From e80fc29d3bb3c133e720993e138f4b9ebe478082 Mon Sep 17 00:00:00 2001 From: MuedeHydra Date: Thu, 29 Jan 2026 00:31:24 +0100 Subject: [PATCH] update --- img/informatik_3/Big_O.svg | 1353 +++++++++++++++++ img/informatik_3/bst.png | Bin 0 -> 21601 bytes img/informatik_3/hash_table.svg | 170 +++ img/informatik_3/set.png | Bin 0 -> 36436 bytes img/informatik_3/unordered_set.png | Bin 0 -> 48627 bytes img/informatik_3/vector.png | Bin 0 -> 32442 bytes img/physik3/Emissionsspektren/actinium.png | Bin 0 -> 769 bytes img/physik3/Emissionsspektren/aluminum.png | Bin 0 -> 570 bytes img/physik3/Emissionsspektren/americium.png | Bin 0 -> 854 bytes img/physik3/Emissionsspektren/antimony.png | Bin 0 -> 563 bytes img/physik3/Emissionsspektren/argon.png | Bin 0 -> 2758 bytes img/physik3/Emissionsspektren/arsenic.png | Bin 0 -> 819 bytes img/physik3/Emissionsspektren/barium.png | Bin 0 -> 2347 bytes img/physik3/Emissionsspektren/berkelium.png | Bin 0 -> 1705 bytes 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frac(minus b plus.minus root(, D), 2 dot a) eq frac(minus b, 2 dot a) plus.minus i dot frac(root(, abs(D)), 2 dot abs(a)) eq underline(underline(minus delta plus.minus i dot omega_d)) $ diff --git a/src/informatik_3.typ b/src/informatik_3.typ index 43a9a61..7a05aa6 100644 --- a/src/informatik_3.typ +++ b/src/informatik_3.typ @@ -68,26 +68,54 @@ Vec3 v; v.x = 1.0; // okay, is public v.y = 2.0; // compiler error! ```] -*Klassen Initialisieren*: Die Funktion "Foo()" wird beim aufrufen von "Foo f;" aufgerufen. Dort wird die Variabel "i" mit 123 initialisiert. Beim aufrufen von "f.bar(456)" wird 456 ausgegeben! Möchte man 123 ausgeben das das "int i" bei der Funktion weglassen damit das i der Klasse verwendet wird. +==== Constructor (Konstruktor) (Klassen Initialisieren) +Die Funktion "Foo()" wird beim aufrufen von "Foo f;" aufgerufen. Dort wird die Variabel "i" mit 123 initialisiert. Beim aufrufen von "f.bar(456)" wird 456 ausgegeben! Möchte man 123 ausgeben das das "int i" bei der Funktion weglassen damit das i der Klasse verwendet wird. #table(columns: 1fr)[```cpp #include class Foo { - public: - int i; - Foo() { - i = 123; - } - void bar(int i) { - printf("%i\n", i); // output is "456" - } + public: + int i; + Foo() { + i = 123; + } + void bar(int i) { + printf("%i\n", i); // output is "456" + } }; int main() { -Foo f; -f.bar(456); + Foo f; + f.bar(456); } ```] -*Args:* In cpp kann eine Funktion mehrmahls aufgerufen werden. Der compiler schaut selbst wie viele argumente mitgegeben werden und linkt dies ensprechend. (Angebliech soll das auch führ normale funktionen gehen 🤔) +==== Destructor +Wenn beispielsweise eine Klasse Speicher alloziert, dann kann dieser mit dem Destructor wieder freigegeben werden. +#table(columns: 1fr, [```cpp +class Speicher { +public: + // Constructor + Speicher() { + std::cout << "Ressourcen wurden reserviert." << std::endl; + } + + // Destructor + ~Speicher() { + std::cout << "Ressourcen wurden sauber freigegeben!" << std::endl; + } +}; + +int main() { + { + Speicher meinObjekt; // Constructor wird hier aufgerufen + } // Hier endet der Bereich: Destructor wird automatisch aufgerufen! + + std::cout << "Programm-Ende." << std::endl; + return 0; +} +```]) + +=== Overloading +In cpp kann eine Funktion mehrmahls aufgerufen werden. Der compiler schaut selbst wie viele argumente mitgegeben werden und linkt dies ensprechend. #table(columns: 1fr)[```cpp class Foo { Foo(){} @@ -108,13 +136,8 @@ class Foo { }; ```] -==== constructor - -==== decounstructor - -=== overloading - === std -> Namespace +*std* steht für die Standardfunktionen. Wenn du z. B. eine eigene Vektor-Funktion programmiert hast, dann weiss der Compiler nicht, ob er die Standard- oder deine Funktion nehmen soll. Darum schreibt man: ```cpp std::vector()```. === std::string Für Strings: ```cpp #include ``` @@ -189,6 +212,7 @@ std::vector v2(first, last); std::vector> v{{ 0, 1 }, { -1, 0, 2 }}; ```], ) + ==== std::list Listen sind verkettete Daten. Listen sollten verwendet werden wenn häufig elemente in der mitte hinzugefügt oder enternt werden. #table(columns: (1fr, 1fr), @@ -366,13 +390,61 @@ bool eq = std::equal(v.begin(), v.begin() + 1, v.begin() + 3); ) === Runtime complexity -==== Binary search tree -==== std::set -==== std::unordered_set -==== Hash table -==== Big O notation -==== Performance übersicht +==== Binary search tree (BST) +Da der Baum sortiert ist, musst du nicht jedes Element prüfen. Bei jedem Schritt halbiert sich der Bereich, den du noch durchsuchen musst. +- Zeitkomplexität: Im Idealfall (wenn der Baum ausbalanciert ist) liegt sie bei O(log n). +- Der "Worst Case": Wenn du Zahlen bereits sortiert einfügst (1, 2, 3, 4...), wird der Baum zu einer langen Linie. Dann sinkt die Performance auf O(n). +#image("../img/informatik_3/bst.png", width: 100%) +==== std::set +Ein Set (Menge) ist ein Container, der zwei Regeln hat: +- Einzigartigkeit: Jedes Element darf nur ein einziges Mal vorkommen. Wenn du versuchst, die Zahl 5 doppelt einzufügen, wird das zweite Mal einfach ignoriert. +- Automatische Sortierung: In einem Standard-Set werden die Elemente immer automatisch sortiert (standardmäßig aufsteigend). + +==== std::unordered_set +Ein unordered_set ist im Grunde die "schnellere, aber chaotischere" Version des normalen Sets. Während das normale std::set intern einen Baum nutzt und alles sortiert, basiert das std::unordered_set auf einer Hash Table. + +==== Hash table +Eine Hash Table (Hashtabelle) ist eine Datenstruktur, die Daten extrem schnell speichert und wiederfindet – im Idealfall in O(1) (konstanter Zeit). +#image("../img/informatik_3/hash_table.svg", width: 80%) ++ Key (Schlüssel): Du gibst einen Namen oder eine ID ein (z. B. "Max"). ++ Hash-Funktion: Ein Algorithmus berechnet aus diesem Schlüssel eine Zahl (den Index). ++ Array (Eimer): Die Daten werden an genau diesem Index im Speicher abgelegt. + +==== Big O notation +Die Big O Notation (Groß-O-Notation) ist ein Maßstab in der Informatik, um die Effizienz eines Algorithmus zu beschreiben. Sie gibt an, wie die Laufzeit oder der Speicherbedarf ansteigt, wenn die Menge der Eingabedaten (n) größer wird. +#image("../img/informatik_3/Big_O.svg", width: 90%) + +#table(columns: (60pt, 80pt, 1fr, 1fr), +fill: (x, y) => if y == 0 {gray.lighten(40%)}, +[Notation], [Name], [Erklärung], [Beispiel], +[O(1)], [Konstant], ["Immer gleich schnell, egal wie viele Daten."], [Zugriff auf ein Array-Element per Index.], +[O(log n)], [Logarithmisch], [Wird bei mehr Daten nur minimal langsamer.], [Binäre Suche in einer sortierten Liste.], +[O(n)], [Linear], [Laufzeit wächst genau proportional zur Datenmenge.], [Eine einfache for-Schleife über alle Elemente.], +[O($n^2$)], [Quadratisch], [Doppelte Daten = vierfache Zeit (sehr langsam).], [Zwei verschachtelte Schleifen.], +) + +==== Performance übersicht +#table(columns: (70pt, 1fr, 1fr, 1fr), +fill: (x, y) => if y == 0 {gray.lighten(40%)}, +[Container], [std::vector], [std::set], [std::unordered_set], +[Methode], [Lineare Suche (std::find)], [Binärer Suchbaum], [Hash-Tabelle], +[Verhalten], [Sucht jedes Wort nacheinander ab.], [Teilt die Suchmenge bei jedem Schritt (links/rechts).], [Berechnet einen Index (Hash) und greift direkt darauf zu.], +[Komplexität], [O(n) (Linear)], [O(log n) (Logarithmisch) ], [O(1) (Konstant) ], +[Ergebnis], [Zeit verdoppelt sich bei doppeltem Wörterbuchumfang.], [Deutlich schneller: Bei 100k Wörtern genügen ca. 17 Vergleiche.], [Die schnellste Methode; die Zeit bleibt bei wachsender Datenmenge nahezu gleich.], + +[Einfacher Zugriff], [O(1)], [O(log n)], [O(1)], +[Einfügen], [O(1)], [O(log n)], [O(1)], +[Suchen], [O(n)], [O(log n)], [O(1)], +[Example], [#image("../img/informatik_3/vector.png")], [#image("../img/informatik_3/set.png")], [#image("../img/informatik_3/unordered_set.png")], +) + +*Warum sind die Unterschiede so extrem?* +- Linear (O(n)): In einem *vector* mit 100.000 Wörtern müssen im Schnitt 50.000 Vergleiche durchgeführt werden, um ein Wort zu finden. +- Logarithmisch (O(log n)): Ein *set* nutzt einen Baum. Die maximale Anzahl der Vergleiche entspricht der Tiefe des Baumes. Bei 100.000 Elementen wächst die Tiefe nur auf etwa 17 an ($2^17 approx 131.000$). +- Konstant (O(1)): Das *unordered_set* berechnet mittels einer Hash-Funktion sofort den Speicherort ("Bucket") des Wortes. Dies ist unabhängig von der Gesamtzahl der Wörter. + +#pagebreak() === References In cpp gib es Referenzen. Diese sind einfacher zu handhaben und sicherer als "call by References". #table(columns: (0.4fr, 1fr), @@ -510,21 +582,116 @@ std::cout << G << std::endl; ) ==== Input +#table(columns: 1fr, [```cpp +#include +int main () { + std::cout << "Please enter your name: "; + std::string name; + std::getline(std::cin, name); + std::cout << "Your name is " << name << "." << std::endl; + return 0; +} +```]) +Alternativ: \ +#table(columns: 1fr, [```cpp +double d; +std::cin >> d; +```]) + +Falls man einen ```cpp int``` oder ```cpp double``` will kann man ```cpp int x = stoi(wert_als_string)``` oder ```cpp double x = stod(wert_als_string)``` verwenden. === Stringstream -==== Output -==== Input +*Zahlen in einen String umwandeln* +#table(columns: 1fr, [```cpp +#include +#include +#include + +int main() { + int alter = 25; + double groesse = 1.85; + + std::stringstream ss; + ss << "Ich bin " << alter << " Jahre alt und " << groesse << "m gross."; + + std::string ergebnis = ss.str(); // .str() gibt den fertigen String zurück + std::cout << ergebnis << std::endl; + + return 0; +} +```]) + +*Einen String parsen (zerlegen)* +#table(columns: 1fr, [```cpp +std::string daten = "100 200 300"; +std::stringstream ss(daten); +int a, b, c; + +ss >> a >> b >> c; // Extrahiert die Zahlen automatisch als Integer + +std::cout << a + b + c; // Ergibt 600 +```]) + +#table(columns: (1fr, 2fr), +[`<<`], [Schreibt Daten in dem Stream], +[`>>`], [Liest Daten aus dem Stream heraus], +[`ss.str()`], [String herausholen (du hast *std::string* als typ)], +[`ss.clear()`], [Leert den Stram], +[`ss.to_string(Zahl)`], [Wandelt die Zahl in einen Sting um.], +) === File I/O ==== Output -==== Input +#table(columns: 1fr, [```cpp +#include +#include +#include +int main() { + // Wenn die Datei nicht existiert, wird sie erstellt. + // Wenn sie existiert, wird der Inhalt standardmäßig überschrieben! + std::ofstream datei("ausgabe.txt"); + + if (datei.is_open()) { + datei << "Das ist die erste Zeile.\n"; + datei << "Hier ist eine Zahl: " << 42 << std::endl; + + datei.close(); + std::cout << "Datei erfolgreich gespeichert." << std::endl; + } else { + std::cerr << "Fehler beim Öffnen der Datei!" << std::endl; + } + return 0; +} +```]) file append std::ios::app std::ofstream myfile("hello.txt", std::ios::app); +==== Input +#table(columns: 1fr, [```cpp +#include +#include +#include + +int main() { + std::ifstream datei("beispiel.txt"); + + if (!datei.is_open()) { + std::cerr << "Fehler: Datei konnte nicht geöffnet werden!" << std::endl; + return 1; + } + + std::string zeile; + while (std::getline(datei, zeile)) { + std::cout << zeile << std::endl; + } + return 0; +} +```]) + === Git #table(columns: (0.8fr, 1fr), [```sh git init ```], [Neues git repository erstellen], @@ -572,14 +739,14 @@ for (auto value : values){ } ```]) -#table(columns: 1fr, [```cpp -std::list values = {1, 2, 3}; -for (auto &value : values){ - std::cout << value << std::endl; -} -```]) - - +// #pagebreak() +// +// #table(columns: 1fr, [```cpp +// std::list values = {1, 2, 3}; +// for (auto &value : values){ +// std::cout << value << std::endl; +// } +// ```]) === testing ```cpp diff --git a/src/physik_3.typ b/src/physik_3.typ index 9b58ea6..08a11bd 100644 --- a/src/physik_3.typ +++ b/src/physik_3.typ @@ -3,6 +3,104 @@ == Physik 3 === Physik des Lichts ==== Elektromagnetische Wellen + +Emissionsspektren +#table(columns: (25pt, 80pt, 1fr,)*1, +[Ac], [Actinium], [#image("../img/physik3/Emissionsspektren/actinium.png")], +[Ag], [Silver \ Silber], [#image("../img/physik3/Emissionsspektren/silver.png")], +[Al], [Aluminum \ Aluminium], [#image("../img/physik3/Emissionsspektren/aluminum.png")], +[Am], [Americium], [#image("../img/physik3/Emissionsspektren/americium.png")], +[Ar], [Argon], [#image("../img/physik3/Emissionsspektren/argon.png")], +[As], [Arsenic], [#image("../img/physik3/Emissionsspektren/arsenic.png")], +[Au], [Gold], [#image("../img/physik3/Emissionsspektren/gold.png")], +[B], [Boron], [#image("../img/physik3/Emissionsspektren/boron.png")], +[Ba], [Barium], [#image("../img/physik3/Emissionsspektren/barium.png")], +[Bi], [Bismuth], [#image("../img/physik3/Emissionsspektren/bismuth.png")], +[Bk], [Berkelium], [#image("../img/physik3/Emissionsspektren/berkelium.png")], +[Br], [Bromine], [#image("../img/physik3/Emissionsspektren/bromine.png")], +[C], [Carbon], [#image("../img/physik3/Emissionsspektren/carbon.png")], +[Ca], [Calcium], [#image("../img/physik3/Emissionsspektren/calcium.png")], +[Cd], [Cadmium], [#image("../img/physik3/Emissionsspektren/cadmium.png")], +[Ce], [Cerium], [#image("../img/physik3/Emissionsspektren/cerium.png")], +[Cf], [Californium], [#image("../img/physik3/Emissionsspektren/califirnium.png")], +[Cl], [Chlorine], [#image("../img/physik3/Emissionsspektren/chlorine.png")], +[Cm], [Curium], [#image("../img/physik3/Emissionsspektren/curium.png")], +[Co], [Cobalt], [#image("../img/physik3/Emissionsspektren/cobalt.png")], +[Cr], [Chromium], [#image("../img/physik3/Emissionsspektren/chromium.png")], +[Cs], [Cesium], [#image("../img/physik3/Emissionsspektren/cesium.png")], +[Cu], [Copper], [#image("../img/physik3/Emissionsspektren/copper.png")], +[Dy], [Dysposium], [#image("../img/physik3/Emissionsspektren/dysprosium.png")], +[Er], [Erbium], [#image("../img/physik3/Emissionsspektren/erbium.png")], +[Eu], [Europium], [#image("../img/physik3/Emissionsspektren/europium.png")], +[F], [Flourine], [#image("../img/physik3/Emissionsspektren/fluorine.png")], +[Fe], [Iron], [#image("../img/physik3/Emissionsspektren/iron.png")], +[Ga], [Gallium], [#image("../img/physik3/Emissionsspektren/gallium.png")], +[Gd], [Gadolinium], [#image("../img/physik3/Emissionsspektren/gadolinium.png")], +[Ge], [Germanium], [#image("../img/physik3/Emissionsspektren/germanium.png")], +[H], [Hydrogen], [#image("../img/physik3/Emissionsspektren/hydrogen.png")], +[He], [Helium], [#image("../img/physik3/Emissionsspektren/helium.png")], +[Hf], [Hafnium], [#image("../img/physik3/Emissionsspektren/hafnium.png")], +[Hg], [Mercury], [#image("../img/physik3/Emissionsspektren/mercury.png")], +[Ho], [Holmium], [#image("../img/physik3/Emissionsspektren/holmium.png")], +[I], [Iodine], [#image("../img/physik3/Emissionsspektren/iodine.png")], +[In], [Indium], [#image("../img/physik3/Emissionsspektren/indium.png")], +[Ir], [Iridium], [#image("../img/physik3/Emissionsspektren/iridium.png")], +[K], [Potassium], [#image("../img/physik3/Emissionsspektren/poponium.png")], +[Kr], [Krypton], [#image("../img/physik3/Emissionsspektren/krypton.png")], +[La], [Lanthanum], [#image("../img/physik3/Emissionsspektren/lanthanum.png")], +[Li], [Lithium], [#image("../img/physik3/Emissionsspektren/lithium.png")], +[Lu], [Lutetium], [#image("../img/physik3/Emissionsspektren/lutetium.png")], +[Mg], [Magnesium], [#image("../img/physik3/Emissionsspektren/magnesium.png")], +[Mn], [Maganese], [#image("../img/physik3/Emissionsspektren/managanese.png")], +[Mo], [Molybdenum], [#image("../img/physik3/Emissionsspektren/molybdenum.png")], +[N], [Nitrogen], [#image("../img/physik3/Emissionsspektren/nitrogen.png")], +[Na], [Sodium], [#image("../img/physik3/Emissionsspektren/soduim.png")], +[Nb], [Niobium], [#image("../img/physik3/Emissionsspektren/niobium.png")], +[Nd], [Neodymium], [#image("../img/physik3/Emissionsspektren/neodymium.png")], +[Ne], [Neon], [#image("../img/physik3/Emissionsspektren/neon.png")], +[Ni], [Nickel], [#image("../img/physik3/Emissionsspektren/nickel.png")], +[O], [Oxygen], [#image("../img/physik3/Emissionsspektren/oxygen.png")], +[Os], [Osmium], [#image("../img/physik3/Emissionsspektren/osmium.png")], +[Pa], [Protactinium], [#image("../img/physik3/Emissionsspektren/protactinium.png")], +[Pb], [Lead], [#image("../img/physik3/Emissionsspektren/lead.png")], +[Pd], [Palladium], [#image("../img/physik3/Emissionsspektren/palladium.png")], +[Pm], [Promethuim], [#image("../img/physik3/Emissionsspektren/promethuim.png")], +[Po], [Polonim], [#image("../img/physik3/Emissionsspektren/poponium.png")], +[Pr], [Praseodymium], [#image("../img/physik3/Emissionsspektren/praseodymium.png")], +[Pt], [Platinum], [#image("../img/physik3/Emissionsspektren/platinum.png")], +[Pu], [Plutonium], [#image("../img/physik3/Emissionsspektren/plutonium.png")], +[Ra], [Radium], [#image("../img/physik3/Emissionsspektren/radium.png")], +[Rb], [Rubidium], [#image("../img/physik3/Emissionsspektren/rubidium.png")], +[Re], [Rhenium], [#image("../img/physik3/Emissionsspektren/rehenium.png")], +[Rh], [Rhodium], [#image("../img/physik3/Emissionsspektren/rohdium.png")], +[Rn], [Radon], [#image("../img/physik3/Emissionsspektren/radon.png")], +[Ru], [Ruthenium], [#image("../img/physik3/Emissionsspektren/ruthenium.png")], +[S], [Sulfur], [#image("../img/physik3/Emissionsspektren/sulfur.png")], +[Sb], [Antimony], [#image("../img/physik3/Emissionsspektren/antimony.png")], +[Sc], [Scandium], [#image("../img/physik3/Emissionsspektren/scandium.png")], +[Se], [Selenium], [#image("../img/physik3/Emissionsspektren/selenium.png")], +[Si], [Silicon], [#image("../img/physik3/Emissionsspektren/silicon.png")], +[Sm], [Samarium], [#image("../img/physik3/Emissionsspektren/samarium.png")], +[Sn], [Tin], [#image("../img/physik3/Emissionsspektren/tin.png")], +[Sr], [Strontium], [#image("../img/physik3/Emissionsspektren/strontium.png")], +[Ta], [Tantalum], [#image("../img/physik3/Emissionsspektren/tantalum.png")], +[Tb], [Tertium], [#image("../img/physik3/Emissionsspektren/terbium.png")], +[Tc], [Technetium], [#image("../img/physik3/Emissionsspektren/technetium.png")], +[Te], [Tellurium], [#image("../img/physik3/Emissionsspektren/tellurium.png")], +[Th], [Thorium], [#image("../img/physik3/Emissionsspektren/thorium.png")], +[Ti], [Titanium], [#image("../img/physik3/Emissionsspektren/titanium.png")], +[Tl], [Thalium], [#image("../img/physik3/Emissionsspektren/thallium.png")], +[Tm], [Thulium], [#image("../img/physik3/Emissionsspektren/thulium.png")], +[U], [Uranium], [#image("../img/physik3/Emissionsspektren/uranium.png")], +[V], [Vanadium], [#image("../img/physik3/Emissionsspektren/vanadium.png")], +[W], [Tungsten], [#image("../img/physik3/Emissionsspektren/tungsten.png")], +[Xe], [Xenon], [#image("../img/physik3/Emissionsspektren/xenon.png")], +[Y], [Yttrium], [#image("../img/physik3/Emissionsspektren/yttrium.png")], +[Yb], [Ytterbium], [#image("../img/physik3/Emissionsspektren/ytterbium.png")], +[Zn], [Zinc], [#image("../img/physik3/Emissionsspektren/zinc.png")], +[Zn], [Zirconium], [#image("../img/physik3/Emissionsspektren/zirconium.png")], +) + === Kalorik ==== Druck