Transcript Introduction to Data Structure

Data Structure: Chapter 6
Min Chen
School of Computer Science and Engineering
Seoul National University
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Definition of Trees
Representing Rooted Tree
Tree Traversal
 Preorder Traversal
 Postorder Traversal
 Level Order Traversal
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Tree:
 Set of nodes and edges that connect them
 Exactly one path between any 2 nodes
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Rooted Tree:
 One distinguished node is called the root
 Every node C, except root, has one parent P, the
first node on path from c to the root. C is P’s child
 Root has no parent
 A node can have any number of children
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Leaf
 Node with no children
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Siblings
 Nodes with same parent
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Ancestors
 nodes on path from d to rott, including d, d’s
parent, d’s grand parent, … root
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Descendant
 If A is B’s ancestor, then B is A’s Descendant
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Length of path
 Number of edges in path
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Depth of node n
 Length of path from n to root
 Depth of root is zero
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Height of node n
 Length of path from n to its deepest descendant
 Height of any leaf is zero
 Height of a tree = Height of the root
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Subtree rooted at n
 The tree formed by n and its descendants
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G &T
 Each node has 3 references stored in a list
▪ Item
▪ Parent
▪ Children
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Another Option: Sibling Tree
 Siblings are directly linked
Class SibTreeNode
{
Object
item ;
SibTreeNode
parent ;
SibTreeNode
firstChild;
SibTreeNode
nextSibling;
}
Parent
Item
First Child
Next Sibling
Parent
Item
First Child
First Child
First Child
Next Sibling
Parent
Parent
Parent
Item
Item
Item
Next Sibling
First Child
Next Sibling
First Child
Next Sibling
Parent
Parent
Parent
Parent
Item
Item
Item
Item
Next Sibling
First Child
Next Sibling
First Child
Next Sibling
First Child
Next Sibling
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Rooted Tree
 Preorder Traversal
 Postorder Traversal
 Level Order Traversal
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Binary Tree
 Inorder Traveral
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Visit each node before recursively visiting its
children, left to right
A
A
A’s First Child
B
D
E
B
C
F
G
B’s First Child
D
H
B has no child, no sibling
A has no child, then sibling
C
C’s First Child
G
D has no child, then sibling G has no child, then sibling
E
H
E has no child, then sibling H has no child, no sibling
F
F has no child, no sibling
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Preorder Traversal Realization by Recursion
Class SibTreeNode {
public void preorder() {
this.visit();
if(firstChild!=null){
firstChild.preorder();
}
if(nextSibling!=null){
nextSibling.preorder();
}
}
}
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Preorder Traversal Realization by Stacks
Stack:
A
B
C
D
E
D
E
F
G
G
B
F
H
H
A
C
Visiting Sequence:
A
B
D
E
F
C
G
H
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Visit each node’s children (left-to-right)
before the node itself
A
B
D
E
C
F
G
H
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Postorder Traversal Realization by Recursion
Class SibTreeNode {
public void postorder() {
if(firstChild!=null) {
firstChild.postorder();
}
this.visit();
if(nextSibling!=null) {
nextSibling.postorder();
}
}
}
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Visit root, then all (height-1) nodes, then all
(height-2) nodes, … etc.
A
B
D
E
C
F
G
H
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Level Order Traversal Realization by Queues
Queue:
A
B
H
C
G
F
D
E
F
G
H
E
D
C
B
Visiting Sequence:
A
B
C
D
E
F
G
H
A
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A Binary Tree
 No node has > 2 children
 Every child is either left child or a right child, even
if it is the only child
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Binary Tree Node
Class BiTreeNode
{
Object
item ;
BiTreeNode
parent ;
BiTreeNode
leftChild;
BiTreeNode
rightChild;
}
Parent
Item
Left Child
Right Child
Parent
Item
Left Child
Right Child
Parent
Parent
Item
Item
Left Child
Right Child
Left Child
Right Child
Parent
Parent
Parent
Item
Item
Item
Left Child
Right Child
Left Child
Right Child
Left Child
Right Child
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Visit left child, then node, then right child
Class BiTreeNode {
public void inorder() {
if(leftChild!=null){
leftChild.inorder();
}
this.visit();
if(rightChild!=null) {
rightChild.inorder();
}
}
}
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Visualization of inorder traversal
A
B
D
C
E
F