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Figures_all_in_three.tex
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Figures_all_in_three.tex
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\documentclass[UTF8,nofonts,mathserif]{beamer}
\usepackage{beamerthemeshadow}
\usepackage{beamerthemesplit}
\usepackage[noindent,nofonts]{ctexcap}
\setCJKmainfont[BoldFont=STHeiti]{STXihei}
%\setromanfont{SimSun}
\usepackage{xcolor}
%\usetheme{shadow}
\usecolortheme{default}
\setbeamertemplate{footline}[frame number]
\useinnertheme[shadow=true]{rounded}
%\setbeamertemplate{footline}{\insertframenumber/\inserttotalframenumber}
%\useoutertheme{infolines}
%\setbeamertemplate{headline}{} % removes the headline that infolines inserts
%\usetheme{boxes}
%\usepackage{amsmass}
%\usepackage{amssymb,amsfonts,url}
\usepackage{algorithm}
\usepackage{algorithmic}
\usepackage{graphicx}
\graphicspath{{Problems/}}
\usepackage{tikz}
\usetikzlibrary{shadows}
\usetikzlibrary{positioning}
\usepackage{verbatim}
\usepackage{pgfplots}
\usepackage{verbatim}
\usetikzlibrary{arrows,shapes}
\definecolor{darkblue}{rgb}{0.2,0.2,0.6}
\definecolor{darkred}{rgb}{0.6,0.1,0.1}
\definecolor{darkgreen}{rgb}{0.2,0.6,0.2}
\usetikzlibrary{shadings,shadows,shapes.arrows}
\usetikzlibrary{calc}
\makeatletter
\@namedef{color@3}{blue!20}
\@namedef{color@1}{green!70}
%\@namedef{color@3}{yellow!50}
\@namedef{color@2}{orange!90}
%\@namedef{color@5}{magenta!70}
%\@namedef{color@6}{yellow!70}
\newcommand{\graphitemize}[2]{%
\begin{tikzpicture}[every node/.style={align=center}, scale=0.78]
\draw[fill=green!5, fill opacity=0.1, green, inner sep=0.05cm, outer sep=0.05cm] (5,0) arc(0:360:5);
% \draw[fill=white, fill opacity=0.1, white, inner sep=0.05cm, outer sep=0.05cm] (4,0) arc(0:360:4);
% \shade[ball color=gray!10!] (0,0) coordinate(Hp) circle (.9);
\node[shape=circle, minimum size=1.1cm,fill=red!60,font=\Large,outer sep =.15cm,inner sep=.2cm,drop shadow={ashadow, color=yellow}](ce){#1};
% \shade[ball color=blue!20!] (0,0) coordinate($Algorithm$) circle (1.5cm);
\foreach \gritem [count=\xi] in {#2} {\global\let\maxgritem\xi}
\foreach \gritem [count=\xi] in {#2}
{%
\pgfmathtruncatemacro{\angle}{90+360/\maxgritem*\xi}
\edef\col{\@nameuse{color@\xi}}
\node[shape=circle,
ultra thick,
draw=white,
fill opacity=1,
drop shadow={ashadow, color=blue!60},
fill=\col,outer sep=0.25cm,
minimum size=2cm] (satellite-\xi) at (\angle:5cm) {\gritem };
\draw[line width=0.25cm,-latex, \col] (ce) -- (satellite-\xi);
}%
% \draw[violet, fill=violet!10] (4,0) arc(0:360:4);
\end{tikzpicture}
}%
\newcommand*{\tikzarrow}[2]{%
\tikz[
baseline=(A.base), % Set baseline to the baseline of node content
font=\footnotesize\sffamily % Set fontsize of the node content
]
\node[
single arrow, % Shape of the node
single arrow head extend=2pt, % Actual width of arrow head
draw, % Draw the node shape
inner sep=2pt, % Separation between node content and node shape
top color=white, % Shading color on top of node
bottom color=#1, % Shading color on bottom of node
drop shadow % Draw a shadow
] (A) {#2};%
}
\def\arrow{
(10.05:1.1) -- (6.05:1) arc (6.05:120:1) [rounded corners=0.5] --
(120:0.9) [rounded corners=1] -- (130:1.1) [rounded corners=0.5] --
(120:1.3) [sharp corners] -- (120:1.2) arc (120:5.25:1.2)
[rounded corners=1] -- (10.05:1.1) -- (6.05:1) -- cycle
}
\tikzset{
ashadow/.style={opacity=.25, shadow xshift=0.07, shadow yshift=-0.07},
}
\def\arrows[#1]{
\begin{scope}[scale=#1]
\draw[color=darkred, drop shadow={ashadow, color=red!60!black}] \arrow;
\draw[color=darkgreen, bottom color=green!90!black, top color=green!60, drop shadow={ashadow, color=green!60!black}] [rotate=120] \arrow;
\draw[color=darkblue, right color=blue, left color=blue!60, drop shadow={ashadow, color=blue!60!black}] [rotate=240] \arrow;
% to hide the green shadow
\draw[color=darkred, left color=red, right color=red!60] \arrow;
\end{scope}
}
\tikzstyle{vertex}=[circle,fill=black!25,draw,minimum size=20pt,inner sep=0pt]
\tikzstyle{middlevertex}=[circle,fill=black!25,draw,minimum size=15pt,inner sep=0pt]
\tikzstyle{smallvertex}=[circle,fill=black!25,draw,minimum size=10pt,inner sep=0pt]
\tikzstyle{tinyvertex}=[circle,fill=black!25,draw,minimum size=5pt,inner sep=0pt]
\tikzstyle{selected vertex} = [vertex, draw,fill=yellow!24]
\tikzstyle{blue smallvertex} = [smallvertex, draw,fill=blue]
\tikzstyle{red smallvertex} = [smallvertex, draw,fill=yellow]
\tikzstyle{edge} = [draw,thick,->]
\tikzstyle{undirectededge} = [draw,thick]
\tikzstyle{weight} = [font=\small]
\tikzstyle{selected edge} = [draw,line width=3pt,-,red!50]
\tikzstyle{ignored edge} = [draw,line width=3pt,-,black!20]
\tikzstyle{squarednode}=[draw, fill=blue!20, thick, minimum size=5mm]
\tikzstyle{roundnode}=[circle, draw, fill=blue!20, thick, minimum size=5mm]
\title{CS711008Z Algorithm Design and Analysis }
\author{Dongbo Bu }
\institute{ {\small Institute of Computing Technology \\
Chinese Academy of Sciences, Beijing, China}}
\date{}
\begin{document}
\frame{
\frametitle{LP x1x2-1}
\begin{figure}
\begin{tikzpicture} [auto, scale=0.7]
\node at (4.7,4.5) {$x_{1} + x_{2} = 2$};
\node at (4.6,0.5) {$x_{1} +x_{2} = -1$};
\node[below] at (7, 2) {$x_1$};
\node[right] at (3.2, 5.5) {$x_2$};
\pgfplotsset{my style/.append style={ axis x line=middle, axis y line=middle, axis equal }}
\begin{axis}[thick, my style,
% xlabel=$x_1$,
% ylabel=$x_2$,
xtick={ -1,..., 2},
ytick={ -1,..., 2},
xmin=-1.5,
xmax=2.5,
ymin=-1.5,
ymax=2.5,
];
\addplot[domain=-1.8:2.5]{-1-x};
\addplot[domain=-0.5:2.5]{2-x};
\end{axis};
% \path[draw, thick, ->, blue] (0.56, 0) -- (1.56,0);
% \node[circle, inner sep=1pt,fill, red] at (0.56, 0) {};
\end{tikzpicture}
\end{figure}
}
\frame{
\frametitle{LP example 3D}
\begin{figure}
\begin{tikzpicture}[scale=0.5, auto,swap]
\coordinate (cO) at (0, 0);
\coordinate (cX) at (3.9, -0.15);
\coordinate (cY) at (-2.6, -2.6);
\coordinate (cZ) at (-0.19, 5.5);
% 0,0,3
\coordinate (A) at (-0.14, 4);
% 1,0,3
\coordinate (B) at (1.2, 4);
% 2,0,2
\coordinate (C) at (2.48, 2.4);
% 2,0,0
\coordinate (D) at (2.6,-0.1);
% 2,2,0
\coordinate (E) at (1.1, -1.7);
% 0,2,0
\coordinate (F) at (-1.6, -1.6);
% 0,1,3
\coordinate (G) at (-0.63, 3.24);
\draw [thick, gray] (A)--(B)--(C)--(D)--(E)--(F)--(G)--cycle (B)--(G)--(E)--(C);
\draw [dashed,thick, black] (cO)--(D) (cO)--(A) (cO)--(F);
% \draw [->,green, thick] (cO)->(D);
\draw [->,color=black, thick] (D)->(cX);
\draw [->,color=black, thick] (F)->(cY);
\draw [->,color=black, thick] (A)->(cZ);
\draw (E) node [below]{\tiny(2,2,0)};
\draw (F) node [below right]{\tiny(0,2,0)};
\draw (A) node [above left]{\tiny(0,0,3)};
\draw (B) node [above]{\tiny(1,0,3)};
\draw (G) node [above left]{\tiny(0,1,3)};
\draw (C) node [above right]{\tiny(2,0,2)};
\draw (D) node [below ]{\tiny(2,0,0)};
\draw (cX) node [below]{\small $x_1$};
\draw (cY) node [right]{\small $x_2$};
\draw (cZ) node [right]{\small $x_3$};
% \draw (2.8,1.3) node [above,right,green] {\small $\lambda=[1,0,0,-1,-1,0,0]$};
% \draw (2.8,0.9) node [below,right,green] {\small $\theta=2$};
\end{tikzpicture}
\end{figure}
}
\frame{
\frametitle{LP example 3D with lambda}
\begin{figure}
\begin{tikzpicture}[scale=1., auto,swap]
\coordinate (cO) at (0, 0);
\coordinate (cX) at (3.9, -0.15);
\coordinate (cY) at (-2.2, -2.2);
\coordinate (cZ) at (-0.17, 5.0);
% 0,0,3
\coordinate (A) at (-0.14, 4);
% 1,0,3
\coordinate (B) at (1.2, 4);
% 2,0,2
\coordinate (C) at (2.48, 2.4);
% 2,0,0
\coordinate (D) at (2.6,-0.1);
% 2,2,0
\coordinate (E) at (1.1, -1.7);
% 0,2,0
\coordinate (F) at (-1.6, -1.6);
% 0,1,3
\coordinate (G) at (-0.63, 3.24);
\draw [thick, gray] (A)--(B)--(C)--(D)--(E)--(F)--(G)--cycle (B)--(G)--(E)--(C);
\draw [dashed,thick, black] (cO)--(D) (cO)--(A) (cO)--(F);
% \draw [->,green, thick] (cO)->(D);
\draw [->,color=black, thick] (D)->(cX);
\draw [->,color=black, thick] (F)->(cY);
\draw [->,color=black, thick] (A)->(cZ);
\draw (E) node [below]{\tiny(2,2,0)};
\draw (F) node [below right]{\tiny(0,2,0)};
\draw (A) node [above left]{\tiny(0,0,3)};
\draw (B) node [above]{\tiny(1,0,3)};
\draw (G) node [above left]{\tiny(0,1,3)};
\draw (C) node [above right]{\tiny(2,0,2)};
\draw (D) node [below right]{\tiny(2,0,0)};
\draw (cX) node [below]{\small $x_1$};
\draw (cY) node [right]{\small $x_2$};
\draw (cZ) node [right]{\small $x_3$};
% \draw (2.8,1.3) node [above,right,green] {\small $\lambda=[1,0,0,-1,-1,0,0]$};
% \draw (2.8,0.9) node [below,right,green] {\small $\theta=2$};
\draw (3.37, 3.4) node [above,right] {\tiny $
\mathbf{x}=\left[ \begin{array}{ccccccc}
0 & \textcolor{blue}{2} & 0 & \textcolor{blue}{2} & \textcolor{blue}{2} & \textcolor{blue}{3} & 0
\end{array} \right]
^T$};
\draw (3.3, 2.5) node [above,right] {\tiny $
\mathbf{A}=\left[ \begin{array}{ccccccc}
1 & \textcolor{blue}{1} & 1 & \textcolor{blue}{1} & \textcolor{blue}{0} & \textcolor{blue}{0} & 0 \\
1 & \textcolor{blue}{0} & 0 & \textcolor{blue}{0} & \textcolor{blue}{1} & \textcolor{blue}{0} & 0 \\
0 & \textcolor{blue}{0} & 1 & \textcolor{blue}{0} & \textcolor{blue}{0} & \textcolor{blue}{1} & 0 \\
0 & \textcolor{blue}{3} & 1 & \textcolor{blue}{0} & \textcolor{blue}{0} & \textcolor{blue}{0} & 1\\
\end{array} \right]
$};
\end{tikzpicture}
\end{figure}
}
\frame{
\frametitle{LP example 3D with lambda}
\begin{figure}
\begin{tikzpicture}[scale=0.5, auto,swap]
\coordinate (cO) at (0, 0);
\coordinate (cX) at (3.9, -0.15);
\coordinate (cY) at (-2.2, -2.2);
\coordinate (cZ) at (-0.17, 5.0);
% 0,0,3
\coordinate (A) at (-0.14, 4);
% 1,0,3
\coordinate (B) at (1.2, 4);
% 2,0,2
\coordinate (C) at (2.48, 2.4);
% 2,0,0
\coordinate (D) at (2.6,-0.1);
% 2,2,0
\coordinate (E) at (1.1, -1.7);
% 0,2,0
\coordinate (F) at (-1.6, -1.6);
% 0,1,3
\coordinate (G) at (-0.63, 3.24);
\coordinate (x1) at (-2.1, -1.1);
\coordinate (x2) at (-1.1, -2.1);
\draw [thick, gray] (A)--(B)--(C)--(D)--(E)--(F)--(G)--cycle (B)--(G)--(E)--(C);
\draw [dashed,thick, black] (cO)--(D) (cO)--(A) (cO)--(F);
% \draw [->,green, thick] (cO)->(D);
\draw [->,color=black, thick] (D)->(cX);
\draw [->,color=black, thick] (F)->(cY);
\draw [->,color=black, thick] (A)->(cZ);
\draw (E) node [below]{\tiny(2,2,0)};
\draw (F) node [red, above right, thick]{\small $\mathbf{x}=\left[ 0\ 2\ 0\ 2\ 2\ 3\ 0 \right]^T$};
\draw (A) node [above left]{\tiny(0,0,3)};
\draw (B) node [above]{\tiny(1,0,3)};
\draw (G) node [above left]{\tiny(0,1,3)};
\draw (C) node [above right]{\tiny(2,0,2)};
\draw (D) node [below right]{\tiny(2,0,0)};
\draw (cX) node [below]{\small $x_1$};
\draw (cY) node [right]{\small $x_2$};
\draw (cZ) node [right]{\small $x_3$};
\draw [->, thick, green] (x2) -- (x1);
\draw [fill=red, draw=white] (F) circle(2pt);
\draw [fill=green, draw=white] (x1) circle(2pt);
\draw [fill=green, draw=white] (x2) circle(2pt);
\draw (x1) node [above, left, green, thick] {\small $\mathbf{x'=x+\lambda}$};
\draw (x2) node [below, right, green, thick] {\small $\mathbf{x''=x-\lambda}$};
% \draw (2.8,1.3) node [above,right,green] {\small $\lambda=[1,0,0,-1,-1,0,0]$};
% \draw (2.8,0.9) node [below,right,green] {\small $\theta=2$};
\draw (3.37, 3.4) node [above,right] {\tiny $
\mathbf{x}=\left[ \begin{array}{ccccccc}
0 & \textcolor{blue}{2} & 0 & \textcolor{blue}{2} & \textcolor{blue}{2} & \textcolor{blue}{3} & 0
\end{array} \right]
^T$};
\draw (3.3, 2.5) node [above,right] {\tiny $
\mathbf{A}=\left[ \begin{array}{ccccccc}
1 & \textcolor{blue}{1} & 1 & \textcolor{blue}{1} & \textcolor{blue}{0} & \textcolor{blue}{0} & 0 \\
1 & \textcolor{blue}{0} & 0 & \textcolor{blue}{0} & \textcolor{blue}{1} & \textcolor{blue}{0} & 0 \\
0 & \textcolor{blue}{0} & 1 & \textcolor{blue}{0} & \textcolor{blue}{0} & \textcolor{blue}{1} & 0 \\
0 & \textcolor{blue}{3} & 1 & \textcolor{blue}{0} & \textcolor{blue}{0} & \textcolor{blue}{0} & 1\\
\end{array} \right]
$};
\end{tikzpicture}
\end{figure}
}
\frame{
\frametitle{aaa}
\begin{figure}
\begin{tikzpicture}[domain=0:15]
\pgfplotsset{my style/.append style={ axis x line=middle, axis y line=middle, axis equal }}
\begin{axis}[my style,
xlabel=$n$,
ylabel=$f(n)$,
xtick={ 0,..., 0},
ytick={ 0,..., 0},
xmin=0,
xmax=30,
ymin=0,
ymax=20
];
%draw axis
%\draw[->](0,0)--(9,0) node[right]{N};
%
%\draw[->](0,0)--(0,7) node[above]{Number of Steps};
%draw kedu
\draw[-](1,0)--(1,0.2)node[below=3.6pt]{1};
\draw[-](2,0)--(2,0.2)node[below=3.6pt]{2};
\draw[-](3,0)--(3,0.2)node[below=3.6pt]{3};
\draw[-](4,0)--(4,0.2)node[below=3.6pt]{4};
\draw[-](3.9,15)node[right=3.6pt]{n0};
%draw lines
%\draw[->](1,1.3)--(2.3,2)--(2.4,1.9)--(3,2.6)--(4.5,3)node[right=3.6pt]{Average Case};
%\draw[->](1,1.3)--(1.6,2.2)--(2,2.5)--(3,3.2)--(4,5)--(4.5,5.5)node[right=3.6pt]{Worst Case};
%\draw[->](1,1.3)--(2,1.5)--(3,1)--(4,0.8)--(4.5,0.9)node[right=3.6pt]{Best Case};
%add node
%\addplot[mark=*,only marks] coordinates {(1,1.3)(2,2.5)(2,1.5)(3,2.8)(3,1)(3,3.2)(3,2.4)(3,2)(4,5)(4,4.8)(4,4.5)(4,4.2)(4,4)(4,3.8)(4,3.5)(4,3)(4,2.7)(4,2.5)(4,2)(4,1)(4,0.8)};
%add lines
\draw[->] (0,0) .. controls (3,0.5) and (8,8) .. (25,10)node[below]{lower bound};
\draw[->] (0,0) .. controls (3.9,6) and (8,15) .. (25,18)node[below]{upper bound};
\addplot+[smooth,mark=none] % 设置绘图的类型是光滑线图
coordinates
{
(0,0)(2,5.3)(3.9,6)(6.5,6)(8.5,8.5)(13,8.2)(14.5,13)(19.5,12)(22,15.5)(25.5,14.5)(27,17)
};
draw[dashed] (1,0)--(1,10);
%add imaginary line
\draw[green, thick, densely dotted] (3.9,0) -- (3.9, 20);
%\draw[->] (0,0) .. controls (50,-40) .. (50,-20)-- (50,50) --
%(-50,50) -- (-50,-20) .. controls (-50,-40) .. (0,-60) -- cycle;
%\draw[->] (0,0) .. controls (3,0.5) and (8,10) .. (25,12)node[top]{lower bound};
\end{axis};
draw[dashed]
(1.5,3.5) to (2.5,1.5);
\end{tikzpicture}
\end{figure}
}
\end{document}