Download Traversal of a Binary Tree

Binary Tree
Introduction
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A binary tree is finite set of data items which is either
empty of consists of a single item called the root and
two disjoint binary trees called the left sub tree and
right sub tree.
A binary tree is very important and the most commonly
used non-linear data structure. In a binary tree the
maximum degree of any node is at most two.
That means, there may be zero degree node (empty
tree) or a one degree node and two degree node.
Introduction
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The major operations required to be performed on a
Binary tree are:
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Creation: Creation an empty binary tree to which the ‘root
‘ points
Traversal: Visiting all the nodes in a binary tree
Deletion: Deleting a node from a non-empty binary tree
Insertion: Inserting a node into an existing (may be
empty) binary tree
Merge: Merging two binary tree
Introduction
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Copy: Copying a binary tree
Compare: Comparing two binary tree
Finding a replica or mirror of a binary tree
Binary Tree Representation
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It is often required to maintain binary tree in the
computer memory.
There are two traditional popular technique that are
used to maintain binary tree in the memory:
sequential representation/Array implementation of
Binary tree
linked list representation/Linked list implementation
of Binary tree
Array implementation of Binary tree
Array implementation of Binary tree
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The root node is number as 0 then its left child as 1 &
right child as 2.
Now node 1 is parent and its left child is number 3 and
right child number 4.
Now so on in each level.
Array implementation of Binary tree
Array implementation of Binary tree
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Reverse process to create tree from table:
Here, problem is to find the left child and right child of
current node parent.
For that to remember the formula for children:
 2*root index +1--- for left child
 2*root index +2 --- for right child
Array implementation of Binary tree
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Advantages of representing binary tree using
array:
Any node can be accessed from any other node by
calculating the index.
Here, the data is stored without any pointers to its
successor or predecessor.
In the programming languages, where dynamic
memory allocation is not possible (such as BASIC,
FORTRAN), array representation is the only means
to stored a tree.
Array implementation of Binary tree
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Disadvantages of representing binary tree using
array:
Other than full binary trees, majority of the array
entries may be empty.
It allows only static representation. The array size
cannot be changed during the exception.
Inserting a new node to it or deleting a node from it’s
inefficient with this representation. Because it requires
considerable data movement up and down the array
which demand excessive amount of processing time.
Linked list implementation of Binary tree
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The problem associated with the sequential
representation of binary tree can be overcome through
the use of the linked list representation.
In this representation each node required three fields,
one for the link of left child, second field for
representing the information associated with the node
and the third field is used to represent the link of the
right child.
Linked list implementation of Binary tree
Linked list implementation of Binary tree
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a binary tree contains one root node and some nonterminal and terminal nodes.
It is clear from the observation of a binary tree that the
non-terminal node has their left child and right child
nodes.
But the terminal nodes have no left child and right child
nodes. Their Lchild and Rchild pointer are set to NULL.
Here, non-terminal nodes are called internal nodes and
terminal nodes are called external nodes.
Linked list implementation of Binary tree
Linked list implementation of Binary tree
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Advantages of representing binary tree using Linked
list:
The drawback of the sequential representation is
overcome in this representation.
We may or may not know the tree depth in advance. In
additional, for unbalanced trees, the memory is not
wasted.
Insertion and deletion operations are more efficient in this
representation.
It is useful for dynamic data.
Linked list implementation of Binary tree
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Disadvantages of representing binary tree using
Linked list:
In this representation, there is no direct access to any
node. It has to be traversed from the root to reach to a
particular node.
As compared to sequential representation, the memory
needed per node is more. This is due to two link fields
(left child and right child for binary trees) in the node.
The programming languages not supporting dynamic
memory management would not be useful for this
representation.
Traversal of a Binary Tree
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Tree traversal is one of the most common
operations performed on tree data structures.
It is a way in which each node in the tree is
visited exactly once in a systematic manner.
The binary tree traversal would produce a linear
order for the nodes in a binary tree; there are
three popular ways of binary tree traversal.
Traversal of a Binary Tree
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There are: P/D=process node, L=left child,
R=right child
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Preorder traversal (PLR/DLR)
Inorder traversal(LPR/LDR)
Postorder traversal(LRP/DPD)
Traversal of a Binary Tree
Traversal of a Binary Tree
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Pre-order Traversal perform the following three
operation:
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visit the root
Traverse the left sub-tree in pre-order
Traverse the right sub-tree in pre-order
Pre-order=>1,2,4,7,5,8,3,6,9
Traversal of a Binary Tree
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In-order Traversal perform the following three
operation:
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Traverse the left sub-tree in In-order
visit the root
Traverse the right sub-tree in In-order
In-order=>4,7,2,8,5,1,6,9,3
Traversal of a Binary Tree
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Post-order Traversal perform the following
three operation:
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Traverse the left sub-tree in Post-order
Traverse the right sub-tree in Post-order
visit the root
Post-order=>7,4,8,5,2,9,6,3,1