Anki Deck Changes

Note 1: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: k#~pL>w{_$

modified

Before

Front

What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?

Back

What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?

$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ and $g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ are differentiable
$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty$ they tend to infinity
and $\forall x \in \mathbb{R}^{+} , g'(x) \neq 0$ and $g$ never equals to 0

This guarantees that we can take the fraction f/g

After

Front

What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?

{{c1::$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ and $g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ are differentiable}}
{{c2::$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty$ (they tend to infinity)}}
{{c3::$\forall x \in \mathbb{R}^{+} , g'(x) \neq 0$ and $g$ never equals to 0}}

Back

What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?

{{c1::$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ and $g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ are differentiable}}
{{c2::$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty$ (they tend to infinity)}}
{{c3::$\forall x \in \mathbb{R}^{+} , g'(x) \neq 0$ and $g$ never equals to 0}}

This guarantees that we can take the fraction f/g.

Field-by-field Comparison

Field	Before	After
Text	What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?	What are the prerequisites for $f$ and $g$ to apply l'Hôpital's?<br><ol><li>{{c1::$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ and $g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ are <b>differentiable</b>}}<br></li><li>{{c2::$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty$ (they <b>tend to infinity)</b>}}<br></li><li>{{c3::$\forall x \in \mathbb{R}^{+} , g'(x) \neq 0$ and $g$ <b>never equals to 0</b>}}</li></ol>
Extra	<ol><li>$f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ and $g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}$ are <b>differentiable</b></li><li>$\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty$ they <b>tend to infinity</b></li><li>and $\forall x \in \mathbb{R}^{+} , g'(x) \neq 0$ and $g$ <b>never equals to 0</b></li></ol><div>This guarantees that we can take the fraction f/g~~</div>~~	This guarantees that we can take the fraction f/g.

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 2: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Classic
GUID: D%cpEp.*I3

modified

Before

Front

L'Hôpital's Rule:

Back

L'Hôpital's Rule:

If $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = C \in \mathbb{R}^{+}0$ or $\lim{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = \infty$, then:

\[\lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = \lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)}\]The ratio of the derivatives tend to the same limit

After

Front

What is L'Hôpital's Rule?

Back

What is L'Hôpital's Rule?

If $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = C \in \mathbb{R}^{+}\cup\set0$ or $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = \infty$, then:

\[\lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = \lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)}\]The ratio of the derivatives tend to the same limit.

Field-by-field Comparison

Field	Before	After
Front	L'Hôpital's Rule:	What is L'Hôpital's Rule?
Back	<div>If $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = C \in \mathbb{R}^{+}0$ or $\lim{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = \infty$, then:</div> <div>\[\lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = \lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)}\]The ratio of the <b>derivatives</b> tend to the <b>same limit</b><br></div>	<div>If $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = C \in \mathbb{R}^{+}\cup\set0$ or $\lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)} = \infty$, then:</div> <div>\[\lim_{x \rightarrow \infty} \frac{f(x)}{g(x)} = \lim_{x \rightarrow \infty} \frac{f’(x)}{g’(x)}\]The ratio of the <b>derivatives</b> tend to the <b>same limit.</b><br></div>

Tags: PlsFix::huh ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 3: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Classic
GUID: ch>ShkzK.z

modified

Before

Front

Recursive Equation solved by Master Theorem

Back

Recursive Equation solved by Master Theorem

Recurrences of the form $T(n) \leq aT(n/2) + Cn^b$
where $a$, $C > 0$ and $b \geq 0$ are constants.

After

Front

What is the form of the recursive equations solved by the Master Theorem?

Back

What is the form of the recursive equations solved by the Master Theorem?

Recurrences of the form $T(n) \leq aT(n/2) + Cn^b$
where $a$, $C > 0$ and $b \geq 0$ are constants.

Field-by-field Comparison

Field	Before	After
Front	Recursive Equation solved by Master Theorem	What is the form of the recursive equations solved by the Master Theorem?

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 4: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: bE2IXoJWO/

modified

Before

Front

Master Theorem: $T(n) \leq aT(n/2) + Cn^b$, $a$ is number of recursive subproblems (must be $> 0$).

Back

Master Theorem: $T(n) \leq aT(n/2) + Cn^b$, $a$ is number of recursive subproblems (must be $> 0$).

After

Front

Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$, $a$ is the number of recursive subproblems (must be $> 0$).

Back

Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$, $a$ is the number of recursive subproblems (must be $> 0$).

Field-by-field Comparison

Field	Before	After
Text	Master Theorem: $T(n) \leq aT(n/2) + Cn^b$,  ~~  ~~$a$ is {{c1:: number of <b>recursive subproblems</b> (must be $> 0$)}}.	Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$, $a$ is {{c1::the number of <b>recursive subproblems</b> (must be $> 0$)}}.

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 5: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: Fzt_!E{2Xk

modified

Before

Front

Master Theorem: $T(n) \leq aT(n/2) + Cn^b$, $Cn^b$ is the work done outside the recursive calls ($\geq 0$).

Back

Master Theorem: $T(n) \leq aT(n/2) + Cn^b$, $Cn^b$ is the work done outside the recursive calls ($\geq 0$).

After

Front

Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$, $Cn^b$ is the work done outside the recursive calls ($\geq 0$).

Back

Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$, $Cn^b$ is the work done outside the recursive calls ($\geq 0$).

Field-by-field Comparison

Field	Before	After
Text	Master Theorem: $T(n) \leq aT(n/2) + Cn^b$,   $Cn^b$ is {{c1:: the work done outside the recursive calls ($\geq 0$)}}.	Master Theorem: In $T(n) \leq aT(n/2) + Cn^b$,   $Cn^b$ is {{c1:: the work done outside the recursive calls ($\geq 0$)}}.

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 6: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Classic
GUID: NDIo0EK5KX

modified

Before

Front

If $T(n) \geq aT(n/ 2) + Cn^b$ then the O-Notation gives

Back

If $T(n) \geq aT(n/ 2) + Cn^b$ then the O-Notation gives

$T(n) \geq \Omega(...)$

After

Front

If $T(n) \geq aT(n/ 2) + Cn^b$, then the O-Notation gives

Back

If $T(n) \geq aT(n/ 2) + Cn^b$, then the O-Notation gives

$T(n) \geq \Omega(...)$

Field-by-field Comparison

Field	Before	After
Front	If $T(n) \geq aT(n/ 2) + Cn^b$ then the O-Notation gives	If $T(n) \geq aT(n/ 2) + Cn^b$, then the O-Notation gives

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation PlsFix::ClozeThatBish

Note 7: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Classic
GUID: ms|2]oAD;M

modified

Before

Front

If $T(n) = aT(n/ 2) + Cn^b$ then the O-Notation gives

Back

If $T(n) = aT(n/ 2) + Cn^b$ then the O-Notation gives

$T(n) = \Theta(...)$

After

Front

If $T(n) = aT(n/ 2) + Cn^b$, then the O-Notation gives

Back

If $T(n) = aT(n/ 2) + Cn^b$, then the O-Notation gives

$T(n) = \Theta(...)$

Field-by-field Comparison

Field	Before	After
Front	If $T(n) = aT(n/ 2) + Cn^b$ then the O-Notation gives	If  $T(n) = aT(n/ 2) + Cn^b$, then the O-Notation gives

Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation PlsFix::ClozeThatBish

Note 8: ETH::A&D

Deck: ETH::A&D
Note Type: Horvath Cloze
GUID: Q3:!A9V`D,

modified

Before

Front

Steps of giving a DP solution:

Define the DP table (dimensions, index, range; meaning of entry): ex: DP[1..n+1][1..k+1]
Computation of Entry (Base Case, recursive formula, pay attention to bounds!)
Calculation Order (what depends on what entries, what variable incremented first)
Extract Solution (How to get final solution out)
Running time proof

Back

Steps of giving a DP solution:

Define the DP table (dimensions, index, range; meaning of entry): ex: DP[1..n+1][1..k+1]
Computation of Entry (Base Case, recursive formula, pay attention to bounds!)
Calculation Order (what depends on what entries, what variable incremented first)
Extract Solution (How to get final solution out)
Running time proof

SMIROST (Size, Meaning, Initialisation, Recursive, Order, Solution, Time)

After

Front

Steps of giving a DP solution:

Define the DP table (dimensions, index, range; meaning of entry): ex: DP[1..n+1][1..k+1]
Computation of Entry (Base Case, recursive formula, pay attention to bounds!)
Calculation Order (what depends on what entries, what variable incremented first)
Extract Solution (How to get final solution out)
Running time proof

Back

Steps of giving a DP solution:

Define the DP table (dimensions, index, range; meaning of entry): ex: DP[1..n+1][1..k+1]
Computation of Entry (Base Case, recursive formula, pay attention to bounds!)
Calculation Order (what depends on what entries, what variable incremented first)
Extract Solution (How to get final solution out)
Running time proof

SMIROST (Size, Meaning, Initialisation, Recursive, Order, Solution, Time)

Smiling Monkey In Red Overall Steals Tacos

Field-by-field Comparison

Field	Before	After
Extra	SMIROST (Size, Meaning, Initialisation, Recursive,  Order, Solution, Time)	SMIROST (Size, Meaning, Initialisation, Recursive,  Order, Solution, Time)<br><br><img alt="" src="https://chatgpt.com/backend-api/estuary/content?id=file_00000000b144722fb24d37aefc63a244&ts=490704&p=fs&cid=1&sig=9139f521032b1f527f402bd9e46aa4fc98c1c346920ce78fa1198c460ce702b0&v=0"><img src="b8ad5128-8b94-4df8-a395-8fcd177c0ef6.png"><br><strong>S</strong>miling <strong>M</strong>onkey <strong>I</strong>n <strong>R</strong>ed <strong>O</strong>verall <strong>S</strong>teals <strong>T</strong>acos<img alt="" src="https://chatgpt.com/backend-api/estuary/content?id=file_00000000b144722fb24d37aefc63a244&ts=490704&p=fs&cid=1&sig=9139f521032b1f527f402bd9e46aa4fc98c1c346920ce78fa1198c460ce702b0&v=0">

Tags: ETH::1._Semester::A&D::06._Dynamic_Programming

Note 9: ETH::A&D

Deck: ETH::A&D
Note Type: Algorithms
GUID: gE_4/z}oud

modified

Before

Front

Runtime of Editing Distance?

Back

Runtime of Editing Distance?

$\Theta(n \cdot m)$

After

Front

Runtime of Edit Distance?

Back

Runtime of Edit Distance?

$\Theta(n \cdot m)$

Field-by-field Comparison

Field	Before	After
Name	Edit~~ing~~ Distance	Edit Distance

Tags: ETH::1._Semester::A&D::06._Dynamic_Programming::4._ED ETH::1._Semester::A&D::06._Dynamic_Programming::5._Edit_Distance

Note 10: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Classic
GUID: i;]362(]mf

modified

Before

Front

If two singleton sets are equal, what can we conclude about their elements?

Back

If two singleton sets are equal, what can we conclude about their elements?

For any sets $a$ and $b$, $\{a\} = \{b\} \Longrightarrow a = b$

After

Front

If two singleton sets are equal, what can we conclude about their elements?

Back

If two singleton sets are equal, what can we conclude about their elements?

For any sets $a$ and $b$, $\{a\} = \{b\} \Longrightarrow a = b$

(A singleton is a set with one element.)

Field-by-field Comparison

Field	Before	After
Back	For any sets $a$ and $b$, $\{a\} = \{b\} \Longrightarrow a = b$	For any sets $a$ and $b$, $\{a\} = \{b\} \Longrightarrow a = b$<br><br>(A singleton is a set with one element.)

Tags: ETH::1._Semester::DiskMat::3._Sets,_Relations,_and_Functions::2._Sets_and_Operations_on_Sets::2._Set_Equality_and_Constructing_Sets_From_Sets

Note 11: ETH::DiskMat

Deck: ETH::DiskMat
Note Type: Horvath Cloze
GUID: Ma#P3o/Xx{

modified

Before

Front

A group is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying three axioms: G1 (associativity), G2 (neutral element), and G3 (inverse elements).

Back

A group is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying three axioms: G1 (associativity), G2 (neutral element), and G3 (inverse elements).

After

Front

A group is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying three axioms: G1 (associativity), G2 (neutral element), and G3 (inverse elements).

Back

A group is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying three axioms: G1 (associativity), G2 (neutral element), and G3 (inverse elements).

Field-by-field Comparison

Field	Before	After
Text	<p>A {{c1::group}} is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying three axioms: {{c3::G1 (associativity)}}, {{c4::G2 (neutral element)}}, and {{c5::G3 (inverse elements)}}.</p>	<p>A {{c1::group}} is an algebra $\langle G; *, \widehat{\ \ }, e \rangle$ satisfying {{c2::three}} axioms: {{c3::G1 (associativity)}}, {{c4::G2 (neutral element)}}, and {{c5::G3 (inverse elements)}}.</p>

Tags: PlsFix::DUPLICATE ETH::1._Semester::DiskMat::5._Algebra::2._Monoids_and_Groups::3._Inverses_and_Groups

Note 12: ETH::EProg

Deck: ETH::EProg
Note Type: Horvath Cloze
GUID: OJ16/M<6a6

modified

Before

Front

An option in EBNF can be written as [E] or E | $\epsilon$.

Back

An option in EBNF can be written as [E] or E | $\epsilon$.

After

Front

An option in EBNF can be written as [ E ] or E | $\epsilon$.

Back

An option in EBNF can be written as [ E ] or E | $\epsilon$.

Field-by-field Comparison

Field	Before	After
Text	An option in EBNF can be written as {{c1::[E]}} or {{c2::E \| $\epsilon$}}.	An option in EBNF can be written as {{c1::[ E ]}} or {{c2::E \| $\epsilon$}}.

Tags: ETH::1._Semester::EProg::1._EBNF::3._Control_Forms::2._Decision

Note 13: ETH::EProg

Deck: ETH::EProg
Note Type: Horvath Cloze
GUID: m)$PxVQ^IS

modified

Before

Front

Zwei EBNF-Beschreibungen sind äquivalent falls ihre Sprachen gleich sind

Back

Zwei EBNF-Beschreibungen sind äquivalent falls ihre Sprachen gleich sind

After

Front

Zwei EBNF-Beschreibungen sind äquivalent falls ihre Sprachen gleich sind.

Back

Zwei EBNF-Beschreibungen sind äquivalent falls ihre Sprachen gleich sind.

Field-by-field Comparison

Field	Before	After
Text	Zwei EBNF-Beschreibungen sind äquivalent falls {{c1:: ihre Sprachen gleich sind}}	Zwei EBNF-Beschreibungen sind äquivalent falls {{c1:: ihre Sprachen gleich sind.}}

Tags: ETH::1._Semester::EProg::1._EBNF::4._Derivations

Note 14: ETH::EProg

Deck: ETH::EProg
Note Type: Horvath Cloze
GUID: IQ4$mZs7/D

modified

Before

Front

Primitive types include:
char
short
int
long
double
float
boolean
byte

Back

Primitive types include:
char
short
int
long
double
float
boolean
byte

After

Front

The 8 primitve types of Java are:

byte
char
short
int
long
float
double
boolean

Back

The 8 primitve types of Java are:

byte
char
short
int
long
float
double
boolean

Field-by-field Comparison

Field	Before	After
Text	Primitive types ~~include: <br>{{c1:: char}}<br~~>{{c6:: short}}<br>{{c2:: int}}<br>{{c3:: long }}<~~br>{{c4:: double}}<br~~>{{c7:: float}}<br>{{c5:: ~~boolean}}<br>{{c8:: byte}}~~	The 8 primitve types of Java are:<br><ol><li>{{c1:: byte}}</li><li>{{c2:: char}}</li><li>{{c3:: short}}</li><li>{{c4:: int}}</li><li>{{c5:: long}}</li><li>{{c6:: float}}</li><li>{{c7:: double}}</li><li>{{c8:: boolean}}</li></ol>

Tags: ETH::1._Semester::EProg::2._First_Java_Programs::3._Simple_Calculations::1._Types,_Variables,_Values

Field	Before	After
Text	What are the prerequisites for \(f\) and \(g\) to apply l'Hôpital's?	What are the prerequisites for \(f\) and \(g\) to apply l'Hôpital's?<br><ol><li>{{c1::\(f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}\) and \(g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}\) are <b>differentiable</b>}}<br></li><li>{{c2::\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty\) (they <b>tend to infinity)</b>}}<br></li><li>{{c3::\(\forall x \in \mathbb{R}^{+} , g'(x) \neq 0\) and \(g\) <b>never equals to 0</b>}}</li></ol>
Extra	<ol><li>\(f: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}\) and \(g: \mathbb{R}^{+} \rightarrow \mathbb{R}^{+}\) are <b>differentiable</b></li><li>\(\lim_{x \rightarrow \infty} f(x) = \lim_{x \rightarrow \infty} g(x) = \infty\) they <b>tend to infinity</b></li><li>and \(\forall x \in \mathbb{R}^{+} , g'(x) \neq 0\) and \(g\) <b>never equals to 0</b></li></ol><div>This guarantees that we can take the fraction f/g~~</div>~~	This guarantees that we can take the fraction f/g.