Implementing an Ordered List
In order to implement the ordered list, we must remember that the relative positions of the items are based on some underlying characteristic. The ordered list of integers given above (17, 26, 31, 54, 77, and 93) can be represented by a linked structure as shown in Figure 15. Again, the node and link structure is ideal for representing the relative positioning of the items.
To implement the OrderedList
class, we will use the same technique as seen previously with unordered lists. Once again, an empty list will be denoted by a head
reference to None
(see Listing 8).
Listing 8
class OrderedList: def __init__(self): self.head = None
As we consider the operations for the ordered list, we should note that the isEmpty
and size
methods can be implemented the same as with unordered lists since they deal only with the number of nodes in the list without regard to the actual item values. Likewise, the remove
method will work just fine since we still need to find the item and then link around the node to remove it. The two remaining methods, search
and add
, will require some modification.
The search of an unordered linked list required that we traverse the nodes one at a time until we either find the item we are looking for or run out of nodes (None
). It turns out that the same approach would actually work with the ordered list and in fact in the case where we find the item it is exactly what we need. However, in the case where the item is not in the list, we can take advantage of the ordering to stop the search as soon as possible.
For example, Figure 16 shows the ordered linked list as a search is looking for the value 45. As we traverse, starting at the head of the list, we first compare against 17. Since 17 is not the item we are looking for, we move to the next node, in this case 26. Again, this is not what we want, so we move on to 31 and then on to 54. Now, at this point, something is different. Since 54 is not the item we are looking for, our former strategy would be to move forward. However, due to the fact that this is an ordered list, that will not be necessary. Once the value in the node becomes greater than the item we are searching for, the search can stop and return False
. There is no way the item could exist further out in the linked list.
Listing 9 shows the complete search
method. It is easy to incorporate the new condition discussed above by adding another boolean variable, stop
, and initializing it to False
(line 4). While stop
is False
(not stop
) we can continue to look forward in the list (line 5). If any node is ever discovered that contains data greater than the item we are looking for, we will set stop
to True
(lines 9–10). The remaining lines are identical to the unordered list search.
Listing 9
def search(self,item): current = self.head found = False stop = False while current != None and not found and not stop: if current.getData() == item: found = True else: if current.getData() > item: stop = True else: current = current.getNext() return found
The most significant method modification will take place in add
. Recall that for unordered lists, the add
method could simply place a new node at the head of the list. It was the easiest point of access. Unfortunately, this will no longer work with ordered lists. It is now necessary that we discover the specific place where a new item belongs in the existing ordered list.
Assume we have the ordered list consisting of 17, 26, 54, 77, and 93 and we want to add the value 31. The add
method must decide that the new item belongs between 26 and 54. Figure 17 shows the setup that we need. As we explained earlier, we need to traverse the linked list looking for the place where the new node will be added. We know we have found that place when either we run out of nodes (current
becomes None
) or the value of the current node becomes greater than the item we wish to add. In our example, seeing the value 54 causes us to stop.
As we saw with unordered lists, it is necessary to have an additional reference, again called previous
, since current
will not provide access to the node that must be modified. Listing 10 shows the complete add
method. Lines 2–3 set up the two external references and lines 9–10 again allow previous
to follow one node behind current
every time through the iteration. The condition (line 5) allows the iteration to continue as long as there are more nodes and the value in the current node is not larger than the item. In either case, when the iteration fails, we have found the location for the new node.
The remainder of the method completes the twostep process shown in Figure 17. Once a new node has been created for the item, the only remaining question is whether the new node will be added at the beginning of the linked list or some place in the middle. Again, previous == None
(line 13) can be used to provide the answer.
Listing 10
def add(self,item): current = self.head previous = None stop = False while current != None and not stop: if current.getData() > item: stop = True else: previous = current current = current.getNext() temp = Node(item) if previous == None: temp.setNext(self.head) self.head = temp else: temp.setNext(current) previous.setNext(temp)
The OrderedList
class with methods discussed thus far can be found in ActiveCode 1. We leave the remaining methods as exercises. You should carefully consider whether the unordered implementations will work given that the list is now ordered.
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 Basic Data Structures

Objectives

What Are Linear Structures?

What is a Stack?

The Stack Abstract Data Type

Implementing a Stack in Python

What Is a Queue?

The Queue Abstract Data Type

Implementing a Queue in Python

What Is a Deque?

The Deque Abstract Data Type

Implementing a Deque in Python

Lists

The Unordered List Abstract Data Type

Implementing an Unordered List: Linked Lists

The Ordered List Abstract Data Type

Implementing an Ordered List

Vocabulary and Definitions

 Sorting and Searching
 Trees and Tree Algorithms
 Graphs and Graph Algorithms