From 5cd8e61fbe1b64128551aaa654388f44e8dc6536 Mon Sep 17 00:00:00 2001
From: MZuenni <michi.zuendorf@gmail.com>
Date: Tue, 31 Jan 2023 15:22:19 +0100
Subject: added traingles

---
 geometry/geometry.tex     |   1 +
 geometry/triangle.tex     |  41 +++++++++++++++++++++++++++++++++++++++++
 latexHeaders/commands.sty |   1 +
 string/suffixArray.cpp    |  13 ++++++-------
 tcr.pdf                   | Bin 642993 -> 643813 bytes
 5 files changed, 49 insertions(+), 7 deletions(-)
 create mode 100644 geometry/triangle.tex

diff --git a/geometry/geometry.tex b/geometry/geometry.tex
index e52e454..3e50a8e 100644
--- a/geometry/geometry.tex
+++ b/geometry/geometry.tex
@@ -30,6 +30,7 @@
 \subsection{Formeln~~--~\texttt{std::complex}}
 \sourcecode{geometry/formulars.cpp}
 \sourcecode{geometry/linesAndSegments.cpp}
+\input{geometry/triangle}
 \sourcecode{geometry/triangle.cpp}
 \sourcecode{geometry/polygon.cpp}
 \sourcecode{geometry/circle.cpp}
diff --git a/geometry/triangle.tex b/geometry/triangle.tex
new file mode 100644
index 0000000..3decd54
--- /dev/null
+++ b/geometry/triangle.tex
@@ -0,0 +1,41 @@
+
+\begin{minipage}[T]{0.27\linewidth}
+	Generell:
+	\begin{itemize}
+		\item $\cos(\gamma)=\frac{a^2+b^2-c^2}{2ab}$
+		\item $b=\frac{a}{\sin(\alpha)}\sin(\beta)$
+		%\item $b=\frac{a}{\sin(\pi-\beta-\gamma)}\sin(\beta)$
+		%\item $\sin(\beta)=\frac{b\sin(\alpha)}{a}$ %asin is not uniquely invertible
+		\item $\Delta=\frac{bc}{2}\sin(\alpha)$
+	\end{itemize}
+\end{minipage}
+\hfill
+\begin{minipage}[B]{0.5\linewidth}
+	\centering
+	\begin{tikzpicture}[line cap=round,minimum size=0,x=.7cm,y=0.7cm]
+		\node[circle,inner sep=0] (AA) at (0,0) {$A$};
+		\node[circle,inner sep=0] (BB) at (3,-1) {$B$};
+		\node[circle,inner sep=0] (CC) at (3.666667,1) {$C$};
+		
+		\coordinate (A) at (AA.0);
+		\coordinate (B) at (BB.100);
+		\coordinate (C) at (CC.210);
+		
+		\pic[draw,angle radius=15,pic text=$\gamma$]{angle = A--C--B};
+		\pic[draw,angle radius=15,pic text=$\beta$]{angle = C--B--A};
+		\pic[draw,angle radius=20,pic text=$\alpha$]{angle = B--A--C};
+		
+		\draw (A) to[edge label={$b$},inner sep=1] (C);
+		\draw (A) to[edge label'={$c$},inner sep=1.3] (B);
+		\draw (B) to[edge label'={$a$},inner sep=0.6] (C);
+	\end{tikzpicture}
+\end{minipage}
+\hfill
+\begin{minipage}[T]{0.16\linewidth}
+	$\beta=90^\circ$:
+	\begin{itemize}
+		\item $\sin(\alpha)=\frac{a}{b}$
+		\item $\cos(\alpha)=\frac{c}{b}$
+		\item $\tan(\alpha)=\frac{a}{c}$
+	\end{itemize}
+\end{minipage}
diff --git a/latexHeaders/commands.sty b/latexHeaders/commands.sty
index abe589d..c23fbfc 100644
--- a/latexHeaders/commands.sty
+++ b/latexHeaders/commands.sty
@@ -7,6 +7,7 @@
 \newcommand{\code}[1]{\lstinline[breaklines=true]{#1}}
 
 \usepackage{tikz}
+\usetikzlibrary{angles,quotes}
 
 
 %new environment to define algorithms
diff --git a/string/suffixArray.cpp b/string/suffixArray.cpp
index 3494a0b..df6259a 100644
--- a/string/suffixArray.cpp
+++ b/string/suffixArray.cpp
@@ -1,12 +1,11 @@
 struct SuffixArray {
-	vector<pair<pair<int, int>, int>> L;
 	int n, step, count;
+	vector<int> SA, LCP;
 	vector<vector<int>> P;
-	vector<int> SA, LCP; 
+	vector<pair<pair<int, int>, int>> L;
 
-	SuffixArray(const string& s) : n(sz(s)) {
-		SA.resize(n); LCP.resize(n); L.resize(n);
-		P.assign(__ln(n)*4-2, vector<int>(n));
+	SuffixArray(const string& s) : n(sz(s)), SA(n), LCP(n), L(n) {
+		P.assign(__lg(n)*4-2, vector<int>(n));
 		for (int i = 0; i < n; i++) P[0][i] = s[i];
 		for (step = 1, count = 1; count < n; step++, count *= 2) {
 			for (int i = 0; i < n; i++)
@@ -26,12 +25,12 @@ struct SuffixArray {
 	int lcp(int x, int y) {
 		int ret = 0;
 		if (x == y) return n - x;
-		for (int k = step - 1; k >= 0 && x < n && y < n; k--)
+		for (int k = step - 1; k >= 0 && x < n && y < n; k--) {
 			if (P[k][x] == P[k][y]) {
 				x += 1 << k;
 				y += 1 << k;
 				ret += 1 << k;
-			}
+		}}
 		return ret;
 	}
 };
diff --git a/tcr.pdf b/tcr.pdf
index fe47838..83429b2 100644
Binary files a/tcr.pdf and b/tcr.pdf differ
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