Elementary Statistics

A tree data structure can be defined recursively (locally) as a collection of nodes (starting at a root node), where each node is a data structure consisting of a value, together with a list of references to nodes (the children), with the constraints that no reference is duplicated, and none points to the root. Alternatively, a tree can be defined abstractly as a whole (globally) as an ordered tree, with a value assigned to each node. Both these perspectives are useful: while a tree can be analysed mathematically as a whole, when actually represented as a data structure it is usually represented and worked with separately by node (rather than as a list of nodes and an adjacency list of edges between nodes, as one may represent a digraph, for instance).

For example, looking at a tree as a whole, one can talk about the parent node of a given node, but in general as a data structure a given node only contains the list of its children, but does not contain a reference to its parent (if any).

In the context of relational databases, a foreign key is a field (or collection of fields) in one table that uniquely identifies a row of another table or the same table. In simpler words, the foreign key is defined in a second table, but it refers to the primary key or a unique key in the first table. For example, a table called Employee has a primary key called employee_id. Another table called Employee Details has a foreign key which references employee_id in order to uniquely identify the relationship between both tables. The table containing the foreign key is called the child table, and the table containing the candidate key is called the referenced or parent table. In database relational modeling and implementation, a unique key is a set of zero or more attributes, the value(s) of which are guaranteed to be unique for each tuple (row) in a relation.

The value or combination of values of unique key attributes for any tuple cannot be duplicated for any other tuple in that relation. When more than one column is combined to form a unique key, their combination is used to access each row and maintain uniqueness. The values of the columns are not combined, they are compared using their data types. Defining foreign key In the ISO SQL Standard, foreign keys are defined through a FOREIGN KEY constraint. The syntax to add such a constraint to an existing table is defined in SQL:2003 as shown below.