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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