Binary Tree

In this tutorial, you will learn about binary tree and their various types. Likewise, you will discover working instances of binary trees in C, C++, Java, and Python.

In this article, you will learn-

1 Introduction To Binary Trees
2 Types of Binary Trees
3 Skewed Binary Tree
4 Balanced Binary Tree
5 Binary Tree Representation
6 Python, Java and C/C++ Examples
7 Binary Tree Applications

Introduction To Binary Trees

A binary tree is a hierarchical data structure in which every node has all things considered two children for the most part alluded as left child and right child.

Every node contains three components:

Pointer to left subtree
Pointer to right subtree
Data component

The topmost node in the tree is known as the root. A vacant tree is represented by NULL pointer.

A binary tree is a tree data structure in which each parent node can have at most two children. For instance,

Types of Binary Trees

Full Binary Tree

A full Binary tree is a special type of binary tree where each parent node/internal node has either two or no children.

Perfect Binary Tree

A perfect binary tree is a sort of binary tree wherein each inward node has precisely two child nodes and all the leaf nodes are at a similar level.

Complete Binary Tree

A complete binary tree is much the same as a full binary tree, yet with two significant contrasts

Each level should be totally filled
All the leaf elements should lean towards the left.
The last leaf element probably won’t have a correct sibling for example a complete binary tree doesn’t need to be a full binary tree.

Degenerate or Pathological Tree

A degenerate or pathological tree is the tree having a single child either left or right.

Skewed Binary Tree

A skewed binary tree is a pathological/degenerate tree in which the tree is either overwhelmed by the left nodes or the right nodes. In this manner, there are two types of skewed binary tree: left-skewed binary tree and right-skewed binary tree.

Balanced Binary Tree

It is a sort of binary tree wherein the distinction between the left and the right subtree for every node is either 0 or 1.

Binary Tree Representation

A node of a binary tree is represented by a structure containing a data part and two pointers to different structures of a similar sort.

struct node
{
 int data;
 struct node *left;
 struct node *right;
};

Python, Java and C/C++ Examples

Python

# Binary Tree in Python

class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key

    # Traverse preorder
    def traversePreOrder(self):
        print(self.val, end=' ')
        if self.left:
            self.left.traversePreOrder()
        if self.right:
            self.right.traversePreOrder()

    # Traverse inorder
    def traverseInOrder(self):
        if self.left:
            self.left.traverseInOrder()
        print(self.val, end=' ')
        if self.right:
            self.right.traverseInOrder()

    # Traverse postorder
    def traversePostOrder(self):
        if self.left:
            self.left.traversePostOrder()
        if self.right:
            self.right.traversePostOrder()
        print(self.val, end=' ')


root = Node(1)

root.left = Node(2)
root.right = Node(3)

root.left.left = Node(4)

print("Pre order Traversal: ", end="")
root.traversePreOrder()
print("\nIn order Traversal: ", end="")
root.traverseInOrder()
print("\nPost order Traversal: ", end="")
root.traversePostOrder()

Java

// Binary Tree in Java

// Node creation
class Node {
  int key;
  Node left, right;

  public Node(int item) {
  key = item;
  left = right = null;
  }
}

class BinaryTree {
  Node root;

  BinaryTree(int key) {
  root = new Node(key);
  }

  BinaryTree() {
  root = null;
  }

  // Traverse Inorder
  public void traverseInOrder(Node node) {
  if (node != null) {
    traverseInOrder(node.left);
    System.out.print(" " + node.key);
    traverseInOrder(node.right);
  }
  }

  // Traverse Postorder
  public void traversePostOrder(Node node) {
  if (node != null) {
    traversePostOrder(node.left);
    traversePostOrder(node.right);
    System.out.print(" " + node.key);
  }
  }

  // Traverse Preorder
  public void traversePreOrder(Node node) {
  if (node != null) {
    System.out.print(" " + node.key);
    traversePreOrder(node.left);
    traversePreOrder(node.right);
  }
  }

  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);

  System.out.print("Pre order Traversal: ");
  tree.traversePreOrder(tree.root);
  System.out.print("\nIn order Traversal: ");
  tree.traverseInOrder(tree.root);
  System.out.print("\nPost order Traversal: ");
  tree.traversePostOrder(tree.root);
  }
}

// Tree traversal in C

#include <stdio.h>
#include <stdlib.h>

struct node {
  int item;
  struct node* left;
  struct node* right;
};

// Inorder traversal
void inorderTraversal(struct node* root) {
  if (root == NULL) return;
  inorderTraversal(root->left);
  printf("%d ->", root->item);
  inorderTraversal(root->right);
}

// Preorder traversal
void preorderTraversal(struct node* root) {
  if (root == NULL) return;
  printf("%d ->", root->item);
  preorderTraversal(root->left);
  preorderTraversal(root->right);
}

// Postorder traversal
void postorderTraversal(struct node* root) {
  if (root == NULL) return;
  postorderTraversal(root->left);
  postorderTraversal(root->right);
  printf("%d ->", root->item);
}

// Create a new Node
struct node* createNode(value) {
  struct node* newNode = malloc(sizeof(struct node));
  newNode->item = value;
  newNode->left = NULL;
  newNode->right = NULL;

  return newNode;
}

// Insert on the left of the node
struct node* insertLeft(struct node* root, int value) {
  root->left = createNode(value);
  return root->left;
}

// Insert on the right of the node
struct node* insertRight(struct node* root, int value) {
  root->right = createNode(value);
  return root->right;
}

int main() {
  struct node* root = createNode(1);
  insertLeft(root, 2);
  insertRight(root, 3);
  insertLeft(root->left, 4);

  printf("Inorder traversal \n");
  inorderTraversal(root);

  printf("\nPreorder traversal \n");
  preorderTraversal(root);

  printf("\nPostorder traversal \n");
  postorderTraversal(root);
}

C++

// Binary Tree in C++

#include <stdlib.h>

#include <iostream>

using namespace std;

struct node {
  int data;
  struct node *left;
  struct node *right;
};

// New node creation
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);
}

// Traverse Preorder
void traversePreOrder(struct node *temp) {
  if (temp != NULL) {
    cout << " " << temp->data;
    traversePreOrder(temp->left);
    traversePreOrder(temp->right);
  }
}

// Traverse Inorder
void traverseInOrder(struct node *temp) {
  if (temp != NULL) {
    traverseInOrder(temp->left);
    cout << " " << temp->data;
    traverseInOrder(temp->right);
  }
}

// Traverse Postorder
void traversePostOrder(struct node *temp) {
  if (temp != NULL) {
    traversePostOrder(temp->left);
    traversePostOrder(temp->right);
    cout << " " << temp->data;
  }
}

int main() {
  struct node *root = newNode(1);
  root->left = newNode(2);
  root->right = newNode(3);
  root->left->left = newNode(4);

  cout << "preorder traversal: ";
  traversePreOrder(root);
  cout << "\nInorder traversal: ";
  traverseInOrder(root);
  cout << "\nPostorder traversal: ";
  traversePostOrder(root);
}

Binary Tree Applications

For easy and quick access to data
In router algorithms
To implement the heap data structure
Syntax tree

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