From 3875ac2b8df9145a66e9f6fcf34e77eb3bc2d072 Mon Sep 17 00:00:00 2001
From: Nunigan <michael.schmid2@ost.ch>
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 <michael.schmid2@ost.ch>
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 <michael.schmid2@ost.ch>
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 <michael.schmid2@ost.ch>
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 <michaelschmid13@hotmail.com>
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

