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| author | mzuenni <mzuenni@users.noreply.github.com> | 2024-07-28 22:54:40 +0200 |
|---|---|---|
| committer | GitHub <noreply@github.com> | 2024-07-28 22:54:40 +0200 |
| commit | 8d11c6c8213f46f0fa19826917c255edd5d43cb1 (patch) | |
| tree | 96d75baff33d5a04b5a60f1a41f514a26c716874 /math/tables/nim.tex | |
| parent | 8c33b4e0d3030cfed17fc64b4fe41133339f6d87 (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>
Diffstat (limited to 'math/tables/nim.tex')
| -rw-r--r-- | math/tables/nim.tex | 96 |
1 files changed, 0 insertions, 96 deletions
diff --git a/math/tables/nim.tex b/math/tables/nim.tex deleted file mode 100644 index 8490d42..0000000 --- a/math/tables/nim.tex +++ /dev/null @@ -1,96 +0,0 @@ -\begin{tabularx}{\linewidth}{|p{0.37\linewidth}|X|} - \hline - \multicolumn{2}{|c|}{Nim-Spiele (\ding{182} letzter gewinnt (normal), \ding{183} letzter verliert)} \\ - \hline - Beschreibung & - Strategie \\ - \hline - - $M = [\mathit{pile}_i]$\newline - $[x] := \{1, \ldots, x\}$& - $\mathit{SG} = \oplus_{i = 1}^n \mathit{pile}_i$\newline - \ding{182} Nimm von einem Stapel, sodass $\mathit{SG}$ $0$ wird.\newline - \ding{183} Genauso. - Außer: Bleiben nur noch Stapel der Größe $1$, erzeuge ungerade Anzahl solcher Stapel.\\ - \hline - - $M = \{a^m \mid m \geq 0\}$ & - $a$ ungerade: $\mathit{SG}_n = n \% 2$\newline - $a$ gerade:\newline - $\mathit{SG}_n = 2$, falls $n \equiv a \bmod (a + 1) $\newline - $\mathit{SG}_n = n \% (a + 1) \% 2$, sonst.\\ - \hline - - $M_{\text{\ding{172}}} = \left[\frac{\mathit{pile}_i}{2}\right]$\newline - $M_{\text{\ding{173}}} = - \left\{\left\lceil\frac{\mathit{pile}_i}{2}\right\rceil,~ - \mathit{pile}_i\right\}$ & - \ding{172} - $\mathit{SG}_{2n} = n$, - $\mathit{SG}_{2n+1} = \mathit{SG}_n$\newline - \ding{173} - $\mathit{SG}_0 = 0$, - $\mathit{SG}_n = [\log_2 n] + 1$ \\ - \hline - - $M_{\text{\ding{172}}} = \text{Teiler von $\mathit{pile}_i$}$\newline - $M_{\text{\ding{173}}} = \text{echte Teiler von $\mathit{pile}_i$}$ & - \ding{172} - $\mathit{SG}_0 = 0$, - $\mathit{SG}_n = \mathit{SG}_{\text{\ding{173},n}} + 1$\newline - \ding{173} - $\mathit{ST}_1 = 0$, - $\mathit{SG}_n = \text{\#Nullen am Ende von $n_{bin}$}$\\ - \hline - - $M_{\text{\ding{172}}} = [k]$\newline - $M_{\text{\ding{173}}} = S$, ($S$ endlich)\newline - $M_{\text{\ding{174}}} = S \cup \{\mathit{pile}_i\}$ & - $\mathit{SG}_{\text{\ding{172}}, n} = n \bmod (k + 1)$\newline - \ding{182} Niederlage bei $\mathit{SG} = 0$\newline - \ding{183} Niederlage bei $\mathit{SG} = 1$\newline - $\mathit{SG}_{\text{\ding{174}}, n} = \mathit{SG}_{\text{\ding{173}}, n} + 1$\\ - \hline - - \multicolumn{2}{|l|}{ - Für jedes endliche $M$ ist $\mathit{SG}$ eines Stapels irgendwann periodisch. - } \\ - \hline - - \textsc{Moore}'s Nim:\newline - Beliebige Zahl von maximal $k$ Stapeln. & - \ding{182} - Schreibe $\mathit{pile}_i$ binär. - Addiere ohne Übertrag zur Basis $k + 1$. - Niederlage, falls Ergebnis gleich 0.\newline - \ding{183} - Wenn alle Stapel $1$ sind: - Niederlage, wenn $n \equiv 1 \bmod (k + 1)$. - Sonst wie in \ding{182}.\\ - \hline - - Staircase Nim:\newline - $n$ Stapel in einer Reihe. - Beliebige Zahl von Stapel $i$ nach Stapel $i-1$. & - Niederlage, wenn Nim der ungeraden Spiele verloren ist:\newline - $\oplus_{i = 0}^{(n - 1) / 2} \mathit{pile}_{2i + 1} = 0$\\ - \hline - - \textsc{Lasker}'s Nim:\newline - Zwei mögliche Züge:\newline - 1) Nehme beliebige Zahl.\newline - 2) Teile Stapel in zwei Stapel (ohne Entnahme).& - $\mathit{SG}_n = n$, falls $n \equiv 1,2 \bmod 4$\newline - $\mathit{SG}_n = n + 1$, falls $n \equiv 3 \bmod 4$\newline - $\mathit{SG}_n = n - 1$, falls $n \equiv 0 \bmod 4$\\ - \hline - - \textsc{Kayles}' Nim:\newline - Zwei mögliche Züge:\newline - 1) Nehme beliebige Zahl.\newline - 2) Teile Stapel in zwei Stapel (mit Entnahme).& - Berechne $\mathit{SG}_n$ für kleine $n$ rekursiv.\newline - $n \in [72,83]: \quad 4, 1, 2, 8, 1, 4, 7, 2, 1, 8, 2, 7$\newline - Periode ab $n = 72$ der Länge $12$.\\ - \hline -\end{tabularx} |
