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SortedList<TK, TV> defines the following indexer (which is defined by IDictionary<TK, TV>): public TV this[TK key] { get; set; } You can use this indexer to get or set the value of an element You can also use it to add a new element to the collection Notice that the index is not actually an index, but rather the key of the item Here is an example that demonstrates SortedList<TK, TV> It reworks the employee database example one more time In this version, the database is stored in a SortedList

Now, let V3i, q3i, and IO be the contribution of the ith face Si of the polyhedron to the 3i corresponding integral, Di, ri, and IOi being the area, the position vector of the centroid, D and the inertia matrix of the polygon Si, respectively (The last two quantities are taken with respect to O) Then, V3i = 1 1 n i r dSi = n i ri D i Si 3 3 (765)

/2 /3

// Demonstrate a SortedList<TK, TV> using System; using SystemCollectionsGeneric; class GenSLDemo { static void Main() { // Create a sorted SortedList for // employee names and salary SortedList<string, double> sl = new SortedList<string, double>();

Part II:

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We calculate the polygon area Di and its centroid ri in a plane de ned by the polygon, using the method applied to 2-D regions, as outlined earlier in this subsection By subtracting twice the rightmost-side of Eq (763) from the middle one, we readily obtain an expression for qO as a summation of terms qO having the form 3 3i

// Add elements to the collection slAdd("Butler, John", 73000); slAdd("Swartz, Sarah", 59000); slAdd("Pyke, Thomas", 45000); slAdd("Frank, Ed", 99000); // Get a collection of the keys ICollection<string> c = slKeys; // Use the keys to obtain the values foreach(string str in c) ConsoleWriteLine("{0}, Salary: {1:C}", str, sl[str]); ConsoleWriteLine(); } }

SOLUTION Since cos x is the derivative of sin x, it is natural to attempt the substitution u = sin x Then du = cos x dx [Explain why it would be a bad idea to let u = cos x] We rst treat the improper integral We nd that cos x dx = sin x du = log |u| + C u

The output is shown here:

O q 3i = -

Butler, John, Salary: $73,00000 Frank, Ed, Salary: $99,00000 Pyke, Thomas, Salary: $45,00000 Swartz, Sarah, Salary: $59,00000

Stack<T> is the generic equivalent of the non-generic Stack class Stack<T> supports a first-in, last-out stack It implements the ICollection, IEnumerable, and IEnumerable<T> interfaces Stack<T> directly implements the Clear( ), Contains( ), and CopyTo( ) methods defined by ICollection<T> (The Add( ) and Remove( ) methods are not supported, nor is the IsReadOnly property) Stack<T> is a dynamic collection that grows as needed to accommodate the elements it must store It defines the following constructors: public Stack( ) public Stack(int capacity) public Stack(IEnumerable<T> c) The first form creates an empty stack with a default initial capacity The second form creates an empty stack with the initial capacity specified by capacity The third form creates a stack that contains the elements of the collection specified by c In addition to the methods defined by the interfaces that it implements (and those methods defined by ICollection<T> that it implements on its own), Stack<T> defines the methods shown in Table 24-19 Stack<T> works just like its non-generic counterpart To put an object on the top of the stack, call Push( ) To remove and return the top element, call Pop( ) You can use Peek( ) to return, but not remove, the top object An InvalidOperationException is thrown if you call Pop( ) or Peek( ) when the invoking stack is empty

(766)

24:

Now we resubstitute the x-expressions to obtain cos x dx = log | sin x| + C sin x Finally we can evaluate the original de nite integral:

Method public T Peek( ) public T Pop( ) public void Push(T v) public T[ ] ToArray( ) public void TrimExcess( )

The second integral of Eq (766) is readily identi ed as IOi the second moment of D polygon Si Hence, 1 O O q 3i = - n i I D i 2 (767)

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