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Notice that it first checks if v is null If it is, then it returns a new ThreeD object in which all fields are set to zero The reason for this is that v is set to default(T) by the ByTwos constructor This value is zero for value types and null for object types Thus, (unless SetStart( ) has been called) for the first increment, v will contain null instead of a reference to an object This means that for the first increment, a new object is required

Part I:

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A type parameter for a generic interface can have constraints in the same way as it can for a generic class For example, this version of ISeries restricts its use to reference types:

public interface ISeries<T> where T : class {

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When this version of ISeries is implemented, the implementing class must also specify the same constraint for T, as shown here:

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SOLUTION We know that v0 = 10 and that h(12) = 0 This is the information that we must exploit in solving the problem Now h(t) = 16t 2 10t + h0 Thus 0 = h(12) = 16 122 10 12 + h0 We may solve for h0 to obtain h0 = 2424 ft The initial height is 2424 feet You Try It: A body is thrown straight up with initial velocity 5 feet per second from a height of 40 feet After how many seconds will it hit the ground What will be its maximum height

class ByTwos<T> : ISeries<T> where T : class {

16 17 18 19 20

Because of the reference constraint, this version of ISeries cannot be used on value types Thus, in the preceding program, only ByTwos<ThreeD> would be valid ByTwos<int> and ByTwos<double> would be invalid

Sometimes you will want to compare two instances of a type parameter For example, you might want to write a generic method called IsIn( ) that returns true if some value is contained within an array To accomplish this, you might first try something like this:

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A body is launched straight up from height 100 feet with some initial velocity It hits the ground after 10 seconds What was that initial velocity

// This won t work! public static bool IsIn<T>(T what, T[] obs) { foreach(T v in obs) if(v == what) // Error! return true; return false; }

Unfortunately, this attempt won t work Because T is a generic type, the compiler has no way to know precisely how two objects should be compared for equality Should a bitwise comparison be done Should only certain fields be compared Should reference equality be used The compiler has no way to answer these questions To enable two objects of a generic type parameter to be compared, you must use the CompareTo( ) method defined by one of NET s standard interfaces: IComparable This interface is implemented by all of C# s built-in types, including int, string, and double It is also easy to implement for classes that you create The IComparable interface defines only the CompareTo( ) method shown here: int CompareTo(object obj) CompareTo( ) compares the invoking object to obj It returns zero if the two objects are equal, a positive value if the invoking object is greater than obj, and a negative value if the invoking object is less than obj To use CompareTo( ), you must specify a constraint that requires every type argument to implement the IComparable interface Then, when you need to compare two instances of the type parameter, simply call CompareTo( ) For example, here is a corrected version of IsIn( ):

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// Require IComparable interface public static bool IsIn<T>(T what, T[] obs) where T : IComparable { foreach(T v in obs)

18:

SOLUTION We are given that h0 = 100 Thus h(t) = 16t 2 + v0 t + 100 Our job is to nd v0 We also know that 0 = h(10) = 16 102 + v0 10 + 100 We solve this equation to nd that v0 = 150 ft /sec You Try It: On a certain planet, bodies fall with an acceleration due to gravity of 10 ft/sec2 A certain body is thrown down with an initial velocity of 5 feet per second, and hits the surface 12 seconds later From what height was it launched

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if(vCompareTo(what) == 0) // now OK, uses CompareTo() return true;

return false; }

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