vault backup: 2023-11-13 13:50:53

Algo/B1/CM/CM du 27 septembre.md

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+## 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. 
+