Tree Traversals: Depth First Search (DFS)

March 9, 2023

Tree Traversals: Depth First Search (DFS)

The term traversal means to visit each node in a tree exactly once. In linear lists the order of traversal is vividly first to last. However, in trees there exists no such natural linear order.In this article, depth first search is studied.

More Information About DFS:

DFS can be defined as an algorithm, based on backtracking, dedicated to traversing a tree structure by first visiting the root first and then the left sub-tree and the right sub-tree.

It is of three types:
- In-order traversal.
- Pre-order traversal.
- Post-order traversal.

Preorder Traversal:

For traversal of a non-empty binary tree or binary search tree in Pre-order, following sequence of operations is performed.

Visit the root node.
Traverse the left sub tree in pre-order.
Traverse the right sub tree in post-order.

Inorder Traversal:

For traversal of a non-empty binary tree or binary search tree in In-order, following sequence of operations is performed.

Traverse the left sub tree in in-order.
Visit the root node.
Traverse the right sub tree in in-order.

Postorder Traversal:

For traversal of a non-empty binary tree or binary search tree in Post-order, following sequence of operations is performed.

Traverse the left sub tree in post-order.
Traverse the right sub tree in post-order.
Visit the root node.

BST: Search in a Binary Search Tree

BST: Insertion in a Binary Search Tree

BST: Deletion in a Binary Search Tree

Traversals in Tree

Tree Traversals: Breadth First Search (DFS)

Code Implementation for Tree Traversal : Depth-First Search (DFS) in C++

Run

#include<bits/stdc++.h>
using namespace std;
class Tree
{
public:
  int data;
  Tree *left = NULL, *right = NULL;
  // Constructor initialised
    Tree (int x)
  {
    data = x;
    left = NULL;
    right = NULL;
  }
};
void preorder_traversal (Tree * root)
{
  if (root == NULL)
    return;
  // Print the data
  cout << root->data << " "; // Visit Left subtree preorder_traversal (root->left);
  // Visit right subtree
  preorder_traversal (root->right);
}

void inorder_traversal (Tree * root)
{
  if (root == NULL)
    return;
  // Visit Left subtree
  inorder_traversal (root->left);
  // Print the data
  cout << root->data << " "; // Visit right subtree inorder_traversal (root->right);
}

void postorder_traversal (Tree * root)
{
  if (root == NULL)
    return;
  // Visit Left subtree
  postorder_traversal (root->left);
  // Visit right subtree
  postorder_traversal (root->right);
  // Print the data
  cout << root->data << " "; } int main () { Tree *root = new Tree (17); root->left = new Tree (10);
  root->right = new Tree (11);
  root->left->left = new Tree (7);
  root->right->left = new Tree (27);
  root->right->right = new Tree (9);
  cout << "Preorder => ";
  preorder_traversal (root);
  cout << endl;
  cout << "Inorder => ";
  inorder_traversal (root);
  cout << endl;
  cout << "Postorder => ";
  postorder_traversal (root);
  cout << endl;
  return 0;
}

Output:

Preorder => 17 10 7 11 27 9 
Inorder => 7 10 17 27 11 9 
Postorder => 7 10 27 9 11 17

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Introduction to Trees

Binary Trees

Binary Tree in Data Structures (Introduction)
Tree Traversals: Inorder Postorder Preorder : C | C++ | Java
Inorder Postorder PreOrder Traversals Examples
- Inorder Tree Traversal in Binary Tree: C | C++ | Java
- Preorder Tree Traversal in Binary Tree : C | C++ | Java
- Postorder Tree Traversal in Binary Tree : C | C++ | Java
Tree Traversal without Recursion
- Postorder Preorder Inorder Traversal without recursion
- Inorder Tree Traversal without Recursion – C | C++ | Java
- Preorder Tree Traversal without Recursion – C | C++ | Java
- Postorder Tree Traversal without Recursion – C | C++ | Java

Binary Search Trees

Binary search tree in Data Structures (Introduction)
- BST: Introduction to Binary Search Tree
- BST: Binary Search Tree Program : C | C++ | Java
- BST: Search a node in Binary Search Tree : C | C++ | Java
- BST: Insertion in a Binary Search Tree : C | C++ | Java
- BST: Deletion in a Binary Search Tree : C | C++ | Java

Traversals

Traversal in Trees
Tree Traversals: Breadth-First Search (BFS) : C | C++ | Java
Tree Traversals: Depth First Search (DFS) : C | C++ | Java
Construct a Binary Tree from Postorder and Inorder

B – Trees

B-Tree
- B-Tree: Introduction
- B-Tree: Insertion : C | C++ | Java
- B-Tree: Deletion : C | C++ | Java

AVL Trees

AVL Trees
- AVL Trees: Introduction
- AVL Tree Insertion : C | C++ | Java
- AVL Tree Deletion : C | C++ | Java
- Insertion in a Binary Tree (Level Order) – C | C++ | Java
- Searching in Binary Tree – C | C++ | Java
- Searching in a Binary Search Tree – C | C++ | Java

Complete Programs for Trees

Depth First Traversals – C | C++ | Java
Level Order Traversal – C | C++ | Java
Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
Construct Tree from given Postorder and Inorder traversals – C | C++ | Java
Construct Tree from given Postorder and Preorder traversal – C | C++ | Java
Find size of the Binary tree – C | C++ | Java
Find the height of binary tree – C | C++ | Java
Find maximum in binary tree – C | C++ | Java
Check whether two tree are identical- C| C++| Java
Spiral Order traversal of Tree- C | C++| Java
Level Order Traversal Line by Line – C | C++| Java
Hand shaking lemma and some Impotant Tree Properties.
Check If binary tree if Foldable or not.- C| C++| Java
check whether tree is Symmetric – C| C++| Java.
Check for Children-Sum in Binary Tree- C|C++| Java
Sum of all nodes in Binary Tree- C | C++ | Java
Lowest Common Ancestor in Binary Tree- C | C++ | Java

Introduction to Trees

Binary Trees

Binary Tree in Data Structures (Introduction)
Tree Traversals: Inorder Postorder Preorder : C | C++ | Java
Inorder Postorder PreOrder Traversals Examples
- Inorder Tree Traversal in Binary Tree: C | C++ | Java
- Preorder Tree Traversal in Binary Tree : C | C++ | Java
- Postorder Tree Traversal in Binary Tree : C | C++ | Java
Tree Traversal without Recursion
- Postorder Preorder Inorder Traversal without recursion
- Inorder Tree Traversal without Recursion – C | C++ | Java
- Preorder Tree Traversal without Recursion – C | C++ | Java
- Postorder Tree Traversal without Recursion – C | C++ | Java

Binary Search Trees

Binary search tree in Data Structures (Introduction)
- BST: Introduction to Binary Search Tree
- BST: Binary Search Tree Program : C | C++ | Java
- BST: Search a node in Binary Search Tree : C | C++ | Java
- BST: Insertion in a Binary Search Tree : C | C++ | Java
- BST: Deletion in a Binary Search Tree : C | C++ | Java

Traversals

Traversal in Trees
Tree Traversals: Breadth-First Search (BFS) : C | C++ | Java
Tree Traversals: Depth First Search (DFS) : C | C++ | Java
Construct a Binary Tree from Postorder and Inorder

B – Trees

B-Tree
- B-Tree: Introduction
- B-Tree: Insertion : C | C++ | Java
- B-Tree: Deletion : C | C++ | Java

AVL Trees

AVL Trees
- AVL Trees: Introduction
- AVL Tree Insertion : C | C++ | Java
- AVL Tree Deletion : C | C++ | Java
- Insertion in a Binary Tree (Level Order) – C | C++ | Java
- Searching in Binary Tree – C | C++ | Java
- Searching in a Binary Search Tree – C | C++ | Java

Complete Programs for Trees

Depth First Traversals – C | C++ | Java
Level Order Traversal – C | C++ | Java
Construct Tree from given Inorder and Preorder traversals – C | C++ | Java
Construct Tree from given Postorder and Inorder traversals – C | C++ | Java
Construct Tree from given Postorder and Preorder traversal – C | C++ | Java
Find size of the Binary tree – C | C++ | Java
Find the height of binary tree – C | C++ | Java
Find maximum in binary tree – C | C++ | Java
Check whether two tree are identical- C| C++| Java
Spiral Order traversal of Tree- C | C++| Java
Level Order Traversal LIne by Line – C | C++| Java
Hand shaking lemma and some Impotant Tree Properties.
Check If binary tree if Foldable or not.- C| C++| Java
check whether tree is Symmetric C| C++| Java.
Check for Children-Sum in Binary Tree- C|C++| Java
Sum of all nodes in Binary Tree- C | C++ | Java
Lowest Common Ancestor in Binary Tree. C | C++ | Java

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Tree Traversals: Depth First Search (DFS)