From a3ef6c437ebc166a9c86c4ef6bfbfeefb987a726 Mon Sep 17 00:00:00 2001
From: Arthur Herbette <arthur.herbette@epfl.ch>
Date: Tue, 14 Apr 2026 14:01:39 +0200
Subject: [PATCH 1/2] replace two images in chapter 6 by a tikz diagrams

---
 Notes/TIKZ/determinant-algo-slow.tikz        | 27 +++++++
 Notes/TIKZ/echelon-gaussian-elimination.tikz | 75 ++++++++++++++++++++
 Notes/algorithms.tex                         |  4 +-
 3 files changed, 104 insertions(+), 2 deletions(-)
 create mode 100644 Notes/TIKZ/determinant-algo-slow.tikz
 create mode 100644 Notes/TIKZ/echelon-gaussian-elimination.tikz

diff --git a/Notes/TIKZ/determinant-algo-slow.tikz b/Notes/TIKZ/determinant-algo-slow.tikz
new file mode 100644
index 0000000..65e1ea3
--- /dev/null
+++ b/Notes/TIKZ/determinant-algo-slow.tikz
@@ -0,0 +1,27 @@
+
+\begin{tikzpicture}[
+  level distance=2cm,
+  level 1/.style={->, sibling distance=4cm},
+  level 2/.style={->, sibling distance=2cm},
+  every node/.style={align=center}
+]
+
+\node {$\left[\begin{array}{ccc} 3 & 7 & 5 \\ 2 & 9 & 8 \\ 1 & 3 & 3 \end{array}\right]$}
+child {
+  node {$\left[\begin{array}{cc} 3 & 8 \\ 3 & 3 \end{array}\right]$}
+  child { node {$[3]$} }
+  child { node {$[3]$} }
+}
+child {
+  node {$\left[\begin{array}{cc} 2 & 8 \\ 1 & 3 \end{array}\right]$}
+  child { node {$[3]$} }
+  child { node {$[4]$} }
+}
+child {
+  node {$\left[\begin{array}{cc} 2 & 9 \\ 1 & 3 \end{array}\right]$}
+  child { node {$[3]$} }
+  child { node {$[4]$} }
+};
+
+\end{tikzpicture}
+
diff --git a/Notes/TIKZ/echelon-gaussian-elimination.tikz b/Notes/TIKZ/echelon-gaussian-elimination.tikz
new file mode 100644
index 0000000..8540891
--- /dev/null
+++ b/Notes/TIKZ/echelon-gaussian-elimination.tikz
@@ -0,0 +1,75 @@
+\begin{tikzpicture}[scale=0.6]
+
+% Colors
+\definecolor{mypurple}{RGB}{170,110,200}
+\definecolor{myred}{RGB}{210,120,140}
+\definecolor{myblue}{RGB}{0,150,180}
+
+\definecolor{green}{RGB}{0,140,0}
+
+\draw[thick, green]
+    (2,-0.5) -- (6.3,-0.5) -- (6.3 ,1)
+    -- (6.3,1)
+    -- (6.3,1.8)
+    -- (4.8,1.8)
+    -- (4.8,2.6)
+    -- (3.3,2.6)
+    -- (3.3,3.4)
+    -- (2,3.4)
+    -- cycle;
+
+\node[green] at (3,1.2) {$0$'s only};
+
+\draw[thick, myblue]
+    (2,4.2)
+    -- (6.3 ,4.2)
+    -- (6.3,2)
+    -- (5,2)
+    -- (5,2.8)
+    -- (3.5,2.8)
+    -- (3.5,3.6)
+    -- (2,3.6)
+    -- (2,4.2);
+
+
+
+\draw[thick, myred]
+    (6.5, 4.2)
+    -- (10, 4.2)
+    -- (10, 2)
+    -- (6.5, 2)
+    -- (6.5, 4.2);
+
+\draw[thick, mypurple]
+    (6.5, 1.8)
+    -- (10, 1.8)
+    -- (10, -0.5)
+    -- (6.5, -0.5)
+    -- (6.5, 1.8);
+% Red X marks
+\foreach \x/\y in {
+    2.3/3.9,
+    3.8/3.1,
+    5.3/2.3
+}{
+    \draw[red, thick] (\x-0.15,\y-0.15) -- (\x+0.15,\y+0.15);
+    \draw[red, thick] (\x-0.15,\y+0.15) -- (\x+0.15,\y-0.15);
+}
+
+% "Nonzero" label
+\node[red] at (3.5,6) {Nonzero};
+
+% Red arrows
+\draw[red, ->, thick] (3.1,5.8) to[out=-150,in=90] (2.3,4.25);
+\draw[red, ->, thick] (3.6,5.8) to[out=-90,in=90] (3.8,3.3);
+\draw[red, ->, thick] (4.1,5.8) to[out=-90,in=90] (5.3,2.5);
+
+\node[myblue] at (0.25,1.2) {$i$};
+\draw[myblue, ->, thick](0.75, 1.2) -- (1.5, 1.2);
+\node[myblue] at (5.5, 5.75) {$j$};
+\draw[myblue, ->, thick](5.5, 5.25) -- (5.5,4.5);
+
+\node[mypurple] at (9, 0) {next};
+
+\end{tikzpicture}
+
diff --git a/Notes/algorithms.tex b/Notes/algorithms.tex
index e353873..967735f 100644
--- a/Notes/algorithms.tex
+++ b/Notes/algorithms.tex
@@ -214,7 +214,7 @@ \chapter{Algorithms and running time analysis}
 
 \begin{figure}
   \centering
-  \includegraphics[height=5cm]{figures/DeterminantAlgoSlow.jpg}
+	\input{./TIKZ/determinant-algo-slow.tikz}
   \caption{An example of the recursion tree of the algorithm from Example~\ref{exe:det}. The tree corresponds to the run of the algorithm on input $\protect\smat{         3 & 7 & 5 \\ 2&9&8 \\ 1 & 3 & 3  }.$
 } 
 \end{figure}
@@ -295,7 +295,7 @@ \section{Analysis of Gaussian elimination}
 
 \begin{figure}  
    \centering
-  \includegraphics[height=5cm]{figures/Echelon.jpg}
+  	\input{./TIKZ/echelon-gaussian-elimination.tikz}   
   \caption{Gaussian elimination: The matrix $A'$ before  the $i$-th iteration of the while loop. \label{fig:9}}
 \end{figure}
 

From 80dbf4d614dd0f2a391dd31e03baf4b9f5df0488 Mon Sep 17 00:00:00 2001
From: Arthur Herbette <arthur.herbette@epfl.ch>
Date: Tue, 14 Apr 2026 14:07:43 +0200
Subject: [PATCH 2/2] fix typos in determinant-algo-slow

---
 Notes/TIKZ/determinant-algo-slow.tikz | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/Notes/TIKZ/determinant-algo-slow.tikz b/Notes/TIKZ/determinant-algo-slow.tikz
index 65e1ea3..115db40 100644
--- a/Notes/TIKZ/determinant-algo-slow.tikz
+++ b/Notes/TIKZ/determinant-algo-slow.tikz
@@ -15,12 +15,12 @@ child {
 child {
   node {$\left[\begin{array}{cc} 2 & 8 \\ 1 & 3 \end{array}\right]$}
   child { node {$[3]$} }
-  child { node {$[4]$} }
+  child { node {$[1]$} }
 }
 child {
   node {$\left[\begin{array}{cc} 2 & 9 \\ 1 & 3 \end{array}\right]$}
   child { node {$[3]$} }
-  child { node {$[4]$} }
+  child { node {$[1]$} }
 };
 
 \end{tikzpicture}