Binary Tree | Set 1 (Introduction)
Trees: Unlike Arrays, Linked Lists, Stack and queues, which are linear data structures, trees are hierarchical data structures.
Tree Vocabulary: The topmost node is called root of the tree. The elements that are directly under an element are called its children. The element directly above something is called its parent. For example, ‘a’ is a child of ‘f’, and ‘f’ is the parent of ‘a’. Finally, elements with no children are called leaves.
tree
----
j <-- root
/ \
f k
/ \ \
a h z <-- leaves
Why Trees?
1. One reason to use trees might be because you want to store information that naturally forms a hierarchy. For example, the file system on a computer:
file system
-----------
/ <-- root
/ \
... home
/ \
ugrad course
/ / | \
... cs101 cs112 cs113
2. Trees (with some ordering e.g., BST) provide moderate access/search (quicker than Linked List and slower than arrays).
3. Trees provide moderate insertion/deletion (quicker than Arrays and slower than Unordered Linked Lists).
4. Like Linked Lists and unlike Arrays, Trees don’t have an upper limit on number of nodes as nodes are linked using pointers.
Main applications of trees include:
1. Manipulate hierarchical data.
2. Make information easy to search (see tree traversal).
3. Manipulate sorted lists of data.
4. As a workflow for compositing digital images for visual effects.
5. Router algorithms
6. Form of a multi-stage decision-making (see business chess).
Binary Tree: A tree whose elements have at most 2 children is called a binary tree. Since each element in a binary tree can have only 2 children, we typically name them the left and right child.
Binary Tree Representation in C: A tree is represented by a pointer to the topmost node in tree. If the tree is empty, then value of root is NULL.
A Tree node contains following parts.
1. Data
2. Pointer to left child
3. Pointer to right child
In C, we can represent a tree node using structures. Below is an example of a tree node with an integer data.
C
struct node { int data; struct node *left; struct node *right; }; |
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Python
# A Python 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 |
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Java
/* 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; } } |
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C#
/* 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; } } |
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First Simple Tree in C
Let us create a simple tree with 4 nodes in C. The created tree would be as following.
tree
----
1 <-- root
/ \
2 3
/
4
C
struct node { int data; struct node *left; struct node *right; }; /* newNode() allocates a new node with the given data and NULL left and right pointers. */struct node* newNode(int data) { // Allocate memory for new node struct node* node = (struct node*)malloc(sizeof(struct node)); // Assign data to this node node->data = data; // Initialize left and right children as NULL node->left = NULL; node->right = NULL; return(node); } int main() { /*create root*/ struct node *root = newNode(1); /* following is the tree after above statement 1 / \ NULL NULL */ root->left = newNode(2); root->right = newNode(3); /* 2 and 3 become left and right children of 1 1 / \ 2 3 / \ / \ NULL NULL NULL NULL */ root->left->left = newNode(4); /* 4 becomes left child of 2 1 / \ 2 3 / \ / \ 4 NULL NULL NULL / \ NULL NULL */ getchar(); return 0; } |
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Python
# Python program to introduce Binary Tree # 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 # create root root = Node(1) ''' following is the tree after above statement 1 / \ None None''' root.left = Node(2); root.right = Node(3); ''' 2 and 3 become left and right children of 1 1 / \ 2 3 / \ / \ None None None None''' root.left.left = Node(4); '''4 becomes left child of 2 1 / \ 2 3 / \ / \ 4 None None None / \ None None''' |
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Java
/* 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; } } // A Java program to introduce Binary Tree class BinaryTree { // Root of Binary Tree Node root; // Constructors BinaryTree(int key) { root = new Node(key); } BinaryTree() { root = null; } public static void main(String[] args) { BinaryTree tree = new BinaryTree(); /*create root*/ tree.root = new Node(1); /* following is the tree after above statement 1 / \ null null */ tree.root.left = new Node(2); tree.root.right = new Node(3); /* 2 and 3 become left and right children of 1 1 / \ 2 3 / \ / \ null null null null */ tree.root.left.left = new Node(4); /* 4 becomes left child of 2 1 / \ 2 3 / \ / \ 4 null null null / \ null null */ } } |
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C#
// A C# program to introduce Binary Tree 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; // Constructors BinaryTree(int key) { root = new Node(key); } BinaryTree() { root = null; } // Driver Code public static void Main(String[] args) { BinaryTree tree = new BinaryTree(); /*create root*/ tree.root = new Node(1); /* following is the tree after above statement 1 / \ null null */ tree.root.left = new Node(2); tree.root.right = new Node(3); /* 2 and 3 become left and right children of 1 1 / \ 2 3 / \ / \ null null null null */ tree.root.left.left = new Node(4); /* 4 becomes left child of 2 1 / \ 2 3 / \ / \ 4 null null null / \ null null */ } } // This code is contributed by PrinciRaj1992 |
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Summary: Tree is a hierarchical data structure. Main uses of trees include maintaining hierarchical data, providing moderate access and insert/delete operations. Binary trees are special cases of tree where every node has at most two children.
Below are set 2 and set 3 of this post.
Properties of Binary Tree
Types of Binary Tree
Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.
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