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private int yearsOfSvc = 1; public Employee(int empID) { this.empID = empID; } public Employee(int empID, int yearsOfSvc) { this.empID = empID; this.yearsOfSvc = yearsOfSvc; } public override string ToString( ) { return "ID: " + empID.ToString( ) + ". Years of Svc: " + yearsOfSvc.ToString( ); } public bool Equals(Employee other) { if (this.empID == other.empID) { return true; } else { return false; } } // static method to get a Comparer object public static EmployeeComparer GetComparer( ) { return new Employee.EmployeeComparer( ); } // Comparer delegates back to Employee // Employee uses the integer's default // CompareTo method public int CompareTo(Employee rhs) { return this.empID.CompareTo(rhs.empID); } // Special implementation to be called by custom comparer public int CompareTo(Employee rhs, Employee.EmployeeComparer.ComparisonType which) { switch (which) {

TX = Tsort (n) + TX (sequential)

|

serial 3-11

case Employee.EmployeeComparer.ComparisonType.EmpID: return this.empID.CompareTo(rhs.empID); case Employee.EmployeeComparer.ComparisonType. YearsOfService: return this.yearsOfSvc.CompareTo(rhs.yearsOfSvc); } return 0; }

// nested class which implements IComparer public class EmployeeComparer : IComparer<Employee> { // private state variable private Employee.EmployeeComparer.ComparisonType whichComparison; // enumeration of comparison types public enum ComparisonType { EmpID, YearsOfService }; public bool Equals(Employee lhs, Employee rhs) { return this.Compare(lhs, rhs) == 0; } // Tell the Employee objects to compare themselves public int Compare(Employee lhs, Employee rhs) { return lhs.CompareTo(rhs, WhichComparison); } public Employee.EmployeeComparer.ComparisonType WhichComparison { get { return whichComparison; } set { whichComparison = value; } } } } public class Tester { static void Main( ) { List<Employee> empList = new List<Employee>( ); // generate random numbers for // both the integers and the

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which will be considerably less than n TF for any nontrivial le An analysis of sorting is provided in Section 3-7 For large les the time required to sort all records is approximately Tsort (n) log2 (n/btt)TX (sequential) sort 3-12

We have presented two formal query languages for the relational model Are they equivalent in power Can every query that can be expressed in relational algebra also be expressed in relational calculus The answer is yes, it can Can every query that can be expressed in relational calculus also be expressed in relational algebra Before we answer this question, we consider a major problem with the calculus as we have presented it Consider the query {S | (S Sailors)} This query is syntactically correct However, it asks for all tuples S such that S is not in (the given instance of) Sailors The set of such S tuples is obviously in nite, in the context of in nite domains such as the set of all integers This simple example illustrates an unsafe query It is desirable to restrict relational calculus to disallow unsafe queries We now sketch how calculus queries are restricted to be safe Consider a set I of relation instances, with one instance per relation that appears in the query Q Let Dom(Q, I) be the set of all constants that appear in these relation instances I or in the formulation of the query Q itself Since we only allow nite instances I, Dom(Q, I) is also nite For a calculus formula Q to be considered safe, at a minimum we want to ensure that for any given I, the set of answers for Q contains only values that are in Dom(Q, I) While this restriction is obviously required, it is not enough Not only do we want the set of answers to be composed of constants in Dom(Q, I), we wish to compute the set of answers by only examining tuples that contain constants in Dom(Q, I)! This wish leads to a subtle point associated with the use of quanti ers and : Given a TRC formula of the form R(p(R)), we want to nd all values for variable R that make this formula true by checking only tuples that contain constants in Dom(Q, I) Similarly,.

// employee IDs Random r = new Random( ); // populate the list for (int i = 0; i < 5; i++) { // add a random employee ID empList.Add(new Employee(r.Next(10) + 100, r.Next(20))); } // display all the contents of the Employee list for (int i = 0; i < empList.Count; i++) { Console.Write("\n{0} ", empList[i].ToString( )); } Console.WriteLine("\n"); // sort and display the employee list Employee.EmployeeComparer c = Employee.GetComparer( ); c.WhichComparison = Employee.EmployeeComparer.ComparisonType.EmpID; empList.Sort(c); // display all the contents of the Employee list for (int i = 0; i < empList.Count; i++) { Console.Write("\n{0} ", empList[i].ToString( )); } Console.WriteLine("\n"); c.WhichComparison = Employee.EmployeeComparer.ComparisonType.YearsOfService; empList.Sort(c); for (int i = 0; i < empList.Count; i++) { Console.Write("\n{0} ", empList[i].ToString( )); } Console.WriteLine("\n"); } } }

although many commercial sort packages can improve on that that estimate A derivation and a more precise result is provided in Sect 3-7 as Eq 3-107,

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