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):
# - 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()