From 8d11c6c8213f46f0fa19826917c255edd5d43cb1 Mon Sep 17 00:00:00 2001 From: mzuenni 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 --- math/tables/nim.tex | 96 ----------------------------------------------------- 1 file changed, 96 deletions(-) delete mode 100644 math/tables/nim.tex (limited to 'math/tables/nim.tex') 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} -- cgit v1.2.3