Boundary Traversal of binary tree
Given a binary tree, print boundary nodes of the binary tree Anti-Clockwise starting from the root. The boundary includes left boundary, leaves, and right boundary in order without duplicate nodes. (The values of the nodes may still be duplicates.)
The left boundary is defined as the path from the root to the left-most node. The right boundary is defined as the path from the root to the right-most node. If the root doesn’t have left subtree or right subtree, then the root itself is left boundary or right boundary. Note this definition only applies to the input binary tree, and not apply to any subtrees.
The left-most node is defined as a leaf node you could reach when you always firstly travel to the left subtree if it exists. If not, travel to the right subtree. Repeat until you reach a leaf node.
The right-most node is also defined in the same way with left and right exchanged.
For example, boundary traversal of the following tree is “20 8 4 10 14 25 22”
We break the problem in 3 parts:
1. Print the left boundary in top-down manner.
2. Print all leaf nodes from left to right, which can again be sub-divided into two sub-parts:
…..2.1 Print all leaf nodes of left sub-tree from left to right.
…..2.2 Print all leaf nodes of right subtree from left to right.
3. Print the right boundary in bottom-up manner.
We need to take care of one thing that nodes are not printed again. e.g. The left most node is also the leaf node of the tree.
Based on the above cases, below is the implementation:
C++
#include <iostream>using namespace std;/* A binary tree node has data, pointer to left childand a pointer to right child */struct Node { int data; struct Node *left, *right;};// Utility function to create a new tree nodeNode* newNode(int data){ Node* temp = new Node; temp->data = data; temp->left = temp->right = nullptr; return temp;}// A simple function to print leaf nodes of a binary treevoid printLeaves(Node* root){ if (root == nullptr) return; printLeaves(root->left); // Print it if it is a leaf node if (!(root->left) && !(root->right)) cout << root->data << " "; printLeaves(root->right);}// A function to print all left boundary nodes, except a// leaf node. Print the nodes in TOP DOWN mannervoid printBoundaryLeft(Node* root){ if (root == nullptr) return; if (root->left) { // to ensure top down order, print the node // before calling itself for left subtree cout << root->data << " "; printBoundaryLeft(root->left); } else if (root->right) { cout << root->data << " "; printBoundaryLeft(root->right); } // do nothing if it is a leaf node, this way we avoid // duplicates in output}// A function to print all right boundary nodes, except a// leaf node Print the nodes in BOTTOM UP mannervoid printBoundaryRight(Node* root){ if (root == nullptr) return; if (root->right) { // to ensure bottom up order, first call for right // subtree, then print this node printBoundaryRight(root->right); cout << root->data << " "; } else if (root->left) { printBoundaryRight(root->left); cout << root->data << " "; } // do nothing if it is a leaf node, this way we avoid // duplicates in output}// A function to do boundary traversal of a given binary// treevoid printBoundary(Node* root){ if (root == nullptr) return; cout << root->data << " "; // Print the left boundary in top-down manner. printBoundaryLeft(root->left); // Print all leaf nodes printLeaves(root->left); printLeaves(root->right); // Print the right boundary in bottom-up manner printBoundaryRight(root->right);}// Driver program to test above functionsint main(){ // Let us construct the tree given in the above diagram Node* root = newNode(20); root->left = newNode(8); root->left->left = newNode(4); root->left->right = newNode(12); root->left->right->left = newNode(10); root->left->right->right = newNode(14); root->right = newNode(22); root->right->right = newNode(25); printBoundary(root); return 0;}// This code is contributed by Aditya Kumar (adityakumar129) |
C
/* C program for boundary traversal of a binary tree */#include <stdio.h>#include <stdlib.h>/* A binary tree node has data, pointer to left childand a pointer to right child */struct node { int data; struct node *left, *right;};// A simple function to print leaf nodes of a binary treevoid printLeaves(struct node* root){ if (root == NULL) return; printLeaves(root->left); // Print it if it is a leaf node if (!(root->left) && !(root->right)) printf("%d ", root->data); printLeaves(root->right);}// A function to print all left boundary nodes, except a leaf node.// Print the nodes in TOP DOWN mannervoid printBoundaryLeft(struct node* root){ if (root == NULL) return; if (root->left) { // to ensure top down order, print the node // before calling itself for left subtree printf("%d ", root->data); printBoundaryLeft(root->left); } else if (root->right) { printf("%d ", root->data); printBoundaryLeft(root->right); } // do nothing if it is a leaf node, this way we avoid // duplicates in output}// A function to print all right boundary nodes, except a leaf node// Print the nodes in BOTTOM UP mannervoid printBoundaryRight(struct node* root){ if (root == NULL) return; if (root->right) { // to ensure bottom up order, first call for right // subtree, then print this node printBoundaryRight(root->right); printf("%d ", root->data); } else if (root->left) { printBoundaryRight(root->left); printf("%d ", root->data); } // do nothing if it is a leaf node, this way we avoid // duplicates in output}// A function to do boundary traversal of a given binary treevoid printBoundary(struct node* root){ if (root == NULL) return; printf("%d ", root->data); // Print the left boundary in top-down manner. printBoundaryLeft(root->left); // Print all leaf nodes printLeaves(root->left); printLeaves(root->right); // Print the right boundary in bottom-up manner printBoundaryRight(root->right);}// A utility function to create a nodestruct node* newNode(int data){ struct node* temp = (struct node*)malloc(sizeof(struct node)); temp->data = data; temp->left = temp->right = NULL; return temp;}// Driver program to test above functionsint main(){ // Let us construct the tree given in the above diagram struct node* root = newNode(20); root->left = newNode(8); root->left->left = newNode(4); root->left->right = newNode(12); root->left->right->left = newNode(10); root->left->right->right = newNode(14); root->right = newNode(22); root->right->right = newNode(25); printBoundary(root); return 0;}// This code has been contributed by Aditya Kumar (adityakumar129) |
Java
// Java program to print boundary traversal of binary tree/* A binary tree node has data, pointer to left childand a pointer to right child */class Node { int data; Node left, right; Node(int item) { data = item; left = right = null; }}class BinaryTree { Node root; // A simple function to print leaf nodes of a binary tree void printLeaves(Node node) { if (node == null) return; printLeaves(node.left); // Print it if it is a leaf node if (node.left == null && node.right == null) System.out.print(node.data + " "); printLeaves(node.right); } // A function to print all left boundary nodes, except a leaf node. // Print the nodes in TOP DOWN manner void printBoundaryLeft(Node node) { if (node == null) return; if (node.left != null) { // to ensure top down order, print the node // before calling itself for left subtree System.out.print(node.data + " "); printBoundaryLeft(node.left); } else if (node.right != null) { System.out.print(node.data + " "); printBoundaryLeft(node.right); } // do nothing if it is a leaf node, this way we avoid // duplicates in output } // A function to print all right boundary nodes, except a leaf node // Print the nodes in BOTTOM UP manner void printBoundaryRight(Node node) { if (node == null) return; if (node.right != null) { // to ensure bottom up order, first call for right // subtree, then print this node printBoundaryRight(node.right); System.out.print(node.data + " "); } else if (node.left != null) { printBoundaryRight(node.left); System.out.print(node.data + " "); } // do nothing if it is a leaf node, this way we avoid // duplicates in output } // A function to do boundary traversal of a given binary tree void printBoundary(Node node) { if (node == null) return; System.out.print(node.data + " "); // Print the left boundary in top-down manner. printBoundaryLeft(node.left); // Print all leaf nodes printLeaves(node.left); printLeaves(node.right); // Print the right boundary in bottom-up manner printBoundaryRight(node.right); } // Driver program to test above functions public static void main(String args[]) { BinaryTree tree = new BinaryTree(); tree.root = new Node(20); tree.root.left = new Node(8); tree.root.left.left = new Node(4); tree.root.left.right = new Node(12); tree.root.left.right.left = new Node(10); tree.root.left.right.right = new Node(14); tree.root.right = new Node(22); tree.root.right.right = new Node(25); tree.printBoundary(tree.root); }} |
Python3
# Python3 program for binary traversal of binary tree# A binary tree nodeclass Node: # Constructor to create a new node def __init__(self, data): self.data = data self.left = None self.right = None# A simple function to print leaf nodes of a Binary Treedef printLeaves(root): if(root): printLeaves(root.left) # Print it if it is a leaf node if root.left is None and root.right is None: print(root.data), printLeaves(root.right)# A function to print all left boundary nodes, except a # leaf node. Print the nodes in TOP DOWN mannerdef printBoundaryLeft(root): if(root): if (root.left): # to ensure top down order, print the node # before calling itself for left subtree print(root.data) printBoundaryLeft(root.left) elif(root.right): print (root.data) printBoundaryLeft(root.right) # do nothing if it is a leaf node, this way we # avoid duplicates in output# A function to print all right boundary nodes, except# a leaf node. Print the nodes in BOTTOM UP mannerdef printBoundaryRight(root): if(root): if (root.right): # to ensure bottom up order, first call for # right subtree, then print this node printBoundaryRight(root.right) print(root.data) elif(root.left): printBoundaryRight(root.left) print(root.data) # do nothing if it is a leaf node, this way we # avoid duplicates in output# A function to do boundary traversal of a given binary treedef printBoundary(root): if (root): print(root.data) # Print the left boundary in top-down manner printBoundaryLeft(root.left) # Print all leaf nodes printLeaves(root.left) printLeaves(root.right) # Print the right boundary in bottom-up manner printBoundaryRight(root.right)# Driver program to test above functionroot = Node(20)root.left = Node(8)root.left.left = Node(4)root.left.right = Node(12)root.left.right.left = Node(10)root.left.right.right = Node(14)root.right = Node(22)root.right.right = Node(25)printBoundary(root)# This code is contributed by # Nikhil Kumar Singh(nickzuck_007) |
C#
// C# program to print boundary traversal// of binary treeusing System;/* A binary tree node has data, pointer to left child and a pointer to right child */public class Node { public int data; public Node left, right; public Node(int item) { data = item; left = right = null; }}class GFG { public Node root; // A simple function to print leaf // nodes of a binary tree public virtual void printLeaves(Node node) { if (node == null) return; printLeaves(node.left); // Print it if it is a leaf node if (node.left == null && node.right == null) { Console.Write(node.data + " "); } printLeaves(node.right); } // A function to print all left boundary // nodes, except a leaf node. Print the // nodes in TOP DOWN manner public virtual void printBoundaryLeft(Node node) { if (node == null) return; if (node.left != null) { // to ensure top down order, print the node // before calling itself for left subtree Console.Write(node.data + " "); printBoundaryLeft(node.left); } else if (node.right != null) { Console.Write(node.data + " "); printBoundaryLeft(node.right); } // do nothing if it is a leaf node, // this way we avoid duplicates in output } // A function to print all right boundary // nodes, except a leaf node. Print the // nodes in BOTTOM UP manner public virtual void printBoundaryRight(Node node) { if (node == null) return; if (node.right != null) { // to ensure bottom up order, // first call for right subtree, // then print this node printBoundaryRight(node.right); Console.Write(node.data + " "); } else if (node.left != null) { printBoundaryRight(node.left); Console.Write(node.data + " "); } // do nothing if it is a leaf node, // this way we avoid duplicates in output } // A function to do boundary traversal // of a given binary tree public virtual void printBoundary(Node node) { if (node == null) return; Console.Write(node.data + " "); // Print the left boundary in // top-down manner. printBoundaryLeft(node.left); // Print all leaf nodes printLeaves(node.left); printLeaves(node.right); // Print the right boundary in // bottom-up manner printBoundaryRight(node.right); } // Driver Code public static void Main(string[] args) { GFG tree = new GFG(); tree.root = new Node(20); tree.root.left = new Node(8); tree.root.left.left = new Node(4); tree.root.left.right = new Node(12); tree.root.left.right.left = new Node(10); tree.root.left.right.right = new Node(14); tree.root.right = new Node(22); tree.root.right.right = new Node(25); tree.printBoundary(tree.root); }}// This code is contributed by Shrikant13 |
Javascript
<script> // JavaScript program to print boundary // traversal of binary tree class Node { constructor(item) { this.left = null; this.right = null; this.data = item; } } let root; // A simple function to print leaf nodes of a binary tree function printLeaves(node) { if (node == null) return; printLeaves(node.left); // Print it if it is a leaf node if (node.left == null && node.right == null) document.write(node.data + " "); printLeaves(node.right); } // A function to print all left boundary nodes, // except a leaf node. // Print the nodes in TOP DOWN manner function printBoundaryLeft(node) { if (node == null) return; if (node.left != null) { // to ensure top down order, print the node // before calling itself for left subtree document.write(node.data + " "); printBoundaryLeft(node.left); } else if (node.right != null) { document.write(node.data + " "); printBoundaryLeft(node.right); } // do nothing if it is a leaf node, this way we avoid // duplicates in output } // A function to print all right boundary nodes, // except a leaf node // Print the nodes in BOTTOM UP manner function printBoundaryRight(node) { if (node == null) return; if (node.right != null) { // to ensure bottom up order, first call for right // subtree, then print this node printBoundaryRight(node.right); document.write(node.data + " "); } else if (node.left != null) { printBoundaryRight(node.left); document.write(node.data + " "); } // do nothing if it is a leaf node, this way we avoid // duplicates in output } // A function to do boundary traversal of a given binary tree function printBoundary(node) { if (node == null) return; document.write(node.data + " "); // Print the left boundary in top-down manner. printBoundaryLeft(node.left); // Print all leaf nodes printLeaves(node.left); printLeaves(node.right); // Print the right boundary in bottom-up manner printBoundaryRight(node.right); } root = new Node(20); root.left = new Node(8); root.left.left = new Node(4); root.left.right = new Node(12); root.left.right.left = new Node(10); root.left.right.right = new Node(14); root.right = new Node(22); root.right.right = new Node(25); printBoundary(root); </script> |
Output
20 8 4 10 14 25 22
Time Complexity: O(n) where n is the number of nodes in binary tree.
Auxiliary Space: O(n)
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
.png)