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added first exampled for rbtree delete stuff...

release0.1.5
Georg Hopp 12 years ago
parent
commit
94bc5bc41a
  1. 107
      docs/rbdelete.txt

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docs/rbdelete.txt

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Properties of a rbtree
======================
1. A node is either red or black.
2. The root is black. (This rule is sometimes omitted. Since the root can
always be changed from red to black, but not necessarily vice-versa,
this rule has little effect on analysis.)
3. All leaves (NIL) are black. (All leaves are same color as the
root.)
4. Every red node must have two black child nodes.
5. Every simple path from a given node to any of its
descendant leaves contains the same number of black nodes.
Assumptions in addition to wikipedia
====================================
lets assume that NULL pointer are black B nodes. But we mark them with a (N)
Example
=======
we start with the tree from the insert example
----------------------------------------------
B(11)
R(8) R(13)
B(3) B(9) B(12) B(16)
B(N) B(N) B(N) R(10) B(N) B(N) B(N) B(N)
B(N) B(N)
we remove R(10) / remove a red node (replace with its child):
wikipedia explains why this can only happen with two leaf children (our B(N))
B(11)
R(8) R(13)
B(3) B(9) B(12) B(16)
B(N) B(N) B(N) B(N) B(N) B(N) B(N) B(N)
again start with the insert example result
------------------------------------------
B(11)
R(8) R(13)
B(3) B(9) B(12) B(16)
B(N) B(N) B(N) R(10) B(N) B(N) B(N) B(N)
B(N) B(N)
remove B(9) (which is the second simple case described on wikipedia)
M black, C red
After remove just repaint child black. As I do not replace the node,
but the value this is simplified in my case to simply do nothing after
normal delete... :D
B(11)
R(8) R(13)
B(3) B(10) B(12) B(16)
B(N) B(N) B(N) B(N) B(N) B(N) B(N) B(N)
again start with the insert example result
------------------------------------------
B(11)
R(8) R(13)
B(3) B(9) B(12) B(16)
B(N) B(N) B(N) R(10) B(N) B(N) B(N) B(N)
B(N) B(N)
now lets delete B(3)... which is stated on wikipedia as the complicated case
where 6 subcases could be distinguished.
Wikipedia says we begin with replacing B(3) which one if its childs, in my
case this means, setting r(8)->left to NULL....
So, what is called in on Wikipedia is simply a nullpointer for me...hopefully
I don't have to do anything with it.
Get an overview over our variables now:
N : Nullpointer set in R(8)->left
P : R(8)
S : B(9)
Sl: Nullpointer
Sr: R(10)
# vim: set et ts=4:
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