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User:Realazthat/Notes/Scrap: Difference between revisions
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Line 44:
\begin{array}{lcl}
m\left(C,F,E,p \in C\right)\in\left\{0,1,2,3,\infty\right\}
& = &
\underset{\begin{array}{c}
\left(r \notin [p,q]\right)
\wedge \left(s \notin [p,q] \right)
\wedge \left(\left|s-r\right|=1
\right)\\
\left(c\left(C,E,p,q,r,s\right)\neq0\right)\rightarrow\left(d\left(C,E,F,p,q,r,s\right)\neq0\right)\end{array}}
{\min}
Line 61 ⟶ 64:
<math>
m\left(C,F,E,p\right) \in O\left(\left|n\right|^2\right)
</math>
<pre>
Line 85 ⟶ 88:
m(C,F,E,p):
min = infinity
n = |C|
Line 104 ⟶ 107:
</pre>
== Better algorithm ==
<math>
\begin{array}{lcl}
T_{q}
& = &
\left\{ C{s} : s \notin [p,q] \wedge \exists_{r,|r-s|=1,r \notin [p,q]}
\left[
b(E,C_{p},C_{r})=0
\right]
\right\}\\
U_{q}
& = &
\left\{ C{s} : s \notin [p,q] \wedge \exists_{r,|r-s|=1,r \notin [p,q]}
\left[
b(E,C_{p},C_{r})=1 \wedge f(E,F,C_{p},C_{r})=1
\right]
\right\}\\
V_{q}
& = &
\left\{ C{s} : s \notin [p,q] \wedge \exists_{r,|r-s|=1,r \notin [p,q]}
\left[
b(E,C_{p},C_{r})=1 \wedge f(E,F,C_{p},C_{r})=0
\right]
\right\}\\
D_{q}
& = &
\left\{ v : (C_{q},v) \in E
\right\}\\
H_{q}
& = &
\left\{ v \in D_{q} : f(E,F,v,C_{q})=0
\right\}\\
\end{array}
</math>
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