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IEnumerable is the non-generic interface that a class must implement if it is to support enumerators As explained, all of the non-generic collection classes implement IEnumerable because it is inherited by ICollection The sole method defined by IEnumerable is GetEnumerator( ), which is shown here: IEnumerator GetEnumerator( ) It returns the enumerator for the collection Also, implementing IEnumerable allows the contents of a collection to be obtained by a foreach loop IEnumerator is the interface that defines the functionality of an enumerator Using its methods, you can cycle through the contents of a collection For collections that store key/value pairs (dictionaries), GetEnumerator( ) returns an object of type IDictionaryEnumerator, rather than IEnumerator IDictionaryEnumerator inherits IEnumerator and adds functionality to facilitate the enumeration of dictionaries IEnumerator defines the methods MoveNext( ) and Reset( ) and the Current property The techniques needed to use them are described in detail later in this chapter Briefly, Current holds the element currently being obtained MoveNext( ) moves to the next element Reset( ) restarts the enumeration from the beginning

where Eq (710) has been used An expression for k can now be derived in terms of the geometric variables of the cam pro le from Eqs (712a and b) It is apparent that the expression sought is a scalar, which calls for a scalar operation between the vectors of those equations However, the dot product of the right-hand side of those equations will not be very helpful Indeed, on dotmultiplying those two sides, the term in k will vanish because vectors en and et are mutually orthogonal An alternative consists in rst rotating vector et through an angle of 90 counterclockwise, which can be done by multiplying both sides of Eq (712b) by matrix E, de ned as 0 -1 E= 1 0 Thus, Ep ( q ) = l ( q )Ee t + l 2 ( q )kEe n where Ee t = e n Hence, Eq ( q ) = - l 2 ( q )k e t + l ( q )e n (716) and Ee n = - e t (715) (714) (713)

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The IComparer interface defines a method called Compare( ), which defines the way two objects are compared It is shown here: int Compare(object v1, object v2) It must return greater than zero if v1 is greater than v2, less than zero if v1 is less than v2, and zero if the two values are the same This interface can be used to specify how the elements of a collection should be sorted IEqualityComparer defines these two methods: bool Equals(object obj1, object obj2) int GetHashCode(object obj)

1 = 2

24:

Second, on dot-multiplying the corresponding sides of Eqs (712a) and (716), we obtain p ( q ) Ep ( q ) = - l 3 ( q )k and, if we recall Eq (73), p ( q ) Ep ( q ) = - p ( q ) sgn[l ( q )]k

Equals( ) must return true if obj1 and obj2 are equal GetHashCode( ) must return the hash code for obj

SystemCollections defines one structure type called DictionaryEntry Non-generic collections that hold key/value pairs store those pairs in a DictionaryEntry object This structure defines the following two properties: public object Key { get; set; } public object Value { get; set; } These properties are used to access the key or value associated with an entry You can construct a DictionaryEntry object by using the following constructor: public DictionaryEntry(object k, object v) Here, k is the key and v is the value

You Try It: Calculate (d/dx)Tan 1 [ln x + x 3 ] and (d/dx) ln[Tan 1 x]

(717)

Now that you are familiar with the non-generic collection interfaces, we can examine the standard classes that implement them With the exception of BitArray, described later, the non-generic collection classes are summarized here:

Class ArrayList Hashtable Queue SortedList Stack Description A dynamic array This is an array that can grow as needed A hash table for key/value pairs A first-in, first-out list A sorted list of key/value pairs A first-in, last-out list

(718)

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