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Splay Trees
1
Splay Trees
6
3
8
4
v
z
Splay Trees
2
all the keys in the yellow
region are
≤
20
all the keys in the blue
region are
≥
20
Splay Trees are
Binary Search Trees
±
BST Rules:
²
items stored only at internal
nodes
²
keys stored at nodes in the
left subtree of
v
are less
than or equal to the key
stored at
²
keys stored at nodes in the
right subtree of
are
greater than or equal to the
key stored at
±
An inorder traversal will
return the keys in order
(20,Z)
(37,P)
(21,O)
(14,J)
(7,T)
(35,R)
(10,A)
(1,C)
(1,Q)
(5,G)
(2,R)
(5,H)
(6,Y)
(5,I)
(8,N)
(7,P)
(36,L)
(10,U)
(40,X)
note that two keys of
equal value may be well
separated
Splay Trees
3
Searching in a Splay Tree:
Starts the Same as in a BST
±
Search proceeds down
the tree to found item
or an external node.
±
Example: Search for
time with key 11.
(20,Z)
(37,P)
(21,O)
(14,J)
(7,T)
(35,R)
(10,A)
(1,C)
(1,Q)
(5,G)
(2,R)
(5,H)
(6,Y)
(5,I)
(8,N)
(7,P)
(36,L)
(10,U)
(40,X)
Splay Trees
4
Example Searching in a BST,
continued
±
search for key 8, ends at
an internal node.
(20,Z)
(37,P)
(21,O)
(14,J)
(7,T)
(35,R)
(10,A)
(1,C)
(1,Q)
(5,G)
(2,R)
(5,H)
(6,Y)
(5,I)
(8,N)
(7,P)
(36,L)
(10,U)
(40,X)
Splay Trees
5
Splay Trees do Rotations after
Every Operation (Even Search)
±
new operation:
splay
²
splaying moves a node to the root using rotations
²
right rotation
²
makes the left child
x
of a node
y
into
y
’s parent;
y
becomes the right child
of
x
y
x
T
1
T
2
T
3
y
x
T
1
T
2
T
3
²
left rotation
²
makes the right child
y
of a node
x
into
x
’s parent;
x
becomes the left
child of
y
y
x
T
1
T
2
T
3
y
x
T
1
T
2
T
3
(structure of tree above y
is not modified)
(structure of tree above x
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This note was uploaded on 03/24/2010 for the course CS cs 5329 taught by Professor Wang during the Spring '10 term at Southwest Texas Junior College.
 Spring '10
 wang
 Binary Search

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