Add 数据结构基础, 数据库系统原理.

Author: zhanghai

数据库系统原理/作业/张海/4.pdf

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+# Introduction
+
+(Nothing particular)

数据库系统原理/作业/张海/5.pdf

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+# Relation Model
+
+## Database Structure
+
+Table (表) / Relation (关系): Cartesian product of domains.
+
+Relationship: Relationship in ER model.
+
+Row (行) / Tuple (元组)
+
+Tuple variable: Variable representing a tuple.
+
+Attribute (属性)
+
+Domain (域): Allowed attribute values.
+
+Atomic (原子): Domain elements cannot be divided.
+
+Null: Value unknown or does not exist, should be eliminated if possible.
+
+## Schema
+
+Database schema (数据库模式): Logical design of the database.
+
+Database instance (数据库实例): Snapshot of the data in the database at a given instant in time.
+
+Relation schema (关系模式): Relation is instance, then relation schema is type definition.
+
+Schema: R = (attribute, ...), definition of a schema.
+
+Instance: r(R) = instance(attribute, ...), instance is a relation on schema.
+
+Use more relations to avoid null.
+
+## Key
+
+A tuple in a relation must be unique.
+
+Superkey (超码): A set of one or more attributes that can uniquely identify a tuple in a relation.
+
+Candidate key (候选码): Minimum superkey.
+
+Primary key (主码): Chosen candidate key, as principal means of identifying tuples within a relation.
+
+Foreign key (外码)：Attribute that is the primary key of another relation. The relation is referencing relation, the other relation is referenced relation.
+
+Schema diagram: Rectangles for relations, relation name, primary key, attributes from top to bottom, arrows for foreign key dependencies.
+
+## Query Language
+
+Query language: Language in which user request information from database.
+
+Procedural query language: User instruct system to get result.
+
+Non-procedural query language: User describe the desired information.
+
+## Fundamental Relational-Algebra
+
+Operations can be composed together.
+
+* Select (选择)
+
+    $$\sigma_{predicate}(relation)$$
+
+    Select tuple that satisfy a given predicate.
+
+* Project (投影)
+
+    $$\Pi_{attribute, ...}(relation)$$
+
+    Return relation with certain attributes left out.
+
+* Union (并)
+
+    $$r{\cup}s$$
+
+    Removes duplicates because result is a set.
+
+    Need to be compatible.
+
+    Compatible:
+
+    * r and s should be of the same arity, i.e. they have same number of attributes.
+
+    * Corresponding domains of r and s should be the same.
+
+* Set-Difference (差)
+
+    $$r-s$$
+
+    Need to be compatible.
+
+* Cartesian product (笛卡尔积)
+
+    $$r{\times}s$$
+
+    Attributes should have distinct names, and relation name prefix can be dropped for simplicity if there is no ambiguity.
+
+    The result relation schema is the concatenation of r's and s'.
+
+    The result relation contains all tuples for which the sub-tuples satisfy.
+
+* Rename (重命名)
+
+    $$\rho_{x(A_1, ...)}(E)$$
+
+    Return E evaluated and give E the name x, optionally rename attributes to A_1, ... if given.
+
+Positional notation: \$n for n-th attribute
+
+## Additional Relational-Algebra
+
+* Set-Intersection
+
+    $$r{\cap}s$$
+
+    $$r{\cap}s=r-(r-s)$$
+
+* Natural Join
+
+    $$r{\bowtie}s$$
+
+    Cartesian product, select with common attribute, remove duplicate attribute.
+
+    Associative
+
+    Theta join
+
+    Natural join with extra predicate for select.
+
+    $$r{\bowtie}_{\theta}s$$
+
+* Division
+
+    $$r{\div}s$$
+
+    When r on R-S have all values in S.
+
+    $r{\div}s=\Pi_{R-S}(r)-\Pi_{R-S}((\Pi_{R-S}(r){\times}s)-\Pi_{R-S,S}(r))$ ($\Pi_{R-S,S}(r)$ is only for attribute reordering)
+
+* Assignment
+
+    $$name \leftarrow $$
+
+## Extended Relational-Algebra
+
+* Generalized Projection
+
+    $$\Pi_{F_1,F_2,...F_n}(E)$$
+
+    Allow function in projection.
+
+* Aggregation Function
+
+    $$_{G_1,G_2,...,G_n}\mathcal{G}_{F_1(A_1) as H_1,F_2(A_2) as H_2,...,F_n(A_n) as H_n}(E)$$
+
+    Input a multiset and output a single value.
+
+    Multiset: Elements not unique, but unordered.
+
+    Function: avg, count, min, max, *-distint.
+
+* Outer join
+
+    Pad result with null, instead of dropping.
+
+    * Left outer join
+
+        $$r{\leftouterjoin}s$$
+
+        Include all rows in left.
+
+        $$(r{\bowtie}s)\cup(r-\Pi_R(r{\bowtie}s))\times{(null,...,null)}$$
+
+    * Right outer join
+
+        $$r{\rightouterjoin}s$$
+
+    * Full outer join
+
+        $$r{\fullouterjoin}s$$
+
+## Null
+
+* Arithmetic operations involving null returns null.
+
+* Comparison operations involving null returns unknown.
+
+* Boolean operations:
+
+    * true and unknown = unknown, false and unknown = false, unknown and unknown  = unknown
+
+    * true or unknown = true, false or unknown = unknown, unknown or unknown  = unknown
+
+    * not unknown = unknown
+
+* Select: Discard row when predicate returns unknown or false.
+
+* Join: According to select, common null returns unknown, so discarded.
+
+* Projection: Null is the same. (Kind of arbitrary)
+
+* Union, Intersection, Difference: Null is the same. (Kind of arbitrary too)
+
+* Generalized projection: As projection.
+
+* Aggregate: Null is the same when grouping, discarded when aggregating.
+
+* Outer join: As join.
+
+## Database Modification
+
+* Delete
+
+    $$r{\leftarrow}r-E$$
+
+* Insert
+
+    $$r{\leftarrow}r{\cup}E$$
+
+* Update
+
+    $$r{\leftarrow}\Pi_{F_1,F_2,...,F_n}(\sigma_P(r))\cup\Pi_{F_1,F_2,...,F_n}(r-\sigma_P(r))$$
+
+    Where $F_i$ is the update function when modification is needed, or original attribute value otherwise.