This document discusses binary trees, including their basic structure and components. A binary tree is composed of nodes, with each node containing a value and references to a left and right child node. It describes traversing binary trees in preorder, inorder, and postorder sequences by recursively visiting each node. Various properties are also covered, such as a tree's size, depth, balance, and copying an entire binary tree using postorder traversal.
this presentation is made for the students who finds data structures a complex subject
this will help students to grab the various topics of data structures with simple presentation techniques
best regards
BCA group
(pooja,shaifali,richa,trishla,rani,pallavi,shivani)
Common Use of Tree as a Data Structure
ADVANCE
1. Nodes
2. Parent Nodes & Child Nodes
3. Leaf Nodes
4. Root Node
5. Sub Tree
6. Level of a tree:
7. m-ary Tree
8. Binary Tree (BT)
9. Complete and Full Binary Tree
10. Traversal
11. Binary Search Tree (BST)
12. Inorder Traversal – Left_ParentNode_Right
13. Postorder Traversal – Left_Right_ParentNode
14. Preorder Traversal – ParentNode_Left_Right
15. Binary Search Tree (BST)
16. BST - Insert, Delete
In computer science, tree traversal (also known as tree search) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
this presentation is made for the students who finds data structures a complex subject
this will help students to grab the various topics of data structures with simple presentation techniques
best regards
BCA group
(pooja,shaifali,richa,trishla,rani,pallavi,shivani)
Common Use of Tree as a Data Structure
ADVANCE
1. Nodes
2. Parent Nodes & Child Nodes
3. Leaf Nodes
4. Root Node
5. Sub Tree
6. Level of a tree:
7. m-ary Tree
8. Binary Tree (BT)
9. Complete and Full Binary Tree
10. Traversal
11. Binary Search Tree (BST)
12. Inorder Traversal – Left_ParentNode_Right
13. Postorder Traversal – Left_Right_ParentNode
14. Preorder Traversal – ParentNode_Left_Right
15. Binary Search Tree (BST)
16. BST - Insert, Delete
In computer science, tree traversal (also known as tree search) is a form of graph traversal and refers to the process of visiting (checking and/or updating) each node in a tree data structure, exactly once. Such traversals are classified by the order in which the nodes are visited. The following algorithms are described for a binary tree, but they may be generalized to other trees as well.
Tree and Binary search tree in data structure.
The complete explanation of working of trees and Binary Search Tree is given. It is discussed such a way that everyone can easily understand it. Trees have great role in the data structures.
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Whether you’re tweaking your current setup or building from the ground up, this session will arm you with the tools and insights needed to transform your FME usage into a powerhouse of productivity. Join us to discover effective strategies that simplify complex processes, enhancing your productivity and transforming your data management practices with FME. Let’s turn complexity into clarity and make your workspaces work wonders!
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How can you help your company evolve, adapt, and succeed using Artificial Intelligence and the Metaverse to stay ahead of the competition? What are the potential issues, complications, and benefits that these technologies could bring to us and our organizations? In this session, Jen Stirrup will explain how to start thinking about these technologies as an organisation.
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2. Parts of a binary tree
A binary tree is composed of zero or more nodes
Each node contains:
A value (some sort of data item)
A reference or pointer to a left child (may be null), and
A reference or pointer to a right child (may be null)
A binary tree may be empty (contain no nodes)
If not empty, a binary tree has a root node
Every node in the binary tree is reachable from the root
node by a unique path
A node with neither a left child nor a right child is
called a leaf
In some binary trees, only the leaves contain a value
2
3. Picture of a binary tree
a
b c
d e f
g h i j k
l
3
4. Size and depth
The size of a binary tree is the
a number of nodes in it
This tree has size 12
b c The depth of a node is its
distance from the root
d e f
a is at depth zero
e is at depth 2
g h i j k
The depth of a binary tree is
l the depth of its deepest node
This tree has depth 4
4
5. Balance
a a
b c b
c e
d e f g
d f
h i j
g h
A balanced binary tree
i j
An unbalanced binary tree
A binary tree is balanced if every level above the lowest is “full”
(contains 2n nodes)
In most applications, a reasonably balanced binary tree is
desirable
5
6. Binary search in an array
Look at array location (lo + hi)/2
Searching for 5:
(0+6)/2 = 3
Using a binary
hi = 2;
(0 + 2)/2 = 1 lo = 2; search tree
(2+2)/2=2
7
3 13
0 1 2 3 4 5 6
2 3 5 7 11 13 17 2 5 11 17
6
7. Tree traversals
A binary tree is defined recursively: it consists of a root, a
left subtree, and a right subtree
To traverse (or walk) the binary tree is to visit each node in
the binary tree exactly once
Tree traversals are naturally recursive
Since a binary tree has three “parts,” there are six possible
ways to traverse the binary tree:
root, right, left
root, left, right
right, root, left
left, root, right
right, left, root
left, right, root
7
8. Preorder traversal
In preorder, the root is visited first
Here’s a preorder traversal to print out all the
elements in the binary tree:
public void preorderPrint(BinaryTree bt) {
if (bt == null) return;
System.out.println(bt.value);
preorderPrint(bt.leftChild);
preorderPrint(bt.rightChild);
}
8
9. Inorder traversal
In inorder, the root is visited in the middle
Here’s an inorder traversal to print out all the
elements in the binary tree:
public void inorderPrint(BinaryTree bt) {
if (bt == null) return;
inorderPrint(bt.leftChild);
System.out.println(bt.value);
inorderPrint(bt.rightChild);
}
9
10. Postorder traversal
In postorder, the root is visited last
Here’s a postorder traversal to print out all the
elements in the binary tree:
public void postorderPrint(BinaryTree bt) {
if (bt == null) return;
postorderPrint(bt.leftChild);
postorderPrint(bt.rightChild);
System.out.println(bt.value);
}
10
11. Tree traversals using “flags”
The order in which the nodes are visited during a tree
traversal can be easily determined by imagining there is a
“flag” attached to each node, as follows:
preorder inorder postorder
To traverse the tree, collect the flags:
A A A
B C B C B C
D E F G D E F G D E F G
ABDECFG DBEAFCG DEBFGCA
11
12. Copying a binary tree
In postorder, the root is visited last
Here’s a postorder traversal to make a complete
copy of a given binary tree:
public BinaryTree copyTree(BinaryTree bt) {
if (bt == null) return null;
BinaryTree left = copyTree(bt.leftChild);
BinaryTree right = copyTree(bt.rightChild);
return new BinaryTree(bt.value, left, right);
}
12
13. Other traversals
The other traversals are the reverse of these three
standard ones
That is, the right subtree is traversed before the left subtree
is traversed
Reverse preorder: root, right subtree, left subtree
Reverse inorder: right subtree, root, left subtree
Reverse postorder: right subtree, left subtree, root
13