6. Binary Trees, Part 1
MIT OpenCourseWare
50 min, 59 sec
An in-depth exploration of binary trees and their operations, including traversal, insertion, and deletion.
Summary
- Binary trees are introduced as a versatile data structure that can represent sequences or sets efficiently.
- Traversal order is key to binary trees, defining a natural order of items in the tree which can correspond to sequence order or sorted key order.
- Basic operations such as finding the first or last item in a subtree, the successor of a node, and insertion or deletion of nodes are explained in detail.
- For sequences, the traversal order of the tree is set to match the sequence order. For sets, it's sorted by the increasing key value.
- The efficiency of operations is tied to the height of the tree, and the goal is to ensure all operations can run in logarithmic time relative to the number of items.
Chapter 1
Overview of binary trees and their significance in data structures.
- Binary trees are considered one of the most interesting and powerful data structures.
- They have wide-ranging applications, including their use as a tool for establishing lower bounds within the decision tree model.
- A binary tree consists of nodes with parent pointers, left and right child pointers, and an item within each node.
Chapter 2
Explains the concept of traversal order in binary trees and the definition of tree height.
- Traversal order in a binary tree defines a natural sequence of items based on the tree structure.
- Height (h) of a binary tree is defined as the number of edges in the longest downward path from the root to any leaf.
- Operations are aimed to be performed in order of the height (h) of the tree, with an eventual goal of keeping the height logarithmic to the number of items.
Chapter 3
Details the basic operations possible on binary trees.
- Operations like finding the first or last item in a subtree, computing the successor of a node, and binary search are covered.
- Insertion and deletion operations in a binary tree are explained with considerations for different cases like leaf or root nodes.
- These operations form the foundation for more complex tasks such as maintaining sequences or sets.
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