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authormzuenni <mzuenni@users.noreply.github.com>2024-07-28 22:54:40 +0200
committerGitHub <noreply@github.com>2024-07-28 22:54:40 +0200
commit8d11c6c8213f46f0fa19826917c255edd5d43cb1 (patch)
tree96d75baff33d5a04b5a60f1a41f514a26c716874 /math/tables/numbers.tex
parent8c33b4e0d3030cfed17fc64b4fe41133339f6d87 (diff)
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>
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-\begin{expandtable}
-\begin{tabularx}{\linewidth}{|l|X|}
- \hline
- \multicolumn{2}{|c|}{Berühmte Zahlen} \\
- \hline
- \textsc{Fibonacci} &
- $f(0) = 0 \quad
- f(1) = 1 \quad
- f(n+2) = f(n+1) + f(n)$ \\
- \grayhline
-
- \textsc{Catalan} &
- $C_0 = 1 \qquad
- C_n = \sum\limits_{k = 0}^{n - 1} C_kC_{n - 1 - k} =
- \frac{1}{n + 1}\binom{2n}{n} = \frac{2(2n - 1)}{n+1} \cdot C_{n-1}$ \\
- \grayhline
-
- \textsc{Euler} I &
- $\eulerI{n}{0} = \eulerI{n}{n-1} = 1 \qquad
- \eulerI{n}{k} = (k+1) \eulerI{n-1}{k} + (n-k) \eulerI{n-1}{k-1} $ \\
- \grayhline
-
- \textsc{Euler} II &
- $\eulerII{n}{0} = 1 \quad
- \eulerII{n}{n} = 0 \quad$\\
- & $\eulerII{n}{k} = (k+1) \eulerII{n-1}{k} + (2n-k-1) \eulerII{n-1}{k-1}$ \\
- \grayhline
-
- \textsc{Stirling} I &
- $\stirlingI{0}{0} = 1 \qquad
- \stirlingI{n}{0} = \stirlingI{0}{n} = 0 \qquad
- \stirlingI{n}{k} = \stirlingI{n-1}{k-1} + (n-1) \stirlingI{n-1}{k}$ \\
- \grayhline
-
- \textsc{Stirling} II &
- $\stirlingII{n}{1} = \stirlingII{n}{n} = 1 \qquad
- \stirlingII{n}{k} = k \stirlingII{n-1}{k} + \stirlingII{n-1}{k-1} =
- \frac{1}{k!} \sum\limits_{j=0}^{k} (-1)^{k-j}\binom{k}{j}j^n$\\
- \grayhline
-
- \textsc{Bell} &
- $B_1 = 1 \qquad
- B_n = \sum\limits_{k = 0}^{n - 1} B_k\binom{n-1}{k}
- = \sum\limits_{k = 0}^{n}\stirlingII{n}{k}$\\
- \grayhline
-
- \textsc{Partitions} &
- $p(0,0) = 1 \quad
- p(n,k) = 0 \text{ für } k > n \text{ oder } n \leq 0 \text{ oder } k \leq 0$ \\
- & $p(n,k) = p(n-k,k) + p(n-1,k-1)$\\
- \grayhline
-
- \textsc{Partitions} &
- $f(0) = 1 \quad f(n) = 0~(n < 0)$ \\
- & $f(n)=\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k+1)}{2})+\sum\limits_{k=1}^\infty(-1)^{k-1}f(n - \frac{k(3k-1)}{2})$\\
-
- \hline
-\end{tabularx}
-\end{expandtable}