improved binary search animation version
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271e150077
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a655236529
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@ -1,92 +1,112 @@
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from manim import *
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class Sequence(VMobject):
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# evenly spaced characters
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class Main(Scene):
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def construct(self):
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n = 13
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k = 8
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def __init__(self, seq):
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VMobject.__init__(self)
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seq = [t.move_to(i * 0.5 * RIGHT) for i, t in enumerate(seq)]
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self.add(VGroup(*seq).move_to(ORIGIN + 2*UP))
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class Pointer(VMobject):
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# pointer to sequence element
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def __init__(self, pointee, name):
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VMobject.__init__(self)
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arrow = Arrow(ORIGIN, DOWN).next_to(pointee, UP)
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name_tex = Tex(name).next_to(arrow, UP)
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self.add(arrow, name_tex)
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class ProgramCounter(VMobject):
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# pointer to current code line
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def __init__(self, line):
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VMobject.__init__(self)
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self.add(Arrow(ORIGIN, RIGHT).next_to(line, LEFT))
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class Base(Scene):
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def construct(self, n, k):
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# initial situation
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seq = [Tex("1")] + [Tex("?") for _ in range(n-2)] + [Tex("0")]
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self.play(Create(Sequence(seq)))
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# source code binary search
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code = Code(file_name="binary-search.py", language="Python", insert_line_no=False, style='monokai')
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code.move_to(DOWN)
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self.play(Write(code))
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line_lr, line_while, line_m, line_test, line_l, _, line_r = code[2]
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def test(x):
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def check(x):
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return 1 if x <= k else 0
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def update_pc(pc, line):
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npc = ProgramCounter(line)
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self.play(ReplacementTransform(pc, npc))
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return npc
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# initial situation
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seq = Matrix([[1] + ["?" for _ in range(n-1)] + [0]], h_buff=1.0).elements.move_to(0.5*UP)
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self.play(Create(seq))
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# source code binary search
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# while(high - low > 1){ // line_while
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# int mid = (low + high) / 2; // line_mid
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# if(check(mid)) // line_check
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# low = mid; // line_low
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# else
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# high = mid; // line_high
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# }
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code = Code(file_name="binary-search.cpp", language="c++", insert_line_no=False, style='monokai', tab_width=4, line_spacing=0.5).code
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code.move_to(4*RIGHT + 2.5*DOWN)
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while_line, mid_line, check_line, low_line, __, high_line, __ = code
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# check code
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check_code = Code(code="check(x)", language="c++", insert_line_no=False, style='monokai', tab_width=4, line_spacing=0.5).code
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check_background, check_code = check_code.move_to(2.5*UP).add_background_rectangle(opacity=1.0)
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self.play(Create(check_background), Write(check_code), Write(code))
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def pointer(name):
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arrow = Arrow(start=ORIGIN, end=UP)
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label = Tex(name).next_to(arrow, DOWN)
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return VGroup(arrow, label).scale(0.7)
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# initialize borders
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pc = ProgramCounter(line_lr)
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self.play(Create(pc))
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l, r = 0, n-1
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lp = Pointer(seq[l], "l")
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rp = Pointer(seq[r], "r")
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self.play(Write(lp), Create(rp))
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low = 0
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high = n
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low_pointer = pointer("low").next_to(seq[low], DOWN)
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high_pointer = pointer("high").next_to(seq[high], DOWN)
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self.play(Write(low_pointer), Create(high_pointer))
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while r - l > 1:
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# calculate m
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pc = update_pc(pc, line_m)
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m = (l + r) // 2
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mp = Pointer(seq[m], "m")
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self.play(Create(mp))
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mid_pointer = pointer("mid")
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# test
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pc = update_pc(pc, line_test)
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old = seq.copy()
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seq[m] = Tex(str(test(m)))
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self.play(ReplacementTransform(Sequence(old), Sequence(seq)))
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def indicate_start(line):
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line.save_state()
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self.play(line.animate.scale(1.3).set_color(YELLOW))
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if test(m):
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# update left
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pc = update_pc(pc, line_l)
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l = m
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op = lp
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lp = Pointer(seq[m], "l")
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self.play(Uncreate(mp), ReplacementTransform(op, lp))
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def indicate_end(line):
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self.play(Restore(line))
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def high_low_test():
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indicate_start(while_line)
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brace = BraceText(VGroup(*seq[low:high]), "high - low = " + str(high - low), brace_direction=UP)
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brace.label.scale(0.7)
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self.play(FadeIn(brace))
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self.wait(1)
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self.play(FadeOut(brace))
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indicate_end(while_line)
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while high_low_test() or high - low > 1:
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# calculate mid
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indicate_start(mid_line)
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mid = (low + high) // 2
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mid_pointer.next_to(seq[mid], DOWN)
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self.play(Write(mid_pointer))
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indicate_end(mid_line)
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# check
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indicate_start(check_line)
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seq[mid].add_background_rectangle(opacity=1.0)
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path = Line(start=seq[mid].get_center(), end=check_background.get_center())
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rpath = Line(start=path.get_end(), end=path.get_start())
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laser = path.copy().set_length(0.3)
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self.bring_to_back(laser)
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self.play(MoveAlongPath(laser, path))
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color = GREEN if (ans := check(mid)) else RED
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self.play(Indicate(check_code, color=color))
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self.bring_to_back(laser)
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self.play(MoveAlongPath(laser, rpath))
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self.remove(laser)
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# TODO: mark tested
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range_seq = seq[low+1:mid+1] if ans else seq[mid:high]
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self.play(*[Transform(s, Tex(ans).move_to(s)) for s in range_seq])
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indicate_end(check_line)
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if check(mid):
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# update low
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indicate_start(low_line)
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low = mid
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low_pointer.generate_target().move_to(mid_pointer)
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self.play(FadeOut(mid_pointer), MoveToTarget(low_pointer))
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indicate_end(low_line)
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else:
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# update right
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pc = update_pc(pc, line_r)
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r = m
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op = rp
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rp = Pointer(seq[m], "r")
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self.play(Uncreate(mp), ReplacementTransform(op, rp))
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# update high
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indicate_start(high_line)
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high = mid
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high_pointer.generate_target().move_to(mid_pointer)
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self.play(FadeOut(mid_pointer), MoveToTarget(high_pointer))
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indicate_end(high_line)
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self.wait(2)
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class Main(Base):
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def construct(self):
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Base.construct(self, 20, 6)
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@ -0,0 +1,7 @@
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while(high - low > 1){
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int mid = (low + high) / 2;
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if(check(mid))
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low = mid;
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else
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high = mid;
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}
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@ -1,7 +0,0 @@
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l, r = 0, n-1
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while r - l > 1:
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m = (l + r) / 2
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if test(m):
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l = m
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else:
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r = m
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