Depth-First Search (DFS) is a method used to explore all the nodes in a tree by going as deep as possible along each branch before moving to the next one. It starts at the root node and visits every node in the tree.
Depth-First Search (DFS) can be classified into three main types based on the order in which the nodes are visited:
- Pre-order Traversal: Visits the root node first, then recursively explores the left and right subtrees.
- In-order Traversal: Explores the left subtree first, then visits the root, and finally the right subtree.
- Post-order Traversal: Explores the left and right subtrees first, then visits the root node.
Different DFS Traversals of a Tree
1. Inorder Traversal
- Traverse the left subtree, i.e., call Inorder(left-subtree)
- Visit the root
- Traverse the right subtree, i.e., call Inorder(right-subtree)
C++ #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; Node(int data) { this->data = data; left = right = NULL; } }; /* 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); } int main() { struct Node* 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); root->right->right = new Node(6); printInorder(root); return 0; } #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); } 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); root->right->right = newNode(6); printInorder(root); getchar(); return 0; } class Node { int key; Node left, right; public Node(int item) { key = item; left = right = null; } } class GfG { // 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); } // Wrappers over above recursive functions void printInorder() { printInorder(root); } 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); tree.root.right.right = new Node(6); tree.printInorder(); } } 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), # now recur on right child printInorder(root.right) root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.right.right = Node(6) printInorder(root)
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; } } public 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); } 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); tree.root.right.right = new Node(6); tree.printInorder(); } } class Node { constructor(val) { this.key = val; this.left = null; this.right = 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 */ process.stdout.write(node.key + " "); /* now recur on right child */ printInorder(node.right); } var 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); root.right.right = new Node(6); printInorder(root); OutputInorder traversal of binary tree is 4 2 5 1 3
Time Complexity: O(N)
Auxiliary Space: O(log N)
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.
2. Preorder Traversal
- Visit the root
- Traverse the left subtree, i.e., call Preorder(left-subtree)
- Traverse the right subtree, i.e., call Preorder(right-subtree)
C++ #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; Node(int data) { this->data = data; left = right = NULL; } }; /* 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); } int main() { struct Node* 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); root->right->right = new Node(6); printPreorder(root); return 0; } #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); } 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); root->right->right = newNode(6); printPreorder(root); getchar(); return 0; } 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); } // Wrappers over above recursive functions void printPreorder() { printPreorder(root); } // 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); tree.root.left.right = new Node(6); tree.printPreorder(); } } 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), # Then recur on left child printPreorder(root.left) # Finally recur on right child printPreorder(root.right) root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.left.right = Node(6) printPreorder(root)
using System; /* Class containing left and right child of current node and key value*/ public class Node { public int key; public Node left, right; public Node(int item) { key = item; left = right = null; } } public 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); } // Wrappers over above recursive functions void printPreorder() { printPreorder(root); } public static void Main() { 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); tree.root.left.right = new Node(6); tree.printPreorder(); } } // A class that represents an individual node in a // Binary Tree class Node{ constructor(key){ this.left = null this.right = null this.val = key } } // A function to do preorder tree traversal function printPreorder(root){ if(root){ // First print the data of node process.stdout.write(root.val," ") // Then recur on left child printPreorder(root.left) // Finally recur on right child printPreorder(root.right) } } let 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) printPreorder(root) OutputPreorder traversal of binary tree is 1 2 4 5 3
Time Complexity: O(N)
Auxiliary Space: O(log N)
Uses of Preorder Traversal
Preorder traversal is used to create a copy of the tree. Preorder traversal is also used to get prefix expressions of an expression tree.
3. Postorder Traversal
- Traverse the left subtree, i.e., call Postorder(left-subtree)
- Traverse the right subtree, i.e., call Postorder(right-subtree)
- Visit the root
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; Node(int data) { this->data = data; left = right = NULL; } }; /* 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 << " "; } int main() { struct Node* 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); root->right->right = new Node(6); printPostorder(root); return 0; } #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); } 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); root->right->right = newNode(6); printPostorder(root); getchar(); return 0; } // 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 + " "); } // Wrappers over above recursive functions void printPostorder() { printPostorder(root); } 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); tree.root.right.right = new Node(6); tree.printPostorder(); } } # 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), root = Node(1) root.left = Node(2) root.right = Node(3) root.left.left = Node(4) root.left.right = Node(5) root.right.right = Node(6) printPostorder(root)
// C# program for different tree traversals using System; /* Class containing left and right child of current node and key value*/ public class Node { public int key; public Node left, right; public Node(int item) { key = item; left = right = null; } } public 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 + " "); } // Wrappers over above recursive functions void printPostorder() { printPostorder(root); } 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); tree.root.right.right = new Node(6); tree.printPostorder(); } } /* Class containing left and right child of current node and key value*/ class Node { constructor(item) { this.key = item; this.left = this.right = null; } } var root; /* * 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 process.stdout.write(node.key + " "); } 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); root.right.right = new Node(6); printPostorder(root); OutputPostorder traversal of binary tree is 4 5 2 3 1
Time Complexity: O(N)
Auxiliary Space: O(log N)
Uses of Postorder Traversal:
Postorder traversal is used to delete every node of the tree. Postorder traversal is also useful to get the postfix expression of an expression tree
Related Article : Breadth First Traversal.
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