Tree What is a TREE Node Edge Path

Tree What is a TREE ? • Node • Edge • Path • Root • Parent • Child • Leaf • Subtree • Level

Tree Binary Tree

Tree • Tree: • Tree generally implemented in the computer using pointers Unbalanced Trees means that : • Most of the nodes are on one side of the root. • Individual subtrees may also be unbalanced.

Binary Tree • Binary Tree: • It is a tree whose nodes have two children (possibly empty), and each child is designed as either a left child or a right child.

Operations on a Binary Tree: 1. 2. 3. 4. 5. Finding node(Binary Search Tree) Inserting node Deleting Node Traversing Finding Minimum and Maximum Values

Operations on a Binary Tree: 1. Finding node : 57

Operations on a Binary Tree: 2. Inserting node : 45

Operations on a Binary Tree: 3. Deleting Node : A- The node to be deleted has no children

Operations on a Binary Tree: 3. Deleting Node : B- The node to be deleted has one child

Operations on a Binary Tree: 3. Deleting Node : C- The node to be deleted has two children

Operations on a Binary Tree: 4. Traversing the Tree: • Visiting each node in a specified order. • Three simple ways to traverse a tree: – Inorder – Preorder – Postorder

Operations on a Binary Tree: Inorder traversal : the left child is recursively visited, the node is visited, and the right child is recursively visited. Steps involved in Inorder traversal (recursion) are: 1. Call itself to traverse the node’s left subtree 2. Visit the node (e. g. display a key) 3 Call itself to traverse the node’s right subtree. Void in. Order(Node* p. Root) { If (p. Root!= null) { in. Order(p. Root->left. Child); cout<< p. Root->Data<<“ “; in. Order(p. Root->right. Child); } }

Operations on a Binary Tree: Preorder traversal: a node is visited and then its children are visited recursively. Sequence of preorder traversal: -- Visit the node -- Call itself to traverse the node’s left subtree -- Call itself to traverse the node’s right subtree. Void preorder (Node* p. Root) { If (p. Root!= null) { cout<< p. Root->Data<<“ “; preorder (p. Root->left. Child); preorder (p. Root->right. Child); } }

Operations on a Binary Tree: Postorder traversal : a node is visited after both children are visited. Sequence of postorder traversal: -- Call itself to traverse the node’s left subtree -- Call itself to traverse the node’s right subtree -- Visit the node. Void Postorder (Node* p. Root) { If (p. Root!= null) { Postorder (p. Root->left. Child); Postorder (p. Root->right. Child); cout<< p. Root->Data<<“ “; } }

Binary Search Tree 5. Finding Minimum Values :

Binary Search Tree 6. Finding Maximum Values :

Representing the Tree in C++ Code The Node Class class Node { public: int day; float temp; Node* p. Leftchild; Node* p. Rightchild; //constructor Node(int d, float t) {day = d; temp = t; p. Leftchild = NULL; p. Rightchild = NULL; } //display the data as: {1, 5. 76} void displaynode() {cout<<'{'<<day<<', '<<temp<<'}'; } }; //end class node

Representing the Tree in C++ Code The Tree Class class Tree { private: Node* p. Root; public: //constructor Tree(){p. Root=NULL; }

Inserting node in C++ code //insert node void insert(int d, float t) {Node* p. Newnode=new Node(d, t); if (p. Root==NULL) p. Root=p. Newnode; else { Node* p. Current=p. Root; Node* p. Parent; while (true) {p. Parent=p. Current; if(d<p. Current->day) { p. Current=p. Current->p. Leftchild; if(p. Current==NULL) {p. Parent->p. Leftchild=p. Newnode; return; } } else {p. Current=p. Current->p. Rightchild; if(p. Current==NULL) {p. Parent->p. Rightchild=p. Newnode; return; } } }

Finding node in C++ Node* find(int key) { Node* p. Current=p. Root; while(p. Current->day!=key) { if(key<p. Current->day) p. Current=p. Current->p. Leftchild; else p. Current=p. Current->p. Rightchild; if(p. Current==NULL) return NULL; } return p. Current; }

Finding Minimum Value in c++ : Node* minimum() { Node* p. Current=p. Root; Node* p. Last; while(p. Current!=NULL) { p. Last=p. Current; p. Current=p. Current>p. Leftchild; } return p. Last; }

Finding Maximum Value in c++ : Node* maximum() { Node* p. Current=p. Root; Node* p. Last; while(p. Current!=NULL) { p. Last=p. Current; p. Current=p. Current>p. Rightchild; } return p. Last; }

Finding sum in c++ : void sum 1(float &s ) {sum(s, p. Root); } void sum(float &s, Node* plocat. Root) { if(plocat. Root!=NULL) {s=s+plocat. Root->temp; sum(s, plocat. Root->p. Leftchild); sum(s, plocat. Root->p. Rightchild); } }

Finding count in c++ : void count (int &c ) {count 1(c, p. Root); } void count 1(int &conut, Node* plocat. Root) { if(plocat. Root!=NULL) {conut++; count 1(conut, plocat. Root->p. Leftchild); count 1(conut, plocat. Root->p. Rightchild); } } };

void main(){ Tree tree 1; int n; cin>>n; int day 1; float temp 1; for(int i=1; i<=n; i++) { cin>>day 1>>temp 1; tree 1. insert(day 1, temp 1); } //Finding a node with a given key cout<<"n Enter day number to search about: "; int findkey; cin>>findkey; Node* pfind=tree 1. find(findkey); if(pfind!=NULL) { cout<<"n found node with key"<< findkey<<""; pfind->displaynode(); } else cout<<"can not find node"<<endl;

//minimum & maximum value Node*min=tree 1. minimum(); Node*max=tree 1. maximum(); cout<<"nthe Minimum value int the tree is: "<<min->day; cout<<"nthe maximum value int the tree is: "<<max->day; cout<<endl; float sum=0; tree 1. sum_temp(sum); cout<<"the sum of tempretures: "<<sum<<endl; int count=0; tree 1. count_day(count); cout<<"the count of day: "<<count<<endl; }

Evolution questions Answer the following questions for the tree shown below. • What is the path length of the path from node 20 to node 12? • Which node is the parent of node 35? • Draw the sub-tree rooted at node 43. • Traverse the tree in Preorder, Inorder and postorder. • Show what would this tree look like after: • Deleting 11 • Deleting 18