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datovky
ds2-notes
Commits
ca65177d
Commit
ca65177d
authored
5 years ago
by
Martin Mareš
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Linear probing: Bug fixes
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e901e8a6
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06-hash/hash.tex
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ca65177d
...
...
@@ -599,7 +599,7 @@ This is a~sequence of possible locations of the element in the array in decreasi
order of preference. The cells will be numbered from~0 to~
$
m
-
1
$
and indexed modulo~
$
m
$
.
\alg
{
Insert
}
follows the probe sequence until it finds an~empty cell.
\alg
{
Find
}
follows the probe sequence until it either finds a~mat
h
ching item,
\alg
{
Find
}
follows the probe sequence until it either finds a~matching item,
or it finds an~empty cell.
\alg
{
Delete
}
is more complicated, since we generally cannot remove items
from their cells --- a~probe sequence for a~different item could have been
...
...
@@ -660,7 +660,7 @@ in most probability theory textbooks).
\theoremn
{
Chernoff bound for the right tail
}{
Let
$
X
_
1
,
\ldots
,X
_
k
$
be independent random variables taking values in
$
\{
0
,
1
\}
$
.
Let further
$
X
=
X
_
1
+
\ldots
+
X
_
k
$
,
$
\mu
=
\E
[
X
]
$
, and
$
c>
1
$
. Then
$$
\Pr
[
X > c
\mu
]
=
\left
(
\e
^{
c
-
1
}
\over
c
^
c
\right
)
^
\mu
.
$$
$$
\Pr
[
X > c
\mu
]
\le
\left
(
\e
^{
c
-
1
}
\over
c
^
c
\right
)
^
\mu
.
$$
}
\lemma
{
...
...
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