Convert a Binary Tree to Threaded binary tree | Set 2 (Efficient)
Idea of Threaded Binary Tree is to make inorder traversal faster and do it without stack and without recursion. In a simple threaded binary tree, the NULL right pointers are used to store inorder successor. Where-ever a right pointer is NULL, it is used to store inorder successor.
Following diagram shows an example Single Threaded Binary Tree. The dotted lines represent threads.
Following is structure of a single-threaded binary tree.
struct Node { int key; Node *left, *right; // Used to indicate whether the right pointer is a normal right // pointer or a pointer to inorder successor. bool isThreaded; }; |
How to convert a Given Binary Tree to Threaded Binary Tree?
We have discussed a Queue-based solution here. In this post, space-efficient solution is discussed that doesn’t require a queue.
The idea is based on the fact that we link from inorder predecessor to a node. We link those inorder predecessor which lie in subtree of node. So we find inorder predecessor of a node if its left is not NULL. Inorder predecessor of a node (whose left is NULL) is a rightmost node in the left child. Once we find the predecessor, we link a thread from it to the current node.
Following is the implementation of the above idea.
C++
/* C++ program to convert a Binary Tree to Threaded Tree */#include <bits/stdc++.h> using namespace std; /* Structure of a node in threaded binary tree */struct Node { int key; Node *left, *right; // Used to indicate whether the right pointer // is a normal right pointer or a pointer // to inorder successor. bool isThreaded; }; // Converts tree with given root to threaded // binary tree. // This function returns rightmost child of // root. Node *createThreaded(Node *root) { // Base cases : Tree is empty or has single // node if (root == NULL) return NULL; if (root->left == NULL && root->right == NULL) return root; // Find predecessor if it exists if (root->left != NULL) { // Find predecessor of root (Rightmost // child in left subtree) Node* l = createThreaded(root->left); // Link a thread from predecessor to // root. l->right = root; l->isThreaded = true; } // If current node is rightmost child if (root->right == NULL) return root; // Recur for right subtree. return createThreaded(root->right); } // A utility function to find leftmost node // in a binary tree rooted with 'root'. // This function is used in inOrder() Node *leftMost(Node *root) { while (root != NULL && root->left != NULL) root = root->left; return root; } // Function to do inorder traversal of a threadded // binary tree void inOrder(Node *root) { if (root == NULL) return; // Find the leftmost node in Binary Tree Node *cur = leftMost(root); while (cur != NULL) { cout << cur->key << " "; // If this Node is a thread Node, then go to // inorder successor if (cur->isThreaded) cur = cur->right; else // Else go to the leftmost child in right subtree cur = leftMost(cur->right); } } // A utility function to create a new node Node *newNode(int key) { Node *temp = new Node; temp->left = temp->right = NULL; temp->key = key; return temp; } // Driver program to test above functions int main() { /* 1 / \ 2 3 / \ / \ 4 5 6 7 */ Node *root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); root->right->left = newNode(6); root->right->right = newNode(7); createThreaded(root); cout << "Inorder traversal of created " "threaded tree is\n"; inOrder(root); return 0; } |
Java
/* Java program to convert a Binary Tree to Threaded Tree */import java.util.*; class solution { /* structure of a node in threaded binary tree */static class Node { int key; Node left, right; // Used to indicate whether the right pointer // is a normal right pointer or a pointer // to inorder successor. boolean isThreaded; }; // Converts tree with given root to threaded // binary tree. // This function returns rightmost child of // root. static Node createThreaded(Node root) { // Base cases : Tree is empty or has single // node if (root == null) return null; if (root.left == null && root.right == null) return root; // Find predecessor if it exists if (root.left != null) { // Find predecessor of root (Rightmost // child in left subtree) Node l = createThreaded(root.left); // Link a thread from predecessor to // root. l.right = root; l.isThreaded = true; } // If current node is rightmost child if (root.right == null) return root; // Recur for right subtree. return createThreaded(root.right); } // A utility function to find leftmost node // in a binary tree rooted with 'root'. // This function is used in inOrder() static Node leftMost(Node root) { while (root != null && root.left != null) root = root.left; return root; } // Function to do inorder traversal of a threadded // binary tree static void inOrder(Node root) { if (root == null) return; // Find the leftmost node in Binary Tree Node cur = leftMost(root); while (cur != null) { System.out.print(cur.key + " "); // If this Node is a thread Node, then go to // inorder successor if (cur.isThreaded) cur = cur.right; else // Else go to the leftmost child in right subtree cur = leftMost(cur.right); } } // A utility function to create a new node static Node newNode(int key) { Node temp = new Node(); temp.left = temp.right = null; temp.key = key; return temp; } // Driver program to test above functions public static void main(String args[]) { /* 1 / \ 2 3 / \ / \ 4 5 6 7 */ Node root = newNode(1); root.left = newNode(2); root.right = newNode(3); root.left.left = newNode(4); root.left.right = newNode(5); root.right.left = newNode(6); root.right.right = newNode(7); createThreaded(root); System.out.println("Inorder traversal of created "+"threaded tree is\n"); inOrder(root); } } //contributed by Arnab Kundu |
Python3
# Python3 program to convert a Binary Tree to # Threaded Tree # A utility function to create a new node class newNode: def __init__(self, key): self.left = self.right = None self.key = key self.isThreaded = None # Converts tree with given root to threaded # binary tree. # This function returns rightmost child of # root. def createThreaded(root): # Base cases : Tree is empty or has # single node if root == None: return None if root.left == None and root.right == None: return root # Find predecessor if it exists if root.left != None: # Find predecessor of root (Rightmost # child in left subtree) l = createThreaded(root.left) # Link a thread from predecessor # to root. l.right = root l.isThreaded = True # If current node is rightmost child if root.right == None: return root # Recur for right subtree. return createThreaded(root.right) # A utility function to find leftmost node # in a binary tree rooted with 'root'. # This function is used in inOrder() def leftMost(root): while root != None and root.left != None: root = root.left return root # Function to do inorder traversal of a # threaded binary tree def inOrder(root): if root == None: return # Find the leftmost node in Binary Tree cur = leftMost(root) while cur != None: print(cur.key, end = " ") # If this Node is a thread Node, then # go to inorder successor if cur.isThreaded: cur = cur.right else: # Else go to the leftmost child # in right subtree cur = leftMost(cur.right) # Driver Code if __name__ == '__main__': # 1 # / \ # 2 3 # / \ / \ # 4 5 6 7 root = newNode(1) root.left = newNode(2) root.right = newNode(3) root.left.left = newNode(4) root.left.right = newNode(5) root.right.left = newNode(6) root.right.right = newNode(7) createThreaded(root) print("Inorder traversal of created", "threaded tree is") inOrder(root) # This code is contributed by PranchalK |
C#
using System; /* C# program to convert a Binary Tree to Threaded Tree */public class solution { /* structure of a node in threaded binary tree */public class Node { public int key; public Node left, right; // Used to indicate whether the right pointer // is a normal right pointer or a pointer // to inorder successor. public bool isThreaded; } // Converts tree with given root to threaded // binary tree. // This function returns rightmost child of // root. public static Node createThreaded(Node root) { // Base cases : Tree is empty or has single // node if (root == null) { return null; } if (root.left == null && root.right == null) { return root; } // Find predecessor if it exists if (root.left != null) { // Find predecessor of root (Rightmost // child in left subtree) Node l = createThreaded(root.left); // Link a thread from predecessor to // root. l.right = root; l.isThreaded = true; } // If current node is rightmost child if (root.right == null) { return root; } // Recur for right subtree. return createThreaded(root.right); } // A utility function to find leftmost node // in a binary tree rooted with 'root'. // This function is used in inOrder() public static Node leftMost(Node root) { while (root != null && root.left != null) { root = root.left; } return root; } // Function to do inorder traversal of a threadded // binary tree public static void inOrder(Node root) { if (root == null) { return; } // Find the leftmost node in Binary Tree Node cur = leftMost(root); while (cur != null) { Console.Write(cur.key + " "); // If this Node is a thread Node, then go to // inorder successor if (cur.isThreaded) { cur = cur.right; } else // Else go to the leftmost child in right subtree { cur = leftMost(cur.right); } } } // A utility function to create a new node public static Node newNode(int key) { Node temp = new Node(); temp.left = temp.right = null; temp.key = key; return temp; } // Driver program to test above functions public static void Main(string[] args) { /* 1 / \ 2 3 / \ / \ 4 5 6 7 */ Node root = newNode(1); root.left = newNode(2); root.right = newNode(3); root.left.left = newNode(4); root.left.right = newNode(5); root.right.left = newNode(6); root.right.right = newNode(7); createThreaded(root); Console.WriteLine("Inorder traversal of created " + "threaded tree is\n"); inOrder(root); } } // This code is contributed by Shrikant13 |
Output:
Inorder traversal of created threaded tree is 4 2 5 1 6 3 7
This algorithm works in O(n) time complexity and O(1) space other than function call stack.
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