Splay tree is another varient of binary search tree. In a
splay tree, the recently accessed element is placed at the root of the
tree. A splay tree is defined as follows...
Every Splay tree must be a binary search tree but it is need not to be balanced tree.
Splay Tree is a self - adjusted Binary Search Tree
in which every operation on an element rearrange the tree so that the
element is placed at the root position of the tree.
In a splay tree, every operation is performed at root of
the tree. All the operations on a splay tree are involved with a common
operation called "Splaying".
Splaying an element is the process of bringing it to the root position by performing suitable rotation operations.
In a splay tree, splaying an element rearrange all the
elements in the tree so that splayed element is placed at root of the
tree.
With the help of splaying an element we can bring most frequently used element closer to the root of the tree so that any operation on those element performed quickly. That means the splaying operation automatically brings more frequently used elements closer to the root of the tree.
Every operation on a splay tree performs the splaying operation. For example, the insertion operation first inserts the new element as it inserted into the binary search tree, after insertion the newly inserted element is splayed so that it is placed at root of the tree. The search operation in a splay tree is search the element using binary search process then splay the searched element so that it placed at the root of the tree.
In a splay tree, to splay any element we use the following rotation operations...
With the help of splaying an element we can bring most frequently used element closer to the root of the tree so that any operation on those element performed quickly. That means the splaying operation automatically brings more frequently used elements closer to the root of the tree.
Every operation on a splay tree performs the splaying operation. For example, the insertion operation first inserts the new element as it inserted into the binary search tree, after insertion the newly inserted element is splayed so that it is placed at root of the tree. The search operation in a splay tree is search the element using binary search process then splay the searched element so that it placed at the root of the tree.
In a splay tree, to splay any element we use the following rotation operations...
Rotations in Splay Tree
- 1. Zig Rotation
- 2. Zag Rotation
- 3. Zig - Zig Rotation
- 4. Zag - Zag Rotation
- 5. Zig - Zag Rotation
- 6. Zag - Zig Rotation
Example
Zig Rotation
The Zig Rotation in a splay tree is
similar to the single right rotation in AVL Tree rotations. In zig
rotation every node moves one position to thr righ from its current
position. Consider the following example...
Zag Rotation
The Zag Rotation in a splay tree is
similar to the single left rotation in AVL Tree rotations. In zag
rotation every node moves one position to the left from its current
position. Consider the following example...
Zig-Zig Rotation
The Zig-Zig Rotation in a splay tree is
a double zig rotation. In zig-zig rotation every node moves two
position to the right from its current position. Consider the following
example...
Zag-Zag Rotation
The Zag-Zag Rotation in a splay tree is
a double zag rotation. In zag-zag rotation every node moves two
position to the left from its current position. Consider the following
example...
Zig-Zag Rotation
The Zig-Zag Rotation in a splay tree is
a sequence of zig rotation followed by zag rotation. In zig-zag
rotation every node moves one position to the right followed by one
position to the left from its current position. Consider the following
example...
Zag-Zig Rotation
The Zag-Zig Rotation in a splay tree is
a sequence of zag rotation followed by zig rotation. In zag-zig
rotation every node moves one position to the left followed by one
position to the right from its current position. Consider the following
example...
Insertion Operation in Splay Tree
The insertion operation in Splay tree is performed using following steps...
- Step 1: Check whether tree is Empty.
- Step 2: If tree is Empty then insert the newNode as Root node and exit from the operation.
- step 3: If tree is not Empty then insert the newNode as a leaf node using Binary Search tree insertion logic.
- Step 4: After insertion, Splay the newNode
Deletion Operation in Splay Tree
In a Splay Tree, the deletion operation is similar to
deletion operation in Binary Search Tree. But before deleting the
element first we need to splay that node then delete it from the root position then join the remaining tree.