Tree
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A tree is a hierarchical data structure composed of nodes and edges, with specific terminology such as root, parent, and leaf nodes. The document explains binary trees, including binary search trees (BSTs), which allow for efficient insertion, deletion, and searching of nodes based on their values. It outlines the structure and properties of trees and provides algorithms for inserting and searching elements within a BST.
![ If(tree=NULL),then allocate space for node
NEW[data]=NEW
NEW[left]=NEW[right]=NULL
Else IF(data<tree[data]),insert
element(tree(left),data)
Else insert element(tree (right),data)
[End of if statement]
[End of if statement]
Exit](https://image.slidesharecdn.com/tree-170708003329/85/Tree-9-320.jpg)
![•Searchelement(tree,val)
•If(tree=NULL),then
•Write:Tree is empty
•If(tree[data]=val),then
•Write:search is successful
•Else
•If(val<tree[data]),then
•Searchelement(tree[left],val)
•Else( (searchelement (tree[right],val).
•[End of if statement]
•[End of if statement]
•Exit](https://image.slidesharecdn.com/tree-170708003329/85/Tree-11-320.jpg)
Tree
- 2. A tree is a (possibly non-linear) data structure made up of nodes or vertices and edges without having any cycle. The tree with no nodes is called the null or empty tree. A tree that is not empty consists of a root node and potentially many levels of additional nodes that form a hierarchy.
- 3. Root – The top node in a tree. Parent – The converse notion of child. Siblings – Nodes with the same parent. Leaf – a node with no children. Degree – number of sub trees of a node. Edge – connection between one node to another. Height of tree –The height of a tree is the number of edges on the longest downward path between the root and a leaf. Height of node –The height of a node is the number of edges on the longest downward path between that node and a leaf. Depth –The depth of a node is the number of edges from the node to the tree's root node.
- 4. The simplest form of tree is a binary tree. A binary tree consists of a node called the root node and left and right sub-trees. Both the sub-trees are themselves binary trees .A binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child
- 6. •Root Node:-Node at the "top" of a tree - the one from which all operations on the tree commence. The root node may not exist or have 0, 1 or 2 children in a binary tree. •Leaf Node:-Node at the "bottom" of a tree - farthest from the root. Leaf nodes have no children. •Complete Tree:-Tree in which each leaf is at the same distance from the root. •Height:-Number of nodes which must be traversed from the root to reach a leaf of a tree.
- 7. Binary search trees (BST) are also known as sorted binary trees, on which we can implement “deletion, searching and inserting operation. They store data items, known as nodes, and allow fast insertion and deletion of such nodes, as well as checking whether a node is present in a tree. A binary search tree is a node- based binary tree data structure where root node has a comparable node and if node is larger than the root node then it goes to right sub-tree and smaller than the root node then the node's goes to left sub-tree
- 8. •Check whether root node is present or not(tree available or not). If root is NULL, create root node. •If the element to be inserted is less than the element present in the root node , traverse the left sub-tree recursively. •If the element to be inserted is greater than the element present in root node , traverse the right sub-tree recursively.
- 9. If(tree=NULL),then allocate space for node NEW[data]=NEW NEW[left]=NEW[right]=NULL Else IF(data<tree[data]),insert element(tree(left),data) Else insert element(tree (right),data) [End of if statement] [End of if statement] Exit
- 10. Check whether node to be searched is greater then or smaller then then the root node and the perform following steps. If the element to be searched is less than the element present in the root node , traverse the left sub-tree recursively. If the element to be searched is greater than the element present in root node , traverse the right sub-tree recursively.
- 11. •Searchelement(tree,val) •If(tree=NULL),then •Write:Tree is empty •If(tree[data]=val),then •Write:search is successful •Else •If(val<tree[data]),then •Searchelement(tree[left],val) •Else( (searchelement (tree[right],val). •[End of if statement] •[End of if statement] •Exit