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The public properties available in SortedList are those defined by the interfaces that it implements As is the case with Hashtable, two especially important properties are Keys and Values because they let you obtain a read-only collection of a SortedList s keys or values They are specified by IDictionary and are shown here: public virtual ICollection Keys { get; } public virtual ICollection Values { get; } The order of the keys and values reflects that of the SortedList Like Hashtable, a SortedList stores key/value pairs in the form of a DictionaryEntry structure, but you will usually access the keys and values individually using the methods and properties defined by SortedList The following program demonstrates SortedList It reworks and expands the Hashtable demonstration program from the previous section, substituting SortedList When you examine the output, you will see that the SortedList version is sorted by key

(724)

// Demonstrate a SortedList using System; using SystemCollections;

d Tan 1 [ln(x 2 + x)] dx d Sec 1 (tan x) (d) dx 10 Calculate each of these integrals (a) 2x x dx 1 + x4

Part II:

(725)

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class SLDemo { static void Main() { // Create a sorted SortedList SortedList sl = new SortedList(); // Add elements to the table slAdd("house", "Dwelling"); slAdd("car", "Means of transport"); slAdd("book", "Collection of printed words"); slAdd("apple", "Edible fruit"); // Can also add by using the indexer sl["tractor"] = "Farm implement"; // Get a collection of the keys ICollection c = slKeys; // Use the keys to obtain the values ConsoleWriteLine("Contents of list via indexer"); foreach(string str in c) ConsoleWriteLine(str + ": " + sl[str]); ConsoleWriteLine(); // Display list using integer indexes ConsoleWriteLine("Contents by integer indexes"); for(int i=0; i < slCount; i++) ConsoleWriteLine(slGetByIndex(i)); ConsoleWriteLine(); // Show integer indexes of entries ConsoleWriteLine("Integer indexes of entries"); foreach(string str in c) ConsoleWriteLine(str + ": " + slIndexOfKey(str)); } }

The output is shown here:

(b) (c)

with similar de nitions for y and y Conditions in Eq (724) can be satis ed by resorting i i to a periodic parametric cubic spline, as discussed in Rogers (2001) and outlined below

Contents of list via indexer apple: Edible fruit book: Collection of printed words car: Means of transport house: Dwelling tractor: Farm implement Contents by integer indexes Edible fruit Collection of printed words Means of transport Dwelling Farm implement

24:

If cusps are allowed at the endpoints P1(x1, y1) and P2(x2, y2), then the slope and curvature conditions of Eq (724) must be relaxed

Integer indexes of entries apple: 0 book: 1 car: 2 house: 3 tractor: 4

We learned in Section 45 that the integral of the sum of two functions is the sum of the respective integrals But what of the integral of a product The following reasoning is incorrect: x 2 dx = x x dx = x dx x dx

As most readers know, a stack is a first-in, last-out list To visualize a stack, imagine a stack of plates on a table The first plate put down is the last one to be picked up The stack is one of the most important data structures in computing It is frequently used in system software, compilers, and AI-based backtracking routines, to name just a few examples The collection class that supports a stack is called Stack It implements the ICollection, IEnumerable, and ICloneable interfaces Stack is a dynamic collection that grows as needed to accommodate the elements it must store Each time the capacity must be increased, the capacity is doubled Stack defines the following constructors: public Stack( ) public Stack(int capacity) public Stack(ICollection c) The first form creates an empty stack 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 and an initial capacity equal to the number of elements In addition to the methods defined by the interfaces that it implements, Stack defines the methods shown in Table 24-7 In general, here is how you use Stack 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

Let (x, y) be the coordinates of one point of the cam pro le The curve describing the cam pro le can be represented in parametric form as x( p) = Axi ( p - pi ) + Bxi ( p - pi ) + Cxi ( p - pi ) + Dxi

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