buff=MED_LARGE_BUFF)
self.play(ShowCreation(t1))
self.wait(duration=2)
t1.generate_target()
t1.target.center().to_edge(TOP)
t2 = TextMobject('But why?').next_to(t1.target, DOWN, buff=LARGE_BUFF)
self.play(
MoveToTarget(t1),
FadeInFromDown(t2),
*[FadeOut(o) for o in self.mobjects if o != t1],
)