Data Structures Notes

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Data structures

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Notes Lecture 1: Abstract Data Types

• Introduction
• Basic Definitions
• Common Structures
• Abstract Data Type
• Specification
• Layered Software

Notes Lecture 2: Efficient Use Of Memory

• Dynamic Memory Allocation
• Linked Data Structures
• Operations Needed To Support Dynamic Allocation And Linked Structures
• Node And Arc Diagrams
• Linked Implementation Of Stacks

Notes Lecture 3: Recursion

• Foreword On Recursion
• Recursive Definitions
• Using Recursion To Solve Problems
• Recursion As A Programming Technique
• List Specification

Notes Lecture 4: Specifications Of Lists And Collections

• Our Specification Of Lists - General Considerations
• Our Specification Of Collection - Details
• Our Specification Of Lists - Details

Handout specifications of collection and list.

Notes Lecture 5: Implementation Of Lists

• General Considerations For Designing An Implementation
• List Variations

Notes Lecture 6: Further List Variations

• Multiple Values Per Node
• Multi-Linked Lists
• Circular Lists
• Ordered Lists
• Sorted Lists

Notes Lecture 7: Sorting Algorithms

Handout examples of programs to analyze.

• General Sorting Strategy (Recursive)
• Merge Sort
• Insertion Sort
• QuickSort
• Radix Sort
• Sorting Summary
• Asymptotic Complexity

Notes Lecture 8: Tree Structures

Handouts:

• from last lecture, simple programs to analyze.
• specification of binary tree.
• C type definitions for binary tree implementation.

lecture begins by discussing briefly any of the simple programs that the students found difficult to analyze. This should take no more than 20 minutes.

• Introduction To Trees
• Tree Traversal
• Tree Specification

Notes Lecture 9: Binary Search Trees

We have defined binary trees in general, and for the next couple of lectures we are going to look at special kinds of binary trees - binary trees - that have specific properties that make certain kinds of processing very efficient.
The first special kind of binary tree we will look at is Binary Search Trees. These are binary trees with specific properties that make it very efficient to search for a value in the tree.

• Binary Search
• Operations on Binary Search Trees
• A Problem With Binary Search Trees
• Details of Rotation And Insertion, Sketch of Deletion, For AVL Trees

Notes Lecture 10: B-Trees And HeapsIn this lecture we will look at two kinds of balanced trees, B-trees and Heaps.

B-trees are extremely widely used in practice for storing large amounts of data on disk. A B-tree is perfectly height-balanced version of a data structure called an M-way search tree, so we will begin by discussing M-way search trees.

• M-way Search Trees
• B-trees: Perfectly Height-balanced M-way search trees
• Abstract Type HEAP
• Implementing a Tree in an Array

Notes Lecture 11: Tables And Graphs

Handout specification of Table

• Tables
• Familar Examples
• Representing Tables
• Hashing
• Minimizing The Number Of Collisions
• Resolving Collisions
• Open Addressing
• Chaining
• Graphs
• Operations
• Graph Traversal

Notes Lecture 12: Graph Algorithms

This lecture will probably not take a full 3 hours. Use the additional time to summarize the course and review for the exam.

In this lecture we conclude our discussion of graphs. First we look at standard algorithms for two very common problems; then we look at two common ways of implementing graphs.

• Shortest Path Algorithm
• Spanning Trees
• Algorithm For Computing a Minimum Spanning Tree
• How To Implement A Graph