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This constraint ensures that only types that implement IComparable are valid type arguments for IsIn( ) The following program demonstrates IsIn( ) It also shows how IComparable can be easily implemented by a class:

1 Sketch the graph of f (x) = x/[x 2 + 3], indicating all local maxima and minima together with concavity properties 2 What is the right circular cylinder of greatest volume that can be inscribed upright in a right circular cone of radius 3 and height 6 3 An air mattress (in the shape of a rectangular parallelepiped) is being in ated in such a way that, at a given moment, its length is increasing by 1 inch per minute, its width is decreasing by 05 inches per minute, and its height is increasing by 03 inches per minute At that moment its dimensions are = 100 , w = 60 , and h = 15 How is its volume changing at that time 4 A certain body is thrown straight down at an initial velocity of 15 ft /sec It strikes the ground in 5 seconds What is its initial height 5 Because of viral infection, the shape of a certain cone-shaped cell is changing The height is increasing at the rate of 3 microns per minute For metabolic reasons, the volume remains constantly equal to 20 cubic microns At the moment that the radius is 5 microns, what is the rate of change of the radius of the cell 6 A silo is to hold 10,000 cubic feet of grain The silo will be cylindrical in shape and have a at top The oor of the silo will be the earth What dimensions of the silo will use the least material for construction 7 Sketch the graph of the function g(x) = x sin x Show maxima and minima

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// Demonstrate IComparable using System; class MyClass : IComparable { public int Val; public MyClass(int x) { Val = x; } // Implement IComparable public int CompareTo(object obj) { return Val - ((MyClass) obj)Val; } } class CompareDemo { // Require IComparable interface public static bool IsIn<T>(T what, T[] obs) where T : IComparable { foreach(T v in obs) if(vCompareTo(what) == 0) // now OK, uses CompareTo() return true; return false; } // Demonstrate comparisons static void Main() { // Use IsIn() with int int[] nums = { 1, 2, 3, 4, 5 }; if(IsIn(2, nums)) ConsoleWriteLine("2 is found"); if(IsIn(99, nums)) ConsoleWriteLine("This won t display");

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Part I:

string[] strs = { "one", "two", "Three"}; if(IsIn("two", strs)) ConsoleWriteLine("two is found"); if(IsIn("five", strs)) ConsoleWriteLine("This won t display");

On a real number line, plot the numbers 4, 1, 2, 6 Also plot the sets S = {x R: 8 x < 5} and T = {t R: 7 < t 9} Label the plots

// Use IsIn with MyClass MyClass[] mcs = { new MyClass(1), new MyClass(2), new MyClass(3), new MyClass(4) }; if(IsIn(new MyClass(3), mcs)) ConsoleWriteLine("MyClass(3) is found"); if(IsIn(new MyClass(99), mcs)) ConsoleWriteLine("This won t display"); } }

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The output is shown here:

Although the preceding program is correct, there is still one potential trouble spot Notice how CompareTo( ) is implemented by MyClass:

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SOLUTION Figure 12 exhibits the indicated points and the two sets These sets are called half-open intervals because each set includes one endpoint and not the other

public int CompareTo(object obj) { return Val - ((MyClass) obj)Val; }

Because the parameter to CompareTo( ) must be of type object, obj must be explicitly cast to MyClass in order for Val to be accessed However, it s precisely this type of thing that generics were designed to eliminate! To solve this problem, C# provides a generic version of IComparable, which is declared like this: public interface IComparable<T> In this version, the type of data being compared is passed as a type argument to T This causes the declaration of CompareTo( ) to be changed, as shown next: int CompareTo(T obj) Now, the parameter to CompareTo( ) can be specified as the proper type and no cast from object is needed IComparable<T> is also implemented by all built-in types Here is an improved version of MyClass that implements IComparable<T>:

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