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In initializing a Popup in code with content that is, setting its Child property you should avoid creating and initializing the entire content in code, especially if the content represents a fairly complex UI. You almost always want to take advantage of tools like Expression Blend to do that. In the recipe code sample that we are about to discuss, we simply need a single ListBox to be the only child of the Popup, as you will see soon. Therefore, we are not burdened with creating an overtly complex UI in code. However, in the event you are faced with this challenge elsewhere and want to avoid the need to code an UI tree, one approach you can take is to use the ContentControl and data templates shown here: Popup popupProducts = new Popup(); ContentControl popupContent = new ContentControl(); popupContent.ContentTemplate = this.Resources["dtPopupData"] as DataTemplate; popupProducts.Child = popupContent; popupContent.DataContext = ProdList; We set the ContentTemplate of the ContentControl to a data template resource, initialize Popup.Child with the ContentControl, and then bind the ContentControl to appropriate data. This affords you the opportunity to host a fairly complex UI in a Popup but design it as a data template using a tool like Expression Blend, thus expressing it as XAML and keeping your code free of significant element creation and initialization logic.

Figure 1-4. The control toolbox in Expression Blend The Objects and Timeline area to the immediate right of the toolbox provides a place to create and manage animation storyboards, but more importantly for us right now, it shows the object hierarchy in XAML. After creating our application, we see [UserControl] and LayoutRoot. Click [UserControl] to highlight it and then click Properties in the top-right portion of the screen. The control with the gray highlight is the control that shows up in the Properties pane (see Figure 1-5). Go to the Layout section of the Properties pane and set the Width and Height properties of the UserControl to 900 and 100, respectively, as shown in Figure 1-6.

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Now that we have an overview of some important orders of growth, we can formulate two simple rules: In a sum, only the dominating summand matters. For example, (n2 + n3 + 42) = (n3). In a product, constant factors don t matter. For example, (4.2n lg n) = (n lg n). In general, we try to keep the asymptotic expressions as simple as possible, eliminating as many unnecessary parts as we can. For O and , there is a third principle we usually follow: Keep your upper or lower limits tight. In other words, we try to make the upper limits low and the lower limits high. For example, although n2 might technically be O(n3), we usually prefer the tighter limit, O(n2). In most cases, though, the best thing is to simply use . A practice that can make asymptotic expressions even more useful is that of using them instead of actual values, in arithmetic expressions. Although this is technically incorrect (each asymptotic expression yields a set of functions, after all), it is quite common. For example, (n2) + (n3) simply means f + g, for some (unknown) functions f and g, where f is (n2) and g is (n3). Even though we cannot find the exact sum f + g, because we don t know the exact functions, we can find the asymptotic expression to cover it, as illustrated by the following two bonus rules: (f) + (g) = (f + g) (f) (g) = (f g)

The code sample for this recipe uses the Popup type to build a cascading menu that looks similar to the ones in Visual Studio. Figure 5-18 shows the resulting menu look and feel. Keep in mind that the sample does not aim to illustrate a full-scale menu framework but rather just a usage pattern for the Popup type. However, if you do undertake the building of a menu system using Silverlight, we anticipate you will be using the Popup type, and the code in this sample will most likely come in handy.

Let s take a look at some very simple programs and see whether we can determine their asymptotic running times. To begin with, let s consider programs where the (asymptotic) running time varies only with the problem size, not the specifics of the instance in question. (The next section deals with what happens if the actual contents of the instances matter to the running time.) This means, for example, that if statements are rather irrelevant for now. What s important is loops, in addition to straightforward code blocks. Function calls don t really complicate things; they just calculate the complexity for the call and insert it at the right place.

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