4 - Introduction to Tree, Binary Tree and Expression Tree - 2101702130 - Andrean

Pertemuan ke - 4
20-03-2018

Tree & Binary Tree

Tree Concept

DEGREE of TREE = 3

DEGREE of C = 2

HEIGHT = 3

PARENT of C = A

CHILDREN of  A = B, C, D

SIBILING of F = G

ANCESTOR of F = A, C

DESCENDANT of C = F, G

Node at the top is called as root..

Nodes that do not have children are called leaf.

Nodes that have the same parent are called sibling.

Degree of node is the total sub tree of the node.

Height/Depth is the maximum degree of nodes in a tree.

If there is a line that connects p to q, then p is called the ancestor of q, and q is a descendant of p.

Binary Tree Concept

is a rooted tree data structure in which each node has at most two children.

•Those two children usually distinguished as left child and right child.

•Node which doesn’t have any child is called leaf.

 Type of Binary Tree

•PERFECT binary tree is a binary tree in which every level are at the same depth.A perfect binary tree is a complete binary tree.

•COMPLETE binary tree is a binary tree in which every level, except possibly the last, is completely filled, and all nodes are as far left as possible. 

•SKEWED binary tree is a binary tree in which each node has at most one child.

•BALANCED binary tree is a binary tree in which no leaf is much farther away from the root than any other leaf (different balancing scheme allows different definitions of “much farther”).

Property of Binary Tree

Maximum number of nodes on level k of a binary tree is 2k.

Maximum number of nodes on a binary tree of height h is 2h+1 - 1.

Binary Tree Using Linked List

struct node {

  int data;

  struct node *left;

  struct node *right;

  struct node *parent;

}root=NULL;

Expression Tree Concept

Prefix      : *+ab/-cde

Postfix    : ab+cd-e/*

Infix        : (a+b)*((c-d)/e)

2101702130 - Andrean