epicours/Algo/CM/CM du 27 septembre.md

Outline

• Abstract Algebraic Data types
• Elementary types
  • List
  • Stack
  • Queue
  • Set
• Searching algorithms
• Tree
  • Binary
  • General
  • BST
  • AVL
  • A234

Abstract Algebraic Data Types

Signature and hierarchy

• a signature is composed by
  • a type (integer, stack, queue, graph)
  • an operations (name: profile)
  • Exemple:
    • insert: list x integer x element -> list
    • insert(l, i, e)
    • return a result of type list
  • We can use the _to pass an argument without parentheses
    • facotrial: interger -> integer= _!: interger -> integer
    • power: integer x integer -> integer= _^_: integer x integer -> integer
    • Operations
      • 0: -> integer
      • false: -> boolean
      • pi: -> real
    • Types
      • Boolean
        • Opération:
          • false: -> boolean
          • true: -> boolean
          • not_: boolean -> boolean
          • _and_: boolean x boolean -> boolean
          • _or_: boolean x boolean -> boolean
      • Vectors (defined type)
        • Uses: integer and element (predefined types)
        • Operations:
          • modify: vector x integer x element -> vector (internal operation)
          • nth: vector x integer -> element (observers)
          • lowerlimit: vector -> integer (observers)
          • upperlimit: vector -> integer (observers)
        • Use
          • nth(v, i+2)

Every time that an operation return a defined type, is a internal operation. An internal operation will really modify the data

An observer is when there is AT LEAST 1 defined type vector and who return a predefined type. The observer just look into the data and return the selected value, but he don't change any values.