The Most Commonly-used Data Structures

1. The Most Commonly-usedData Structures Terence Parr USF

2. Introduction • Abstract data types • Data structures (implementations) • Combinations

3. Abstract Data Types • List • stack, queue, prioritized queue, … • Set (unordered, unique) • Dictionary (also called Map) • Graph (directed or undirected) • Tree • Binary tree • Choose via: • access pattern, properties, element relationships • Implementations chosen to optimize time/space

4. List • Operations: add, get, insert, delete, find • queue: add to tail, get only from head • stack: add to “top”, delete from “top” • Typical implementation: array or linked list • Examples: list of users, list of books

5. Set • Operations: add, delete, contains • Typical implementation: bit vector (if elements are integers) or hash table • Examples: set of universities, set of students

6. Dictionary • Operations: map x->y, get x, delete x • Typical implementation: hash table • Examples: • student -> userid • student -> list of classes

7. Graph • Collection of nodes connected by directed or undirected edges with or without labels • Path==sequence of edges • Operations: add node, add edge x->y, delete node, delete edge • Typical implementation: node has list of edges that point to other nodes • Examples: network simulation, email trail between employees (social network), finite automata

8. Tree • A kind of directed graph with unique edge path from node x to y • Children: emanating edges, Root: topmost node, Leaves: nodes w/o children • Operations: add child, delete a child • Typical implementation: node has list of children (again, a restricted graph) • Examples: organization chart, class hierarchy, expression tree • Binary tree: at most 2 children per node

9. Implementations

10. Linked list • head, tail pointers • wrapper to hold value and “next” • Operations: • get O(1) • others O(n)

11. Hash table • Fast implementation of a dictionary; like an associative memory; maps key to value • Idea: break up large search space into many smaller spaces • “hash function” tells you which of the smaller spaces (“buckets”) has element of interest • search linearly within smaller space • simple hash of int: hash(x)=x; hash of string: sum of char values • Array of lists; each list is a bucket of key/value pairs • bucket index(key) = hash(key) % num_buckets

12. Hash table 2

13. Tree • Node has list of children; need root ptr CEO + 3 * President 4 5 VP Sales VP Eng.

14. Graph • States or nodes have list of edges to other states Mary Jim Chris Tim Jen