Data Structures and Algorithms in Java[1].pdf - Fulvio Frisone

Figure 8.11: Visual justification of the linear running
time of bottom-up heap con struction, where the
paths associated with the internal nodes have been
highlighted with alternating colors. For example, the
path associated with the root consists of the nodes
storing keys 4, 6, 7, and 11. Also, the path associated
with the right child of the root consists of the internal
nodes storing keys 6, 20, and 23.
To summarize, Proposition 8.7 states that the running time for the first phase of
heap-sort can be reduced to be O(n). Unfortunately, the running time of the
second phase of heap-sort cannot be made asymptotically better than O(nlogn)
(that is, it will always be Ω(nlogn) in the worst case). We will not justify this
lower bound until Chapter 11, however. Instead, we conclude this chapter by
discussing a design pattern that allows us to extend the priority queue ADT to
have additional functionality.
8.4 Adaptable Priority Queues
The methods of the priority queue ADT given in Section 8.1.3 are sufficient for most
basic applications of priority queues, such as sorting. However, there are situations
where additional methods would be useful, as shown in the scenarios below, which
refer to the standby airline passenger application.
• A standby passenger with a pessimistic attitude may become tired of waiting and
decide to leave ahead of the boarding time, requesting to be removed from the
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