From 8d11c6c8213f46f0fa19826917c255edd5d43cb1 Mon Sep 17 00:00:00 2001
From: mzuenni <mzuenni@users.noreply.github.com>
Date: Sun, 28 Jul 2024 22:54:40 +0200
Subject: Test (#4)

* update

* moved content in subdir

* rename file

* add test setup

* add test setup

* add github action

* automaticly test all cpp files

* timeout after 10s

* setulimit and dont zero memory

* test build pdf

* install latexmk

* update

* update

* ngerman

* fonts

* removed old code

* add first test

* added tests

* test in sorted order

* more tests

* simplified test

* more tests

* fix suffix tree

* fixes and improvements

* done ust lst directly

* fix swap

* add links to pdf

* fix constants

* add primorial

* add comment

* various improvements

* more tests

* added missing stuf

* more tests

* fix tests

* more tests

* more tests

* more tests

* fix recursion?

* test trie

* more tests

* only use python temporarily for listings

* only use python temporarily for listings

* more tests

* fix longestCommonSubstring

* more tests

* more tests

* made code more similiar

* fix?

* more tests

* more tests

* more tests

* add ahoCorasick test + limit 4GB stack size

* more tests

* fix test

* add additional test

* more tests

* more tests

* fix?

* better fix

* fix virtual tree

* more tests

* more tests

* recursive closest pair

* more tests

* decrease limit

* new tests

* more tests

* fix name

* more tests

* add test

* new test

* more tests

* more tests

* more tests

* more tests

* new test and content

* new code

* new code

* larger tests

* fix and test

* new test

* new test

* update pdf

* remove comments

* new test

* more tests

* more testcases

* more tests

* increased limit

* more tests

* more tests

* more tests

* new tests

* more tests

* shortened code

* new test

* add basic tests for bigint

* more tests

* removed old files

* new test

* ignore some files

* more auto more ccw

* fix test

* more tests

* fix

* new tests

* more tests

* more tests

* stronger test

* actually verify delaunay...

* more tests

* fix header

* more tests

* run tests parallel?

* test parralel?

* add --missing

* separate workflows

* test

* is the pdf checked?

* separate workflows

* fix workflow

* more workflows

---------

Co-authored-by: Yidi <noob999noob999@gmail.com>
---
 content/math/tables/binom.tex | 28 ++++++++++++++++++++++++++++
 1 file changed, 28 insertions(+)
 create mode 100644 content/math/tables/binom.tex

(limited to 'content/math/tables/binom.tex')

diff --git a/content/math/tables/binom.tex b/content/math/tables/binom.tex
new file mode 100644
index 0000000..878a6b0
--- /dev/null
+++ b/content/math/tables/binom.tex
@@ -0,0 +1,28 @@
+\begin{tabularx}{\linewidth}{|XXXX|}
+	\hline
+	\multicolumn{4}{|c|}{Binomialkoeffizienten} \\
+	\hline
+	\multicolumn{4}{|c|}{
+	$\frac{n!}{k!(n - k)!} \hfill=\hfill
+	\binom{n}{k} \hfill=\hfill
+	\binom{n}{n - k} \hfill=\hfill
+	\frac{n}{k}\binom{n - 1}{k - 1} \hfill=\hfill
+	\frac{n-k+1}{k}\binom{n}{k - 1} \hfill=\hfill
+	\binom{n - 1}{k} + \binom{n - 1}{k - 1} \hfill=\hfill
+	(-1)^k \binom{k - n - 1}{k} \hfill\approx\hfill
+	2^{n} \cdot \frac{2}{\sqrt{2\pi n}}\cdot\exp\left(-\frac{2(x - \frac{n}{2})^2}{n}\right)$
+	} \\
+	\grayhline
+	
+	$\sum\limits_{k = 0}^n \binom{n}{k} = 2^n$ &
+	$\sum\limits_{k = 0}^n \binom{k}{m} = \binom{n + 1}{m + 1}$ &
+	$\sum\limits_{i = 0}^n \binom{n}{i}^2 = \binom{2n}{n}$ &
+	$\sum\limits_{k = 0}^n\binom{r + k}{k} = \binom{r + n + 1}{n}$\\
+	
+	$\binom{n}{m}\binom{m}{k} = \binom{n}{k}\binom{n - k}{m - k}$ &
+	$\sum\limits_{k = 0}^n \binom{r}{k}\binom{s}{n - k} = \binom{r + s}{n}$ &
+	\multicolumn{2}{l|}{
+	$\sum\limits_{i = 1}^n \binom{n}{i} F_i = F_{2n} \quad F_n = n\text{-th Fib.}$
+	}\\
+	\hline
+\end{tabularx}
-- 
cgit v1.2.3

