Anki Deck Changes

Commit: a3abae75 - add ad cards

Author: obrhubr <obrhubr@gmail.com>

Date: 2026-01-26T17:51:57+01:00

Changes: 7 note(s) changed (7 added, 0 modified, 0 deleted)

Note 1: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: C5BRbDI3JL
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ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls
j = 1
while j <= n do
    j = 2j
    f()
Sum form of exact calls of f()?

Back

ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls
j = 1
while j <= n do
    j = 2j
    f()
Sum form of exact calls of f()?
\[\sum_{j = 0}^{\lfloor \log_2 n \rfloor}\]
We go from \(0\) to \(\lfloor \log_2 n \rfloor\) not from \(1\).
Field-by-field Comparison
Field Before After
Front <pre><code>j = 1 while j &lt;= n do j = 2j f()<br></code></pre> Sum form of exact calls of f()?
Back <div></div><div>\[\sum_{j = 0}^{\lfloor \log_2 n \rfloor}\]</div><div>We go from \(0\) to \(\lfloor \log_2 n \rfloor\) not from \(1\).</div>
Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls

Note 2: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: Cz/kys?.PN
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ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search
Every undirected graph that contains a Hamilton path also contains an eulerian walk?

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ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search
Every undirected graph that contains a Hamilton path also contains an eulerian walk?
No.
Field-by-field Comparison
Field Before After
Front Every undirected graph that contains a Hamilton path also contains an eulerian walk?
Back No.<br><img alt="" src="paste.png">
Tags: ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search

Note 3: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: FG1IbvZ*6[
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ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search
The depth \(h\) of a seach tree of any comparison-based algorithm satisfies which bound?

Back

ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search
The depth \(h\) of a seach tree of any comparison-based algorithm satisfies which bound?
\(h \geq \Omega(\log n)\) this is information theoretically the least amount of comparisons necessary.

Note that \(h \not \leq O(n)\) necessarily as we could have a really stupid algorithm that compares thrice for example.
Field-by-field Comparison
Field Before After
Front The depth&nbsp;\(h\)&nbsp;of a seach tree of any comparison-based algorithm satisfies which bound?
Back \(h \geq \Omega(\log n)\)&nbsp;this is information theoretically the least amount of comparisons necessary.<br><br>Note that&nbsp;\(h \not \leq O(n)\)&nbsp;necessarily as we could have a really stupid algorithm that compares thrice for example.
Tags: ETH::1._Semester::A&D::03._Searching_Algorithms::2._Binary_Search

Note 4: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Image Occlusion-73a2c
GUID: KoR^|Dl^:[
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image-occlusion:rect:left=.0993:top=.1668:width=.1045:height=.5974
image-occlusion:rect:left=.2342:top=.1117:width=.0565:height=.6158
image-occlusion:rect:left=.3241:top=.1209:width=.1087:height=.625
image-occlusion:rect:left=.4651:top=.0933:width=.1252:height=.6709
image-occlusion:rect:left=.6206:top=.0933:width=.0687:height=.6618
image-occlusion:rect:left=.7196:top=.1393:width=.0656:height=.6158
image-occlusion:rect:left=.8101:top=.1393:width=.068:height=.579
image-occlusion:rect:left=.908:top=.1393:width=.0711:height=.5515

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image-occlusion:rect:left=.0993:top=.1668:width=.1045:height=.5974
image-occlusion:rect:left=.2342:top=.1117:width=.0565:height=.6158
image-occlusion:rect:left=.3241:top=.1209:width=.1087:height=.625
image-occlusion:rect:left=.4651:top=.0933:width=.1252:height=.6709
image-occlusion:rect:left=.6206:top=.0933:width=.0687:height=.6618
image-occlusion:rect:left=.7196:top=.1393:width=.0656:height=.6158
image-occlusion:rect:left=.8101:top=.1393:width=.068:height=.579
image-occlusion:rect:left=.908:top=.1393:width=.0711:height=.5515
Field-by-field Comparison
Field Before After
Occlusion {{c1::image-occlusion:rect:left=.0993:top=.1668:width=.1045:height=.5974}}<br>{{c2::image-occlusion:rect:left=.2342:top=.1117:width=.0565:height=.6158}}<br>{{c3::image-occlusion:rect:left=.3241:top=.1209:width=.1087:height=.625}}<br>{{c4::image-occlusion:rect:left=.4651:top=.0933:width=.1252:height=.6709}}<br>{{c5::image-occlusion:rect:left=.6206:top=.0933:width=.0687:height=.6618}}<br>{{c6::image-occlusion:rect:left=.7196:top=.1393:width=.0656:height=.6158}}<br>{{c7::image-occlusion:rect:left=.8101:top=.1393:width=.068:height=.579}}<br>{{c8::image-occlusion:rect:left=.908:top=.1393:width=.0711:height=.5515}}<br>
Image <img src="paste-89cdffb68fa0e6c27975c01b222032a46336dc8d.jpg">
Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::3._O-Notation

Note 5: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Classic
GUID: MFFs/r0>#}
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ETH::1._Semester::A&D::11._Minimum_Spanning_Trees
Can {f, h} ever be in an MST? Prove it:

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ETH::1._Semester::A&D::11._Minimum_Spanning_Trees
Can {f, h} ever be in an MST? Prove it:
No, because it's the heaviest edge in the cycle.
If there was an MST containing it, we could remove it and replace it by another edge in the cycle.
Then we preserve the tree property yet it's weight is strictly lower.
Field-by-field Comparison
Field Before After
Front Can {f, h} ever be in an MST? Prove it:<br><img src="paste-0451663ce9f1137e81a00020ee38fb0a96908565.jpg">
Back No, because it's the heaviest edge in the cycle.<br>If there was an MST containing it, we could remove it and replace it by another edge in the cycle.<br>Then we preserve the tree property yet it's weight is strictly lower.
Tags: ETH::1._Semester::A&D::11._Minimum_Spanning_Trees

Note 6: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Cloze
GUID: c-L/EL~rI8
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ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls
A while loop that doesn't increase constantly but goes from i = 1 and increases by i = 2*i for example, can be modelled as a sum from 0 to  \(\log_2 n\)?

Back

ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls
A while loop that doesn't increase constantly but goes from i = 1 and increases by i = 2*i for example, can be modelled as a sum from 0 to  \(\log_2 n\)?
Note that we start from 0, as \(2 = 1^0\).
Field-by-field Comparison
Field Before After
Text A while loop that doesn't increase constantly but goes from&nbsp;<b>i = 1</b>&nbsp;and increases by&nbsp;<b>i = 2*i</b>&nbsp;for example, can be modelled as a sum from {{c1::0}} to {{c2::&nbsp;\(\log_2 n\)}}?
Extra Note that we start from 0, as&nbsp;\(2 = 1^0\).
Tags: ETH::1._Semester::A&D::02._Asymptotic_Notation::4._Exact_Calls

Note 7: ETH::1. Semester::A&D

Deck: ETH::1. Semester::A&D
Note Type: Horvath Cloze
GUID: zjEd=>WPZ?
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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs
The number of distinct paths in a complete graph grows  \(O(n!)\).

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ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs
The number of distinct paths in a complete graph grows  \(O(n!)\).
Field-by-field Comparison
Field Before After
Text The number of distinct paths in a complete graph grows {{c1::&nbsp;\(O(n!)\)}}.
Tags: ETH::1._Semester::A&D::07._Graphs::1._Introduction_to_Graphs
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