Trees
Download as PPTX, PDF0 likes952 views
Trees are hierarchical data structures composed of nodes connected by edges. A tree has a root node with child nodes below it. Leaf nodes have no children, while internal nodes have children. Binary trees restrict nodes to having 0, 1, or 2 children. Binary search trees organize nodes so that all left descendants of a node are less than or equal to the node and all right descendants are greater than or equal. Common tree operations include insertion, searching, and deletion.
Trees
- 1. Trees
- 2. Introduction Is a non linear data structure. Is a hierarchical data structure. Is a finite set of nodes. Contains a special node called root node. All nodes are connecting through an edge.
- 4. Terminologies… Degree of a Node Means number of child nodes a node have. Leaf Nodes that have no child nodes. Terminal Nodes Leaf nodes are also called terminal nodes.
- 5. Degree of a tree Maximum degree of tree is called degree of tree. Ancestors All the parent nodes of a node till rood node path called its ancestors. Descendants All the child nodes of a node till leaf node path called its ancestors.
- 6. Generation All nodes with same level called a generation. Height/Depth Number of levels / Generations . Edge Connecting lines that are used to connect nodes.
- 7. Path sequence of consective edges from 1 node to other node. Branch if a path ends at leaf nodes called branch.
- 8. How to construct tree data structure. We can construct it using Linked List.
- 9. Binary Tree A tree having a property that all nodes should have minimum 0 nodes or maximum 2 nodes. >=0 nodes <=2. If 0 nodes called empty tree/null tree.
- 11. Types 1: Full BT - a tree in which each level is filled completely. - non leaf nodes should have left as well as right child's. - all the leaf nodes should be at same level.
- 13. 2: Complete Binary tree each node must have 2 child's (left and right as well) except leaf nodes. 3: Incomplete binary tree tree may violate the property of complete binary tree.
- 15. Almost complete binary tree A tree having all leaf nodes at last or second last level called almost complete binary tree.
- 16. Binary Search Tree A binary tree in which minimum value is placed at the left side of node and maximum value at right side of node.
- 17. Operations Insertion Searching Deletion
- 18. Insertion in BST Place first at root node. Now compare each node value to decide whether your coming value will be placed at right or left side of node. Takes O(n) in worst case Takes Big-Theta (log n) in average case.
- 19. Searching Compare the target value by moving from one node to other starting from root node. Move left if targeted value is smaller than node value else move right. Takes O(n) in worst case Takes Big-Theta (log n) in average case.
- 20. Deletion Cases If the node is leaf If node in non-leaf and have 1 child node. If node is non-leaf and have 2 child nodes.
- 21. If the node is leaf Delete that node and make its father node pointing to Null. Left pointer in case of left leaf Right pointer in case of right leaf
- 22. If node is non-leaf and having 1 child node. If deleted node is right child of its parent Delete the node. If have right child or Left Child Make it the Right child of deleted node’s parent.
- 23. If deleted node is left child of its parent Delete the node. If have right child or Left Child Make it the left child of deleted node’s parent.