# Last Minute Notes – DBMS

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We will discuss the important key points useful for GATE exams in summarized form. For details you may refer this.

**E-R Diagram**: The most common asked questions in ER diagram is minimum number of tables required for a given ER diagram. Generally, following criteria are used:

Cardinality | Minimum No. of tables |

1:1 cardinality with partial participation of both entities | 2 |

1:1 cardinality with total participation of atleast 1 entity | 1 |

1:n cardinality | 2 |

m:n cardinality | 3 |

**Note:** This is a general observation. Special cases need to be taken care. We may need extra table if attribute of a relationship can’t be moved to any entity side.

**Keys of a relation**: There are various types of keys in a relation which are:

**Candidate Key:**The minimal set of attributes which can determine a tuple uniquely. There can be more than 1 candidate key of a relation and its proper subset can’t determine tuple uniquely and it can’t be NULL.**Super Key:**The set of attributes which can determine a tuple uniquely. A candidate key is always a super key but vice versa is not true.**Primary Key and Alternate Key:**Among various candidate keys, one key is taken primary key and others are alternate keys.**Foreign Key:**Foreign Key is a set of attributes in a table which is used to refer the primary key or alternative key of the same or other table.

**First Normal Form:**A relation is in first normal form if it does not contain any multi-valued or composite attribute.**Second Normal Form:**A relation is in second normal form if it does not contain any partial dependency. A dependency is called partial dependency if any proper subset of candidate key determines non-prime (which are not part of candidate key) attribute.**Third Normal Form:**A relation is in third normal form if it does not contain any transitive dependency. For a relation to be in Third Normal Form, either LHS of FD should be super key or RHS should be prime attribute.**Boyce-Codd Normal Form:**A relation is in**1NF****⊃****2NF****⊃****3NF****⊃****BCNF**

**Relational Algebra**: Procedural language with basic and extended operators.

Basic Operator | Semantic |

σ(Selection) | Select rows based on given condition |

∏(Projection) | Project some columns |

X (Cross Product) | Cross product of relations, returns m*n rows where m and n are number of rows in R1 and R2 respectively. |

U (Union) | Return those tuples which are either in R1 or in R2. Max no. of rows returned = m+n andMin no. of rows returned = max(m,n) |

−(Minus) | R1-R2 returns those tuples which are in R1 but not in R2. Max no. of rows returned = m and Min no. of rows returned = m-n |

ρ(Rename) | Renaming a relation to other relation. |

Extended Operator | Semantic |

∩ (Intersection) | Returns those tuples which are in both R1 and R2. Max no. of rows returned = min(m,n) and Min no. of rows returned = 0 |

| Selection from two or more tables based on some condition (Cross product followed by selection) |

| It is a special case of conditional join when only equality condition is applied between attributes. |

| In natural join, equality condition on common attributes hold and duplicate attributes are removed by default. Note: Natural Join is equivalent to cross product if two relations have no attribute in common and natural join of a relation R with itself will return R only. |

| When applying join on two relations R and S, some tuples of R or S does not appear in result set which does not satisfy the join conditions. But Left Outer Joins gives all tuples of R in the result set. The tuples of R which do not satisfy join condition will have values as NULL for attributes of S. |

| When applying join on two relations R and S, some tuples of R or S does not appear in result set which does not satisfy the join conditions. But Right Outer Joins gives all tuples of S in the result set. The tuples of S which do not satisfy join condition will have values as NULL for attributes of R. |

| When applying join on two relations R and S, some tuples of R or S does not appear in result set which does not satisfy the join conditions. But Full Outer Joins gives all tuples of S and all tuples of R in the result set. The tuples of S which do not satisfy join condition will have values as NULL for attributes of R and vice versa. |

| Division operator A/B will return those tuples in A which is associated with every tuple of B.Note:Attributes of B should be proper subset of attributes of A. The attributes in A/B will be Attributes of A- Attribute of B. |

How to solve Relational Algebra problems for GATE – SET 1

How to solve Relational Algebra problems for GATE – SET 2

**SQL**: As opposed to Relational Algebra, SQL is a non-procedural language.

Operator | Meaning |

Select | Selects columns from a relation or set of relations.Note: As opposed to Relational Algebra, it may give duplicate tuples for repeated value of an attribute. |

From | From is used to give input as relation or set of relations from which data needs to be selected. |

where | Where is used to give condition to be used to filter tuples |

EXISTS | EXISTS is used to check whether the result of a correlated nested query is empty (contains no tuples) or not. |

Group By | Group By is used to group the tuples based on some attribute or set of attributes like counting the no. of students group by department. |

Order By | Order By is used to sort the fetched data in either ascending or descending according to one or more columns. |

Aggregate functions | Find the aggregated value of an attribute. Used mostly with group by. e.g.; count, sum, min max. select count(*) from student group by dept_idNote: we can select only those columns which are part of group by. |

Nested Queries | When one query is a part of other query. Solving nested queries questions can be learnt in https://www.geeksforgeeks.org/nested-queries-in-sql/ |

**Conflict serializable and Conflict Equivalent**: A schedule is conflict serializable if it is conflict equivalent to a serial schedule.

**Checking for Conflict Serializability**

To check whether a schedule is conflict serializable or not, find all **conflicting operations pair**s of a schedule and draw precedence graph ( For all conflicting operation pair, an edge from T_{i} to T_{j} if one operation of conflicting pair is from T_{i} and other from T_{j} and operation of T_{i} occurs before T_{j} in schedule). If graph does not contain cycle, the schedule is conflict serializable else it is not conflict serializable.

Schedules are said to be conflict equivalent if 1 schedule can be converted into another by swapping non conflicting operations.

**Note:** Two phase locking protocol produce conflict serializable schedule but may suffer from deadlock. On the other hand, Time-Stamp based protocols are free from deadlock yet produce conflict serializable schedule.

**View Serializable and View Equivalence** : Two schedules S1 and S2 are said to be view-equivalent if all conditions are satisfied for all objects:

If the transaction T

_{i}in S1 reads an initial value for object X, in S2 also, T_{i}must read the initial value of X.If the transaction T

_{i}in S1 reads the value written by transaction T_{j }in S1 for object X, same should be done in S2.If the transaction T

_{i}in S1 is the final transaction to write the value for an object X, in S2 also, T_{i}must write the final value of X.

A schedule is view serializable if it is view equivalent to any serial schedule.

**Irrecoverable Schedules: ****For a transaction pair < T**_{i}, T_{j} >, if T_{j} is reading the value updated by Ti and Tj is committed before commit of Ti, the schedule will be irrecoverable.

**Recoverable Schedules: ****For a transaction pair < T**_{i}, T_{j} >, if T_{j} is reading the value updated by Ti and Tj is committed after commit of Ti, the schedule will be recoverable.

**Cascadeless Recoverable Schedules: ****For a transaction pair < T**_{i}, T_{j} >, if value updated by Ti is read by Tj only after commit of T_{i}, the schedule will be cascadeless recoverable.

**Strict Recoverable:** For a transaction pair < T_{i}, T_{j} >, if value updated by Ti is read or written by Tj only after commit of T_{i}, the schedule will be strict recoverable. The relationship between them can be represented as:

**Strict ****⊂**** ****Cascadeless Recoverable ****⊂**** recoverable ****⊂**** all schedules**

##### File structures

**Primary Index :**: A primary index is an ordered file, records of fixed length with two fields. First field is same as primary key as data file and second field is a pointer to data block, where the key is available.

The average number of block accesses using index = **log _{2} Bi + 1**, where Bi = number of index blocks.

**Clustering Index :**Clustering index is created on data file whose records are physically ordered on a non-key field (called Clustering field).

**Secondary Index :**Secondary index provides secondary means of accessing a file for which primary access already exists.

Number of index entries = Number of records

__B Trees__

At every level , we have Key and Data Pointer and data pointer points to either block or record.

**Properties of B-Trees :**

Root of B-tree can have children between **2** and **P**, where P is Order of tree.

**Order of tree** – Maximum number of children a node can have.

Internal node can have children between **⌈ P/2 ⌉** and **P**

Internal node can have keys between **⌈ P/2 ⌉ – 1** and **P-1**

__B+ Trees__

In B+ trees structure of leaf and non-leaf are different, so their order is. Order of non-leaf will be higher as compared to leaf nodes.

Searching time will be less in B+ tress, since it doesn’t have record pointers in non-leaf because of which depth will decrease.

This article has been contributed by Sonal Tuteja.

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