Threaded Binary Tree.pptx

Threaded Binary Tree.pptx

• 1.
  Threaded Binary Trees J.Pavan Kumar
• 2.
  Outline • Introduction • Whatis a Threaded Binary tree? • Types of Threaded Binary tree • Advantages of Threaded Binary Tree • Disadvantages of Threaded Binary tree
• 3.
  Introduction • We knowevery node of the binary tree stores the data value of the node and the address pointers of the left and right children. If a node in a binary tree does not have a left or right child or is a leaf node, then the child node’s absence is represented by a null pointer.
• 4.
  • Many nodespresent in this tree hold a NULL value in their left or right child pointer (Denoted by sketched fields). The space occupied by these null values can be used to store some kind of valuable information.
• 5.
  • One possibleway to utilise this space is to have a special pointer that points to nodes higher in the tree (i.e. ancestors). These special pointers are called threads, and the binary tree having such pointers is called a threaded binary tree. • A Threaded Binary Tree is a variant of a normal Binary Tree that facilitates faster tree traversal and does not require a Stack or Recursion. It decreases the memory wastage by setting the null pointers of a leaf node to the in- order predecessor or in-order successor.
• 6.
  What is aThreaded Binary tree? • In a Threaded Binary Tree, the nodes will store the in-order predecessor/successor instead of storing NULL in the left/right child pointers. • So the basic idea of a threaded binary tree is that for the nodes whose right pointer is null, we store the in-order successor of the node (if-exists), and for the nodes whose left pointer is null, we store the in-order predecessor of the node(if- exists). • One thing to note is that the leftmost and the rightmost child pointer of a tree always points to null as their in-order predecessor and successor do not exist.
• 8.
  • Now, wewill check the left pointer of node 9, and if it is NULL, then we modify the reference to the predecessor of the node, which is 6. • Then, we will check for the right pointer, and if it is also NULL, we will point it to the successor node, which is 10. Thus, it will point to 10. • We point to in-order predecessors/successors in left/right pointers using threads (denoted by dotted lines) as shown in the figure above, and that is why it is known as a Threaded Binary Tree. • Since the leftmost pointer of this tree is the left pointer of node value 5 and the rightmost pointer of this tree is the right pointer of node value 20, they both point to NULL.
• 9.
  • The mainidea behind setting such a structure is to make the inorder and preorder traversal of a binary tree faster without using any additional data structure (e.g. auxiliary stack) or memory for its traversal.
• 10.
  Types of ThreadedBinary tree 1. Single-Threaded Binary Tree • In this type, if a node has a right null pointer, then this right pointer is threaded towards the in-order successor’s node if it exists. • Node Structure of Single-Threaded Binary Trees: In threaded binary trees, we need to use extra boolean variables in the node structure. For single-threaded binary trees, we use only the rightThread variable.
• 11.
  struct Node{ intvalue; Node* left; Node* right; bool rightThread; }
• 12.
  • 2. Double-ThreadedBinary Tree • In this type, the left null pointer of a node is made to point towards the in-order predecessor node and the right null pointer is made to point towards the in-order successor node. • Node Structure of Double-Threaded Binary Trees: For the double- threaded binary tree, we use two boolean variables: rightThread and leftThread.
• 13.
  • Here, theleftThread and rightThread boolean variables help us to differentiate whether the left/right pointer stores the in-order predecessor/successor or left child/right child.
• 14.
  • This ishow a Double-Threaded Binary Tree looks like. You can observe here that node value 40 have no left and right child. So, its left pointer points to its in-order predecessor (node value 30) and its right pointer points towards its in-order successor (node value 50). Similarly, the other nodes of this tree with a left/right null pointer refers to their in- order predecessor/successor using threads.
• 15.
  Advantages of ThreadedBinary Tree • No need for stacks or recursion: Unlike binary trees, threaded binary trees do not require a stack or recursion for their traversal. • Optimal memory usage: Another advantage of threaded binary tree data structure is that it decreases memory wastage. In normal binary trees, whenever a node’s left/right pointer is NULL, memory is wasted. But with threaded binary trees, we are overcoming this problem by storing its inorder predecessor/successor. • Time complexity: In-order traversal in a threaded binary tree is fast because we get the next node in O(1) time than a normal binary tree that takes O(Height). But insertion and deletion operations take more time for the threaded binary tree. • Backward traversal: In a double-threaded binary tree, we can even do a backward traversal.
• 16.
  Disadvantages of ThreadedBinary tree • Complicated insertion and deletion: By storing the inorder predecessor/ successor for the node with a null left/right pointer, we make the insertion and deletion of a node more time-consuming and a highly complex process. • Extra memory usage: We use additional memory in the form of rightThread and leftThread variables to distinguish between a thread from an ordinary link. (However, there are more efficient methods to differentiate between a thread and an ordinary link).
• 17.
  Thank You