Tree Traversal Techniques – Data Structure and Algorithm Tutorials
Unlike linear data structures (Array, Linked List, Queues, Stacks, etc) which have only one logical way to traverse them, trees can be traversed in different ways.
A Tree Data Structure can be traversed in following ways:
- Depth First Search or DFS
- Inorder Traversal
- Preorder Traversal
- Postorder Traversal
- Level Order Traversal or Breadth First Search or BFS
- Boundary Traversal
- Diagonal Traversal
Tree Traversals – Data Structure and Algorithm Tutorials
Inorder Traversal:
Algorithm Inorder(tree)
- Traverse the left subtree, i.e., call Inorder(left->subtree)
- Visit the root.
- Traverse the right subtree, i.e., call Inorder(right->subtree)
Uses of Inorder Traversal:
In the case of binary search trees (BST), Inorder traversal gives nodes in non-decreasing order. To get nodes of BST in non-increasing order, a variation of Inorder traversal where Inorder traversal is reversed can be used.
Code implementation of Inorder traversal.
C
// C program for different tree traversals #include <stdio.h> #include <stdlib.h> // A binary tree node has data, pointer to left child // and a pointer to right child struct node { int data; struct node* left; struct node* right; }; // Helper function that allocates a new node with the // given data and NULL left and right pointers. struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } // Given a binary tree, print its nodes in inorder void printInorder( struct node* node) { if (node == NULL) return ; // First recur on left child printInorder(node->left); // Then print the data of node printf ( "%d " , node->data); // Now recur on right child printInorder(node->right); } // Driver code int main() { struct node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call printf ( "Inorder traversal of binary tree is \n" ); printInorder(root); getchar (); return 0; } |
C++
// C++ program for different tree traversals #include <bits/stdc++.h> using namespace std; // A binary tree node has data, pointer to left child // and a pointer to right child struct Node { int data; struct Node *left, *right; }; // Utility function to create a new tree node Node* newNode( int data) { Node* temp = new Node; temp->data = data; temp->left = temp->right = NULL; return temp; } // Given a binary tree, print its nodes in inorder void printInorder( struct Node* node) { if (node == NULL) return ; // First recur on left child printInorder(node->left); // Then print the data of node cout << node->data << " " ; // Now recur on right child printInorder(node->right); } // Driver code int main() { struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call cout << "Inorder traversal of binary tree is \n" ; printInorder(root); return 0; } |
Java
// Java program for different tree traversals // Class containing left and right child of current // node and key value class Node { int key; Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print its nodes in inorder void printInorder(Node node) { if (node == null ) return ; // First recur on left child printInorder(node.left); // Then print the data of node System.out.print(node.key + " " ); // Now recur on right child printInorder(node.right); } // Driver code public static void main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node( 1 ); tree.root.left = new Node( 2 ); tree.root.right = new Node( 3 ); tree.root.left.left = new Node( 4 ); tree.root.left.right = new Node( 5 ); // Function call System.out.println( "Inorder traversal of binary tree is " ); tree.printInorder(tree.root); } } |
Python3
# Python3 program to for tree traversals # A class that represents an individual node in a # Binary Tree class Node: def __init__( self , key): self .left = None self .right = None self .val = key # A function to do inorder tree traversal def printInorder(root): if root: # First recur on left child printInorder(root.left) # Then print the data of node print (root.val, end = " " ), # Now recur on right child printInorder(root.right) # Driver code if __name__ = = "__main__" : root = Node( 1 ) root.left = Node( 2 ) root.right = Node( 3 ) root.left.left = Node( 4 ) root.left.right = Node( 5 ) # Function call print ( "Inorder traversal of binary tree is" ) printInorder(root) |
C#
// C# program for different // tree traversals using System; // Class containing left and right child of // current node and key value class Node { public int key; public Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print // its nodes in inorder void printInorder(Node node) { if (node == null ) return ; // First recur on left child printInorder(node.left); // Then print the data of node Console.Write(node.key + " " ); // Now recur on right child printInorder(node.right); } // Wrappers over above recursive functions void printInorder() { printInorder(root); } // Driver Code static public void Main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node(1); tree.root.left = new Node(2); tree.root.right = new Node(3); tree.root.left.left = new Node(4); tree.root.left.right = new Node(5); // Function call Console.WriteLine( "Inorder traversal " + "of binary tree is " ); tree.printInorder(); } } // This code is contributed by Arnab Kundu |
Javascript
// javascript program for different tree traversals // Class containing left and right child of current // node and key value class Node { constructor(val) { this .key = val; this .left = null ; this .right = null ; } } // Root of Binary Tree var root = null ; // Given a binary tree, print its nodes in inorder function printInorder(node) { if (node == null ) return ; // First recur on left child */ printInorder(node.left); // Then print the data of node console.log(node.key + " " ); // Now recur on right child printInorder(node.right); } // Driver method root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); console.log( "Inorder traversal of binary tree is " ); printInorder(root); // This code is contributed by aashish1995 |
Inorder traversal of binary tree is 4 2 5 1 3
Time Complexity: O(N)
Auxiliary Space: If we don’t consider the size of the stack for function calls then O(1) otherwise O(h) where h is the height of the tree.
Preorder Traversal:
Algorithm Preorder(tree)
- Visit the root.
- Traverse the left subtree, i.e., call Preorder(left->subtree)
- Traverse the right subtree, i.e., call Preorder(right->subtree)
Uses of Preorder:
Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expressions on an expression tree.
Code implementation of Preorder traversal:
C
// C program for different tree traversals #include <stdio.h> #include <stdlib.h> // A binary tree node has data, pointer to left child // and a pointer to right child struct node { int data; struct node* left; struct node* right; }; // Helper function that allocates a new node with the // given data and NULL left and right pointers. struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } // Given a binary tree, print its nodes in preorder void printPreorder( struct node* node) { if (node == NULL) return ; // First print data of node printf ( "%d " , node->data); // Then recur on left subtree printPreorder(node->left); // Now recur on right subtree printPreorder(node->right); } // Driver code int main() { struct node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call printf ( "Preorder traversal of binary tree is \n" ); printPreorder(root); getchar (); return 0; } |
C++
// C++ program for different tree traversals #include <bits/stdc++.h> using namespace std; // A binary tree node has data, pointer to left child // and a pointer to right child struct Node { int data; struct Node *left, *right; }; // Utility function to create a new tree node Node* newNode( int data) { Node* temp = new Node; temp->data = data; temp->left = temp->right = NULL; return temp; } // Given a binary tree, print its nodes in preorder void printPreorder( struct Node* node) { if (node == NULL) return ; // First print data of node cout << node->data << " " ; // Then recur on left subtree printPreorder(node->left); // Now recur on right subtree printPreorder(node->right); } // Driver code int main() { struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call cout << "Preorder traversal of binary tree is \n" ; printPreorder(root); return 0; } |
Java
// Java program for different tree traversals // Class containing left and right child of current // node and key value class Node { int key; Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print its nodes in preorder void printPreorder(Node node) { if (node == null ) return ; // First print data of node System.out.print(node.key + " " ); // Then recur on left subtree printPreorder(node.left); // Now recur on right subtree printPreorder(node.right); } // Driver code public static void main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node( 1 ); tree.root.left = new Node( 2 ); tree.root.right = new Node( 3 ); tree.root.left.left = new Node( 4 ); tree.root.left.right = new Node( 5 ); // Function call System.out.println( "Preorder traversal of binary tree is " ); tree.printPreorder(tree.root); } } |
Python3
# Python3 program to for tree traversals # A class that represents an individual node # in a Binary Tree class Node: def __init__( self , key): self .left = None self .right = None self .val = key # A function to do preorder tree traversal def printPreorder(root): if root: # First print the data of node print (root.val, end = " " ), # Then recur on left child printPreorder(root.left) # Finally recur on right child printPreorder(root.right) # Driver code if __name__ = = "__main__" : root = Node( 1 ) root.left = Node( 2 ) root.right = Node( 3 ) root.left.left = Node( 4 ) root.left.right = Node( 5 ) # Function call print ( "Preorder traversal of binary tree is" ) printPreorder(root) |
C#
// C# program for different // tree traversals using System; // Class containing left and right child of // current node and key value class Node { public int key; public Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print // its nodes in preorder void printPreorder(Node node) { if (node == null ) return ; // First print data of node Console.Write(node.key + " " ); // Then recur on left subtree printPreorder(node.left); // Now recur on right subtree printPreorder(node.right); } // Driver Code static public void Main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node(1); tree.root.left = new Node(2); tree.root.right = new Node(3); tree.root.left.left = new Node(4); tree.root.left.right = new Node(5); // Function call Console.WriteLine( "Preorder traversal " + "of binary tree is " ); tree.printPreorder(tree.root); } } // This code is contributed by Arnab Kundu |
Javascript
// javascript program for different tree traversals // Class containing left and right child of current // node and key value class Node { constructor(val) { this .key = val; this .left = null ; this .right = null ; } } // Root of Binary Tree var root = null ; // Given a binary tree, print its nodes in preorder function printPreorder(node) { if (node == null ) return ; // First print data of node document.write(node.key + " " ); // Then recur on left subtree printPreorder(node.left); // Now recur on right subtree printPreorder(node.right); } // Driver method root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); console.log( "Preorder traversal of binary tree is " ); printPreorder(root); // This code is contributed by aashish1995 |
Preorder traversal of binary tree is 1 2 4 5 3
Time Complexity: O(N)
Auxiliary Space: If we don’t consider the size of the stack for function calls then O(1) otherwise O(h) where h is the height of the tree.
Postorder Traversal:
Algorithm Postorder(tree)
- Traverse the left subtree, i.e., call Postorder(left->subtree)
- Traverse the right subtree, i.e., call Postorder(right->subtree)
- Visit the root
Uses of Postorder:
Postorder traversal is used to delete the tree. Please see the question for the deletion of a tree for details. Postorder traversal is also useful to get the postfix expression of an expression tree
Below is the implementation of the above traversal methods:
C
// C program for different tree traversals #include <stdio.h> #include <stdlib.h> // A binary tree node has data, pointer to left child // and a pointer to right child struct node { int data; struct node* left; struct node* right; }; // Helper function that allocates a new node with the // given data and NULL left and right pointers. struct node* newNode( int data) { struct node* node = ( struct node*) malloc ( sizeof ( struct node)); node->data = data; node->left = NULL; node->right = NULL; return (node); } // Given a binary tree, print its nodes according to the // "bottom-up" postorder traversal. void printPostorder( struct node* node) { if (node == NULL) return ; // First recur on left subtree printPostorder(node->left); // Then recur on right subtree printPostorder(node->right); // Now deal with the node printf ( "%d " , node->data); } // Driver code int main() { struct node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call printf ( "Postorder traversal of binary tree is \n" ); printPostorder(root); getchar (); return 0; } |
C++
// C++ program for different tree traversals #include <bits/stdc++.h> using namespace std; // A binary tree node has data, pointer to left child // and a pointer to right child struct Node { int data; struct Node *left, *right; }; // Utility function to create a new tree node Node* newNode( int data) { Node* temp = new Node; temp->data = data; temp->left = temp->right = NULL; return temp; } // Given a binary tree, print its nodes according to the // "bottom-up" postorder traversal. void printPostorder( struct Node* node) { if (node == NULL) return ; // First recur on left subtree printPostorder(node->left); // Then recur on right subtree printPostorder(node->right); // Now deal with the node cout << node->data << " " ; } // Driver code int main() { struct Node* root = newNode(1); root->left = newNode(2); root->right = newNode(3); root->left->left = newNode(4); root->left->right = newNode(5); // Function call cout << "Postorder traversal of binary tree is \n" ; printPostorder(root); return 0; } |
Java
// Java program for different tree traversals // Class containing left and right child of current // node and key value class Node { int key; Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print its nodes according to the // "bottom-up" postorder traversal. void printPostorder(Node node) { if (node == null ) return ; // First recur on left subtree printPostorder(node.left); // Then recur on right subtree printPostorder(node.right); // Now deal with the node System.out.print(node.key + " " ); } // Driver code public static void main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node( 1 ); tree.root.left = new Node( 2 ); tree.root.right = new Node( 3 ); tree.root.left.left = new Node( 4 ); tree.root.left.right = new Node( 5 ); // Function call System.out.println( "Postorder traversal of binary tree is " ); tree.printPostorder(tree.root); } } |
Python3
# Python3 program to for tree traversals # A class that represents an individual node # in a Binary Tree class Node: def __init__( self , key): self .left = None self .right = None self .val = key # A function to do postorder tree traversal def printPostorder(root): if root: # First recur on left child printPostorder(root.left) # The recur on right child printPostorder(root.right) # Now print the data of node print (root.val, end = " " ), # Driver code if __name__ = = "__main__" : root = Node( 1 ) root.left = Node( 2 ) root.right = Node( 3 ) root.left.left = Node( 4 ) root.left.right = Node( 5 ) # Function call print ( "Postorder traversal of binary tree is" ) printPostorder(root) |
C#
// C# program for different // tree traversals using System; // Class containing left and right child // of current node and key value class Node { public int key; public Node left, right; public Node( int item) { key = item; left = right = null ; } } class BinaryTree { // Root of Binary Tree Node root; BinaryTree() { root = null ; } // Given a binary tree, print its nodes according to // the "bottom-up" postorder traversal. void printPostorder(Node node) { if (node == null ) return ; // First recur on left subtree printPostorder(node.left); // Then recur on right subtree printPostorder(node.right); // Now deal with the node Console.Write(node.key + " " ); } // Driver Code static public void Main(String[] args) { BinaryTree tree = new BinaryTree(); tree.root = new Node(1); tree.root.left = new Node(2); tree.root.right = new Node(3); tree.root.left.left = new Node(4); tree.root.left.right = new Node(5); // Function call Console.WriteLine( "Postorder traversal " + "of binary tree is " ); tree.printPostorder(tree.root); } } // This code is contributed by Arnab Kundu |
Javascript
// javascript program for different tree traversals // Class containing left and right child of current // node and key value class Node { constructor(val) { this .key = val; this .left = null ; this .right = null ; } } // Root of Binary Tree var root = null ; // Given a binary tree, print its nodes according // to the "bottom-up" postorder traversal function printPostorder(node) { if (node == null ) return ; // First recur on left subtree printPostorder(node.left); // Then recur on right subtree printPostorder(node.right); // Now deal with the node console.log(node.key + " " ); } // Driver method root = new Node(1); root.left = new Node(2); root.right = new Node(3); root.left.left = new Node(4); root.left.right = new Node(5); console.log( "Postorder traversal of binary tree is " ); printPostorder(root); // This code is contributed by aashish1995 |
Postorder traversal of binary tree is 4 5 2 3 1
Some other Tree Traversals Techniques:
Some of the other tree traversals are:
Level Order Treversal
For each node, first, the node is visited and then it’s child nodes are put in a FIFO queue. Then again the first node is popped out and then it’s child nodes are put in a FIFO queue and repeat until queue becomes empty.
Example:
Input:
Level Order Treversal:
1
2 3
4 5
Boundary Traversal
The Boundary Traversal of a Tree includes:
- left boundary (nodes on left excluding leaf nodes)
- leaves (consist of only the leaf nodes)
- right boundary (nodes on right excluding leaf nodes)
Diagonal Traversal
In the Diagonal Traversal of a Tree, all the nodes in a single diagonal will be printed one by one.
Input :
Diagonal Traversal of binary tree:
8 10 14
3 6 7 13
1 4
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