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decode.py
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decode.py
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# Copyright (c) yusancky. All rights reserved.
# Licensed under the Mozilla Public License Version 2.0.
from manim import *
my_font = "HarmonyOS Sans SC Light"
class Makeee0(Scene):
def construct(self):
title0 = MarkupText(
"[CSP-J 2022] 解密", font=my_font, gradient=(BLUE, GREEN)
).scale(2.5)
self.play(Write(title0))
self.wait(1.5)
self.play(FadeOut(title0))
self.wait()
class Makeee1(Scene):
def construct(self):
title1 = MarkupText("题意简述", font=my_font, gradient=(BLUE, GREEN)).scale(2)
a1 = Text("给定正整数", font=my_font)
a2 = Tex("$n,e,d$").scale(1.2)
a3 = Text("，求两个正整数", font=my_font)
a4 = Tex("$p,q(p\leq q)$").scale(1.2)
a5 = Text("，", font=my_font)
a = VGroup(a1, a2, a3, a4, a5).arrange(RIGHT, buff=0.2)
b1 = Text("使", font=my_font)
b2 = Tex(
"$\\begin{cases} n&=p\\cdot q\\\\ e\\cdot d &= (p-1)(q-1)+1 \\end{cases}$"
).scale(1.2)
b3 = Text("。存在多组数据。", font=my_font)
b = VGroup(b1, b2, b3).arrange(RIGHT, buff=0.2)
task = VGroup(a, b).arrange(DOWN, buff=0.4)
self.play(Write(title1))
self.wait(1.5)
self.play(FadeOut(title1))
self.play(*[FadeIn(mob) for mob in task])
self.wait(8)
self.play(*[FadeOut(mob) for mob in task])
self.wait()
class Makeee2(Scene):
def construct(self):
title2 = MarkupText("题目分析", font=my_font, gradient=(BLUE, GREEN)).scale(2)
my_color_map = {
"n": BLUE_D,
"p\\cdot q": TEAL_C,
"e\\cdot d": GREEN_A,
"(p-1)(q-1)+1": PURPLE_B,
"p+q": MAROON_B,
"2": RED_B,
}
a1 = (
MathTex("n", "=", "p\\cdot q", ",", "e\\cdot d", "=", "(p-1)(q-1)+1")
.set_color_by_tex_to_color_map(my_color_map)
.scale(1.5)
)
a2 = (
MathTex("n", "-", "e\cdot d", "=", "p\cdot q", "-[", "(p-1)(q-1)+1", "]")
.set_color_by_tex_to_color_map(my_color_map)
.scale(1.5)
)
a3 = (
MathTex("n", "-", "e\cdot d", "=", "p+q", "-", "2")
.set_color_by_tex_to_color_map(my_color_map)
.scale(1.5)
)
a4 = (
MathTex("p+q", "=", "n", "-", "e\cdot d", "+", "2")
.set_color_by_tex_to_color_map(my_color_map)
.scale(1.5)
)
a5_1 = (
MathTex("{{p}}", "{{+}}", "{{q}}", "{{=}}", "{{n-e\cdot d+2}}")
.move_to(UP)
.scale(1.5)
)
a5_2 = (
MathTex("{{p}}", "{{\\cdot}}", "{{q}}", "{{=}}", "{{n}}")
.move_to(DOWN)
.scale(1.5)
)
a5 = VGroup(a5_1, a5_2)
Vieta1 = Text("Vieta 定理（推论）：一元二次多", font=my_font).scale(1.2)
Vieta2 = Text("项式", font=my_font).scale(1.2)
Vieta3 = Tex("$x^2+bx+c$").scale(1.2)
Vieta4 = Text("的两根", font=my_font).scale(1.2)
Vieta5 = Tex("$x_1,x_2$").scale(1.2)
Vieta6 = Text("总满", font=my_font).scale(1.2)
Vieta7 = Text("足", font=my_font).scale(1.2)
Vieta8 = MathTex(
"\\begin{cases} x_1+x_2=-b \\\\ x_1\\cdot x_2=c \\end{cases}"
).scale(1.2)
Vieta9 = Text("。", font=my_font).scale(1.2)
Vieta = VGroup(
Vieta1,
VGroup(Vieta2, Vieta3, Vieta4, Vieta5, Vieta6).arrange(RIGHT, buff=0.2),
VGroup(Vieta7, Vieta8, Vieta9).arrange(RIGHT, buff=0.2),
).arrange(DOWN, buff=0.4)
Vieta10 = MathTex(
"{{x_1}}",
"+",
"{{x_2}}",
"&=",
"{{-b}}",
"\\\\",
"{{x_1}}",
"\\cdot",
"{{x_2}}",
"&=",
"{{c}}",
).scale(1.5)
Vieta11_1 = MathTex(
"{{p}}", "{{+}}", "{{q}}", "{{=}}", "{{-b}}", "{{=}}", "{{n-e\cdot d+2}}"
).scale(1.5)
Vieta11_2 = MathTex(
"{{p}}", "{{\\cdot}}", "{{q}}", "{{=}}", "{{c}}", "{{=}}", "{{n}}"
).scale(1.5)
Vieta11 = VGroup(Vieta11_1, Vieta11_2).arrange(DOWN, 1)
Vieta12_1 = MathTex("b=e\cdot d-n-2").scale(1.5)
Vieta12_2 = MathTex("c=n").scale(1.5)
Vieta12 = VGroup(Vieta12_1, Vieta12_2).arrange(DOWN, 1)
eq1 = MathTex("x^2+bx+c=0").scale(1.5).move_to(3 * UP)
eq2 = MathTex("x^2+(e\\cdot d-n-2)x+c=0").scale(1.5).move_to(3 * UP)
eq3 = MathTex("x^2+(e\\cdot d-n-2)x+n=0").scale(1.5).move_to(3 * UP)
eq4 = VGroup(
MathTex("p,q").scale(0.8),
Text("是方程").scale(0.8),
MathTex("x^2+(e\\cdot d-n-2)x+n=0").scale(0.8),
Text("的两正整数根").scale(0.8),
).arrange(RIGHT, buff=0.2)
eq4_dl = Line(Dot(8 * LEFT + 2.5 * UP), Dot(8 * RIGHT + 2.5 * UP))
ans1 = MathTex("\\Delta =b^2-4ac").scale(1.5)
ans2 = MathTex("p,q=\\frac{-b\\pm \\sqrt \\Delta}{2}").scale(1.5)
ans3 = Text("（求根公式）", font=my_font)
ans = VGroup(ans1, ans2, ans3).arrange(DOWN, buff=0.4)
self.play(Write(title2))
self.wait(1.5)
self.play(FadeOut(title2))
self.play(GrowFromCenter(a1))
self.wait()
self.play(TransformMatchingTex(a1, a2))
self.wait(2)
self.play(TransformMatchingTex(a2, a3))
self.wait(2)
self.play(TransformMatchingTex(a3, a4))
self.wait(2)
self.play(a4.animate.shift(UP))
self.play(FadeOut(a4), FadeIn(a5_1, a5_2))
self.wait(2)
self.play(
Indicate(a5_1[0:3], scale_factor=1.5),
Indicate(a5_2[0:3], scale_factor=1.5),
run_time=1.5,
)
self.play(*[ScaleInPlace(obj, 0.8) for obj in a5], run_time=0.3)
self.play(a5_1.animate.to_edge(UP), a5_2.animate.to_edge(DOWN), run_time=0.5)
self.play(*[GrowFromEdge(obj, DOWN) for obj in Vieta])
self.play(Wiggle(Vieta))
self.wait(5)
self.play(
*[
FadeOut(obj, scale=0.5)
for obj in VGroup(Vieta[0], Vieta[1], Vieta7, Vieta9)
],
run_time=0.5
)
self.play(TransformMatchingShapes(Vieta8, Vieta10))
self.wait()
self.play(TransformMatchingTex(Group(Vieta10, a5), Vieta11), run_time=3)
self.wait(2)
self.play(TransformMatchingShapes(Vieta11, Vieta12), run_time=1)
self.wait()
self.play(FadeIn(eq1))
self.play(Indicate(Vieta12_1))
self.play(FadeTransform(eq1, eq2, stretch=True))
self.wait(0.5)
self.play(Indicate(Vieta12_2))
self.play(FadeTransform(eq2, eq3, stretch=True))
self.wait()
self.play(*[FadeOut(obj, shift=DOWN) for obj in Vieta12])
self.play(eq3.animate.shift(3 * DOWN))
self.wait(2)
self.play(FadeTransform(eq3, eq4, stretch=True))
self.wait(2)
self.play(eq4.animate.to_edge(UP))
self.play(Write(eq4_dl), run_time=0.4)
self.wait(2)
self.play(*[Write(obj) for obj in ans], run_time=0.5)
self.wait(3)
self.play(*[Unwrite(obj) for obj in VGroup(eq4, eq4_dl, ans1, ans2, ans3)], run_time=0.5)
self.wait()
class Makeee3(Scene):
def construct(self):
title3 = MarkupText("参考代码", font=my_font, gradient=(BLUE, GREEN)).scale(2)
rendered_code = Code(
"decode.cpp",
tab_width=2,
background="window",
language="cpp",
font="Consolas",
font_size=18,
)
self.play(Write(title3))
self.wait(1.5)
self.play(Unwrite(title3))
self.play(Write(rendered_code))
self.wait(10)
self.play(FadeOut(rendered_code))
self.wait()