From 3875ac2b8df9145a66e9f6fcf34e77eb3bc2d072 Mon Sep 17 00:00:00 2001 From: Nunigan Date: Tue, 27 Jul 2021 22:01:05 +0200 Subject: added first part of paper and code --- buch/papers/multiplikation/images/bigo.tex | 107 +++++++++++++++++++++++++++++ 1 file changed, 107 insertions(+) create mode 100644 buch/papers/multiplikation/images/bigo.tex (limited to 'buch/papers/multiplikation/images/bigo.tex') diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex new file mode 100644 index 0000000..e3293e4 --- /dev/null +++ b/buch/papers/multiplikation/images/bigo.tex @@ -0,0 +1,107 @@ +\documentclass[border=10pt,varwidth]{standalone} +\usepackage[left=25mm,right=25mm,top=25mm,bottom=25mm]{geometry} +\usepackage[utf8]{inputenc} +\usepackage[T1]{fontenc} +\usepackage{times} +\usepackage{geometry} +\usepackage{amsmath} +\usepackage{amssymb} +\usepackage{mathrsfs} +\usepackage{amsfonts} +\usepackage{amsthm} +\usepackage{lipsum} +\usepackage{amscd} +\usepackage{graphicx} +\usepackage{fancyhdr} +\usepackage{textcomp} +\usepackage{pgfplots} +\usepackage{txfonts} +\usepackage[all]{xy} +\usepackage{paralist} +\usepackage[colorlinks=true]{hyperref} +\usepackage{array} +\usepackage{tikz} +\usepackage{slashed} +\usepackage{pdfpages} +\usepackage{cite} +\usepackage{url} +\usepackage{amsmath,amsfonts,amssymb} +\usepackage{tikz} +\usetikzlibrary{arrows,matrix,positioning} +\usetikzlibrary{overlay-beamer-styles} +\usetikzlibrary{matrix.skeleton} +\usetikzlibrary{automata,positioning} +\usetikzlibrary{decorations.text} +\usepackage{listings} +\usepackage{multirow} +\usepackage{color} + +\begin{document} + +\begin{tikzpicture} +\begin{axis}[ + axis lines = left, + xlabel = $n$ (Data Input), + ylabel = {$t$ (time)}, + legend pos=north east, + very thick, + ymax = 500, + yticklabels=\empty, + xticklabels=\empty, + scale only axis=true, + width=12cm, height=6cm, + ] +\addplot [ + domain= 1:20, + samples=100, + color=red, +] +{1}; +\addlegendentry{$\mathcal{O}(1)$} +\addplot [ + domain= 1:20, + samples=100, + color=green, +] +{x}; +\addlegendentry{$\mathcal{O}(n)$} +\addplot [ + domain= 1:20, + samples=100, + color=blue, +] +{x^2}; +\addlegendentry{$\mathcal{O}(n^2)$} +\addplot [ + domain= 1:10, + samples=100, + color=purple, +] +{x^3}; +\addlegendentry{$\mathcal{O}(n^3)$} +\addplot [ + domain= 1:10, + samples=100, + color=black, +] +{exp(x)}; +\addlegendentry{$\mathcal{O}(e^n)$} +\addplot [ + domain= 1:20, + samples=100, + color=orange, +] +{log2(x)}; +\addlegendentry{$\mathcal{O}(\log n)$} + +\addplot [ + domain= 1:20, + samples=100, + color=gray, +] +{x*log2(x)}; +\addlegendentry{$\mathcal{O}(n \log n)$} +\end{axis} +\end{tikzpicture} + +\end{document} -- cgit v1.2.1 From a4817013b542cd6aa1a0cd955806c82ac337dca6 Mon Sep 17 00:00:00 2001 From: Nunigan Date: Wed, 28 Jul 2021 22:27:27 +0200 Subject: added corrections from prof mueller --- buch/papers/multiplikation/images/bigo.tex | 36 +++++++++++++++++------------- 1 file changed, 21 insertions(+), 15 deletions(-) (limited to 'buch/papers/multiplikation/images/bigo.tex') diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex index e3293e4..71826f5 100644 --- a/buch/papers/multiplikation/images/bigo.tex +++ b/buch/papers/multiplikation/images/bigo.tex @@ -39,67 +39,73 @@ \begin{document} \begin{tikzpicture} + \begin{axis}[ - axis lines = left, + xmode=log, + ymode=log, + log ticks with fixed point, xlabel = $n$ (Data Input), ylabel = {$t$ (time)}, legend pos=north east, very thick, - ymax = 500, + grid=minor, + ymax = 100000, + ymin = 0.5, + xmin = 1, yticklabels=\empty, xticklabels=\empty, scale only axis=true, width=12cm, height=6cm, ] \addplot [ - domain= 1:20, + domain= 1:50, samples=100, color=red, ] {1}; \addlegendentry{$\mathcal{O}(1)$} \addplot [ - domain= 1:20, + domain= 1:50, samples=100, color=green, ] {x}; \addlegendentry{$\mathcal{O}(n)$} \addplot [ - domain= 1:20, + domain= 1:50, samples=100, color=blue, ] {x^2}; -\addlegendentry{$\mathcal{O}(n^2)$} +\addlegendentry{$\mathcal{O}\left(n^2\right)$} \addplot [ - domain= 1:10, + domain= 1:50, samples=100, color=purple, ] {x^3}; -\addlegendentry{$\mathcal{O}(n^3)$} +\addlegendentry{$\mathcal{O}\left(n^3\right)$} \addplot [ - domain= 1:10, + domain= 1:50, samples=100, color=black, ] -{exp(x)}; -\addlegendentry{$\mathcal{O}(e^n)$} +{exp(x) - 1.7}; +\addlegendentry{$\mathcal{O}\left(e^n\right)$} \addplot [ - domain= 1:20, + domain= 1:50, samples=100, color=orange, ] -{log2(x)}; +{log2(x)+1}; \addlegendentry{$\mathcal{O}(\log n)$} \addplot [ - domain= 1:20, + domain= 1:50, samples=100, color=gray, ] -{x*log2(x)}; +{x*log2(x)+1}; \addlegendentry{$\mathcal{O}(n \log n)$} \end{axis} \end{tikzpicture} -- cgit v1.2.1 From 31b66acba16f525d41c42094601ade8afb3fd549 Mon Sep 17 00:00:00 2001 From: Nunigan Date: Sat, 31 Jul 2021 21:36:30 +0200 Subject: updare --- buch/papers/multiplikation/images/bigo.tex | 12 +++++------- 1 file changed, 5 insertions(+), 7 deletions(-) (limited to 'buch/papers/multiplikation/images/bigo.tex') diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex index 71826f5..a415ccb 100644 --- a/buch/papers/multiplikation/images/bigo.tex +++ b/buch/papers/multiplikation/images/bigo.tex @@ -41,17 +41,15 @@ \begin{tikzpicture} \begin{axis}[ - xmode=log, - ymode=log, - log ticks with fixed point, + xmode=log, ymode=log, + xmin=1e-0, xmax=5e1, + ymin=10e-1, ymax=1e7, + grid=both, + major grid style={black!50}, xlabel = $n$ (Data Input), ylabel = {$t$ (time)}, legend pos=north east, very thick, - grid=minor, - ymax = 100000, - ymin = 0.5, - xmin = 1, yticklabels=\empty, xticklabels=\empty, scale only axis=true, -- cgit v1.2.1 From 872595e81de60c85b18408f8de5a49c535518edc Mon Sep 17 00:00:00 2001 From: Nunigan Date: Fri, 6 Aug 2021 17:37:58 +0200 Subject: update multiplikation --- buch/papers/multiplikation/images/bigo.tex | 24 ++++++++++++------------ 1 file changed, 12 insertions(+), 12 deletions(-) (limited to 'buch/papers/multiplikation/images/bigo.tex') diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex index a415ccb..9ee3a68 100644 --- a/buch/papers/multiplikation/images/bigo.tex +++ b/buch/papers/multiplikation/images/bigo.tex @@ -42,56 +42,56 @@ \begin{axis}[ xmode=log, ymode=log, - xmin=1e-0, xmax=5e1, + xmin=1e-0, xmax=5000, ymin=10e-1, ymax=1e7, grid=both, major grid style={black!50}, - xlabel = $n$ (Data Input), - ylabel = {$t$ (time)}, - legend pos=north east, + xlabel = data input size, + ylabel = {time}, + legend pos=north west, very thick, yticklabels=\empty, xticklabels=\empty, scale only axis=true, - width=12cm, height=6cm, + width=12cm, height=8cm, ] \addplot [ - domain= 1:50, + domain= 1:5000, samples=100, color=red, ] {1}; \addlegendentry{$\mathcal{O}(1)$} \addplot [ - domain= 1:50, + domain= 1:5000, samples=100, color=green, ] {x}; \addlegendentry{$\mathcal{O}(n)$} \addplot [ - domain= 1:50, + domain= 1:50000, samples=100, color=blue, ] {x^2}; \addlegendentry{$\mathcal{O}\left(n^2\right)$} \addplot [ - domain= 1:50, + domain= 1:500, samples=100, color=purple, ] {x^3}; \addlegendentry{$\mathcal{O}\left(n^3\right)$} \addplot [ - domain= 1:50, + domain= 1:500, samples=100, color=black, ] {exp(x) - 1.7}; \addlegendentry{$\mathcal{O}\left(e^n\right)$} \addplot [ - domain= 1:50, + domain= 1:5000, samples=100, color=orange, ] @@ -99,7 +99,7 @@ \addlegendentry{$\mathcal{O}(\log n)$} \addplot [ - domain= 1:50, + domain= 1:5000, samples=100, color=gray, ] -- cgit v1.2.1 From 0c073915585da20db52db82958d50e159559e5c8 Mon Sep 17 00:00:00 2001 From: Nunigan Date: Fri, 20 Aug 2021 08:50:43 +0200 Subject: update --- buch/papers/multiplikation/images/bigo.tex | 1 + 1 file changed, 1 insertion(+) (limited to 'buch/papers/multiplikation/images/bigo.tex') diff --git a/buch/papers/multiplikation/images/bigo.tex b/buch/papers/multiplikation/images/bigo.tex index 9ee3a68..63fd0fd 100644 --- a/buch/papers/multiplikation/images/bigo.tex +++ b/buch/papers/multiplikation/images/bigo.tex @@ -54,6 +54,7 @@ xticklabels=\empty, scale only axis=true, width=12cm, height=8cm, + legend cell align={left} ] \addplot [ domain= 1:5000, -- cgit v1.2.1