L-3.7: Introduction to Trees (Binary Tree, Almost Complete Binary Tree, Full BT, Complete BT, BST)

Summary

This video explains the binary tree data structure and its variations, which are crucial in algorithms and data structures. The host covers key concepts such as binary trees, full/strict binary trees, almost complete binary trees, complete binary trees, and binary search trees (BST). The video highlights important characteristics, such as the binary tree's structure, conditions for strict or complete binary trees, and the left-to-right filling order for almost complete binary trees. Additionally, the host introduces the BST and directs viewers to a detailed video for more on this complex topic.

Takeaways

• 🌳 Binary tree is a key concept in data structures, commonly used in algorithms.
• 👶 A binary tree means each node has at most 2 children, either 0, 1, or 2.
• 🚫 Trees differ from graphs because trees do not have cycles or loops.
• 🌿 The structure of a tree consists of a root, internal nodes, and leaf nodes.
• 📐 A full binary tree (or strict binary tree) has either 0 or 2 children for each non-leaf node.
• 🔄 Almost complete binary trees (ACBT) are filled from left to right at each level, important for heap structures.
• ✅ A complete binary tree ensures all levels are fully filled, with internal nodes having exactly 2 children.
• ⚠️ A binary tree can fail to be complete if nodes at a higher level are not fully filled while nodes are added at a lower level.
• 💡 Binary search tree (BST) is a special case of binary tree, commonly used in competitive exams.
• 📹 For detailed explanation on binary search trees, refer to the linked video in the description.

Q & A

What is a binary tree?

A binary tree is a tree data structure where each node has at most two children. These children are referred to as the left child and the right child.

What is the main difference between a tree and a graph?

The main difference between a tree and a graph is that trees do not contain cycles or loops. In a tree, there is no way to form a cycle by connecting nodes, whereas graphs can have cycles.

What are the three main parts of a tree structure?

A tree structure consists of three main parts: the root node, internal nodes, and leaf nodes. The root node is the topmost node, internal nodes are those with children, and leaf nodes are the ones without children.

What is a full or strict binary tree?

A full or strict binary tree is a binary tree in which every node has either 0 or 2 children. This means no node in a strict binary tree can have only one child.

What is an almost complete binary tree (ACBT)?

An almost complete binary tree (ACBT) is a binary tree where the nodes are filled from left to right at each level, and no nodes are skipped before moving to the next level.

What is a complete binary tree?

A complete binary tree is a binary tree in which all levels, except possibly the last one, are fully filled, and all nodes are as far left as possible. All internal nodes must have two children.

How does an almost complete binary tree differ from a complete binary tree?

An almost complete binary tree requires nodes to be filled from left to right on each level, but levels don’t need to be fully filled. A complete binary tree requires that all levels be fully filled before moving to the next, except possibly the last level.

What is a binary search tree (BST)?

A binary search tree (BST) is a special type of binary tree where the nodes are organized in such a way that for each node, the left subtree contains values less than the node, and the right subtree contains values greater than the node.

Why is the binary search tree important?

The binary search tree is important because it allows for efficient searching, insertion, and deletion operations. Its structure helps maintain sorted data, making it widely used in various algorithms and applications.

What role does the almost complete binary tree (ACBT) play in heap data structures?

The almost complete binary tree (ACBT) is crucial in heap data structures, as both max heaps and min heaps follow the ACBT structure. This ensures that the tree is filled from left to right without any gaps, which is essential for maintaining the heap property.