1	Binary Search Trees One of the tree applications in Chapter 9 is binary search trees. In Chapter 9, binary search trees are used to implement bags and sets. This presentation illustrates how another data type called a dictionary is implemented with binary search trees.
2	The Dictionary Data Type A dictionary is a collection of items, similar to a bag. But unlike a bag, each item has a string attached to it, called the item's key.
3	The Dictionary Data Type A dictionary is a collection of items, similar to a bag. But unlike a bag, each item has a string attached to it, called the item's key.
4	The Dictionary Data Type A dictionary is a collection of items, similar to a bag. But unlike a bag, each item has a string attached to it, called the item's key.
5	The Dictionary Data Type The insertion method for a dictionary has two parameters.
6	The Dictionary Data Type When you want to retrieve an item, you specify the key...
7	The Dictionary Data Type
8	The Dictionary Data Type We"ll look at how a binary tree can be used as the internal storage mechanism for the dictionary.
9	A Binary Search Tree of States The data in the dictionary will be stored in a binary tree, with each node containing an item and a key.
10	A Binary Search Tree of States Storage rules: Every key to the left of a node is alphabetically before the key of the node.
11	A Binary Search Tree of States Storage rules: Every key to the left of a node is alphabetically before the key of the node.
12	A Binary Search Tree of States Storage rules: Every key to the left of a node is alphabetically before the key of the node. Every key to the right of a node is alphabetically after the key of the node.
13	A Binary Search Tree of States Storage rules: Every key to the left of a node is alphabetically before the key of the node. Every key to the right of a node is alphabetically after the key of the node.
14	Retrieving Data Start at the root. If the current node has the key, then stop and retrieve the data. If the current node's key is too large, move left and repeat 1-3. If the current node's key is too small, move right and repeat 1-3.
15	Retrieve " New Hampshire" Start at the root. If the current node has the key, then stop and retrieve the data. If the current node's key is too large, move left and repeat 1-3. If the current node's key is too small, move right and repeat 1-3.
16	Retrieve "New Hampshire" Start at the root. If the current node has the key, then stop and retrieve the data. If the current node's key is too large, move left and repeat 1-3. If the current node's key is too small, move right and repeat 1-3.
17	Retrieve "New Hampshire" Start at the root. If the current node has the key, then stop and retrieve the data. If the current node's key is too large, move left and repeat 1-3. If the current node's key is too small, move right and repeat 1-3.
18	Retrieve "New Hampshire" Start at the root. If the current node has the key, then stop and retrieve the data. If the current node's key is too large, move left and repeat 1-3. If the current node's key is too small, move right and repeat 1-3.
19	Adding a New Item with a Given Key Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
20	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
21	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
22	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
23	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
24	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
25	Adding Pretend that you are trying to find the key, but stop when there is no node to move to. Add the new node at the spot where you would have moved to if there had been a node.
26	Adding
27	Adding
28	Removing an Item with a Given Key Find the item. If necessary, swap the item with one that is easier to remove. Remove the item.
29	Removing "Florida" Find the item.
30	Removing "Florida"
31	Removing "Florida"
32	Removing "Florida" If necessary, do some rearranging.
33	Removing "Florida" If necessary, do some rearranging.
34	Removing "Florida" If necessary, do some rearranging.
35	Removing "Florida" If necessary, do some rearranging.
36	Removing "Florida" If necessary, do some rearranging.
37	Removing "Florida"
38	Removing "Florida"
39	Removing an Item with a Given Key Find the item. If the item has a right child, rearrange the tree: Find smallest item in the right subtree Copy that smallest item onto the one that you want to remove Remove the extra copy of the smallest item (making sure that you keep the tree connected) else just remove the item.
40	Summary Binary search trees are a good implementation of data types such as sets, bags, and dictionaries. Searching for an item is generally quick since you move from the root to the item, without looking at many other items. Adding and deleting items is also quick. But as you’ll see later, it is possible for the quickness to fail in some cases -- can you see why?
41	THE END