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Figure 28-7. With five script lines, you have programmed your first graphic. By default, Smile did not refresh the window. It is designed that way so you can avoid useless or disgraceful updates. To request that the window refresh explicitly, use the following: draw w Now you ll go further with the text-drawing experiments.

Figure 11-8 shows the binary tree after the remainder of the word list has been added. Do you understand how this scheme works What would the binary tree look like if coulomb was the first word on the list The tree would have no left children and would lean heavily to the right. What if yokel was the first word entered As you can see, this particular use of binary trees depends on the order of the data. Randomized data that starts with a value close to the average produces a balanced tree. If the words had been entered in alphabetical order, you would have ended up with a binary tree that looked like a linked list.

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First you have to position the text. So, click in the form under the Name prompt; the toolbar of the window displays the values for x and y values close to 55 and 702, respectively (see Figure 28-8).

Now that your word list is stored in the binary tree, the next step is to look up a word in the tree. This is known as searching the tree. Suppose you wanted to look up the word tortuous in your tree. You d start with the root node, comparing tortuous with opulent. Since tortuous is greater than opulent, you d follow the right pointer to salubrious. You d follow this algorithm down to yokel and finally tortuous. Searching a binary tree is typically much faster than searching a linked list. In a linked list, you search through your list of nodes, one at a time, until you find the node you are looking for. On average, you ll end up searching half of the list. In a list of 100 nodes, you ll end up checking 50 nodes on average. In a list of 1,000 nodes, you ll end up checking 500 nodes on average. In the worst possible case, you d end up searching all 1,000 nodes.

Figure 28-8. The graphic window s toolbar displays information regarding the location of the mouse pointer. A command analogous to MoveTo sets the position of the pen for writing. This is TextMoveTo. The following script uses the simplest command for writing text, DrawText (see Figure 28-9): BeginFrontFigure(w) TextMoveTo({55, 702}) DrawText("John Smith") EndFrontFigure() draw w

In a balanced binary tree, you reduce the search space in half each time you check a node. Without getting into the mathematics check Donald Knuth s The Art of Computer Programming, Volume 3: Sorting and Searching (Addison-Wesley 1998) for more information the maximum number of nodes searched is approximately log2n, where n is the number of nodes in the tree. On average, you ll search log2n/2 nodes. In a list of 100 nodes, you ll end up searching 3.32 nodes on average. In a list of 1,000 nodes, you ll end up checking about 5 nodes on average. As you can see, a binary tree provides a significant performance advantage over a linked list. A binary tree that contained just words may not be that interesting, but imagine that these words were names of great political leaders. Each node might contain a leader s name, biographical information, perhaps a pointer to another data structure containing great speeches. The value, name, or word that determines the order of the tree is said to be the key. You don t always search a tree based on the key. Sometimes, you ll want to step through every node in the tree. For example, suppose your tree contained the name and birth date of each of the presidents of the United States. Suppose also that the tree was built using each president s last name as a key. Now suppose you wanted to compose a list of all presidents born in July. In this case, searching the tree alphabetically won t do you any good. You ll have to search every node in the tree. This is where recursion comes in.

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