Day 77: Trees and Binary Trees - Harshil Chovatiya

Day 77: Trees and Binary Trees

Brief:

Day 77 introduces us to the hierarchical data structure of trees and its specialized form, binary trees. Trees organize data in a hierarchical manner, with each node having a parent and zero or more children. Binary trees, specifically, have at most two children per node, known as the left child and the right child. We'll explore their properties, traversal methods, common operations, and solve problems to reinforce our understanding.

Topics Covered:

1. Introduction to Trees:

   • Definition: Trees are hierarchical data structures composed of nodes connected by edges, with a single root node at the top.
   • Terminology: Root, parent, child, leaf, subtree, depth, height, etc.
   • Types of Trees: Binary trees, binary search trees, balanced trees, etc.

2. Binary Trees:

   • Definition: Binary trees are trees in which each node has at most two children, left and right.
   • Properties: Full binary trees, complete binary trees, perfect binary trees.
   • Implementations: Using nodes and pointers or arrays.

3. Tree Traversal:

   • Depth-First Traversal: Preorder, inorder, postorder traversals.
   • Breadth-First Traversal: Level-order traversal.

4. Common Operations and Problems:

   • Binary Tree Operations: Insertion, deletion, searching, and traversal.
   • Problem Solving: Solving problems involving binary trees, such as finding the lowest common ancestor, checking if a binary tree is balanced, etc.

In-Depth Examples:

1. Binary Tree Node Implementation:

                       
                       
   class TreeNode {
       constructor(data) {
           this.data = data;
           this.left = null;
           this.right = null;
       }
   }
                       
                   

2. Binary Tree Traversal:

                       
                       
   function preorderTraversal(root) {
       if (root) {
           console.log(root.data);
           preorderTraversal(root.left);
           preorderTraversal(root.right);
       }
   }
   
   function inorderTraversal(root) {
       if (root) {
           inorderTraversal(root.left);
           console.log(root.data);
           inorderTraversal(root.right);
       }
   }
   
   function postorderTraversal(root) {
       if (root) {
           postorderTraversal(root.left);
           postorderTraversal(root.right);
           console.log(root.data);
       }
   }
                       
                   

3. Problem: Lowest Common Ancestor in Binary Tree:

                       
                       
   function lowestCommonAncestor(root, p, q) {
       if (!root || root === p || root === q) {
           return root;
       }
       const leftLCA = lowestCommonAncestor(root.left, p, q);
       const rightLCA = lowestCommonAncestor(root.right, p, q);
       if (leftLCA && rightLCA) {
           return root;
       }
       return leftLCA ? leftLCA : rightLCA;
   }
                       
                   

Conclusion:

Day 77 has provided a comprehensive understanding of trees, particularly binary trees, their properties, traversal methods, and common operations. Trees are versatile data structures with numerous applications in computer science, from representing hierarchical relationships to implementing efficient search and storage algorithms. As we continue our journey, let's explore more advanced tree structures and algorithms to enhance our problem-solving skills and broaden our knowledge base.

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