kristoferssolo/Theory-of-Algorithms-Cheatsheet
1
0
Fork 0
mirror of https://github.com/kristoferssolo/Theory-of-Algorithms-Cheatsheet.git synced 2025-10-21 20:10:39 +00:00
Code Issues Actions Packages Projects Releases Wiki Activity

fix: graph caption

Browse Source
This commit is contained in:
Kristofers Solo 2025-06-15 20:32:39 +03:00
parent 624b3f0ce5
commit 4741efe3dc
Signed by: kristoferssolo
GPG Key ID: 8687F2D3EEE6F0ED
1 changed files with 42 additions and 41 deletions
Show Stats Download Patch File Download Diff File Expand all files Collapse all files

31
main.typ
View File

@ -802,9 +802,9 @@ saprātīgie deterministiskie skaitļošanas modeļi ir polinomiāli ekvivalenti
- Dots grafs $G$ un divas virsotnes $u$, $v$.
- Jautājums: vai eksistē ceļš no $u$ uz $v$?
- Rupjais-spēks: pārbaudīt visus ceļus — eksponenciāls laiks.
- Rupjais-spēks: pārbaudīt visus ceļus -- eksponenciāls laiks.
- Efektīvs algoritms: meklēšana plašumā (breadth-first search); laika
sarežģītība: $O(|V| + |E|)$.
sarežģītība: $O(abs(V) + abs(E))$.
== Piemērs ($"RELPRIME"$)
@ -820,7 +820,7 @@ saprātīgie deterministiskie skaitļošanas modeļi ir polinomiāli ekvivalenti
#NP (nederminēti-polinomiālas) problēmas
ir problēmas (2 ekvivalentas definīcijas):
+ $L in NP$, ja eksistē pārbaudes algoritms - $O(n^c)$ laika Tjūringa mašīna $M$:
+ $L in NP$, ja eksistē pārbaudes algoritms -- $O(n^c)$ laika Tjūringa mašīna $M$:
+ Ja $L(x) = 1$, tad eksistē y: $M(x, y) = 1$.
+ Ja $L(x) = 0$, tad visiem y: $M(x, y) = 0$.
+ _Informācija $y$ var saturēt brīvi definētu informāciju._
@ -1006,7 +1006,8 @@ Vārdiski. Jauns grafs $G$, kurā ir visas virsotnes no $V$, bet
visas šķautnes, kas ir $G$ nav $G'$ un pretēji -- visas šķautnes
kā nav $G$ ir $G'$.
#figure(diagram(
#figure(
diagram(
cell-size: 1mm,
node-stroke: 0pt,
spacing: 1em,
@ -1037,8 +1038,8 @@ kā nav $G$ ir $G'$.
edge(<a2>, <b2>, "--", stroke: yellow),
edge(<c2>, <b2>),
edge(<c2>, <a2>, "--", stroke: yellow),
)),
caption: "Papildgrafa piemērs",
),
caption: "Papildgrafa piemērs",
)
Ir spēkā sakarība $"INDSET"(G, k) = "CLIQUE"(G', k)$.
@ -1118,26 +1119,26 @@ Ir spēkā sakarība $"INDSET"(G, k) = "CLIQUE"(G', k)$.
[Summa], [$ f(x) + g(x) $], [$ f'(x) + g'(x) $],
[Starpība], [$ f(x) - g(x) $], [$ f'(x) - g'(x) $],
[Reizinājums], [$ f(x) * g(x) $],
[Reizinājums], [$ f(x) dot g(x) $],
[
$
f'(x) * g(x) + \
f(x) * g'(x)
f'(x) dot g(x) + \
f(x) dot g'(x)
$
],
/*
[Quotient Rule], [$ (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2 $], [$ (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2 $],
[Chain Rule], [$ f(g(x)) $], [$ f'(g(x)) * g'(x) $],
[Quotient Rule], [$ (f'(x) dot g(x) - f(x) * g'(x)) / (g(x))^2 $], [$ (f'(x) * g(x) - f(x) * g'(x)) / (g(x))^2 $],
[Chain Rule], [$ f(g(x)) $], [$ f'(g(x)) dot g'(x) $],
[Euler’s Number Exponent Rule], [$ e^x $], [$ e^x $],
[Constant Exponent Rule], [$ a^x $], [$ a^x * ln(a) $],
[Constant Exponent Rule], [$ a^x $], [$ a^x dot ln(a) $],
[Natural Log Rule], [$ ln(x) $], [$ 1 / x $],
[Logarithm Rule], [$ log_a(x) $], [$ 1 / (x * ln(a)) $],
[Logarithm Rule], [$ log_a(x) $], [$ 1 / (x dot ln(a)) $],
[Sine Rule], [$ sin(x) $], [$ cos(x) $],
[Cosine Rule], [$ cos(x) $], [$ -sin(x) $],
[Tangent Rule], [$ tan(x) $], [$ sec^2(x) $],
[Cosecant Rule], [$ csc(x) $], [$ -csc(x) * cot(x) $],
[Secant Rule], [$ sec(x) $], [$ sec(x) * tan(x) $],
[Cosecant Rule], [$ csc(x) $], [$ -csc(x) dot cot(x) $],
[Secant Rule], [$ sec(x) $], [$ sec(x) dot tan(x) $],
[Cotangent Rule], [$ cot(x) $], [$ -csc^2(x) $],
*/
)