The priority queue the minimum item in Java

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Priority queue model: Only the minimum element is accessible
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1 / / PriorityQueue protocol (not the STL version) 2 3 template <class Comparable> 4 class PriorityQueue 5 i 6 public: 7 virtual -PriorityQueue( ) { } / / Destructor
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void insert( const Comparable & x ) = 0; void deleteMin( ) = 0; void deleteMin( Comparable & min ) = 0; const Comparable & findMin( ) const = 0;
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Protocol for typical priority queues (but not the STL version)
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The binary heap implements the priority queue in logarithmic time per operation with little extra space
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An important use of priority queues is event-driven simulation
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A typical priority queue protocol is shown in Figure 716 Note that deleteMin has two forms: One form removes the smallest item, and the second form removes the smallest item but passes that item back to the caller The STL protocol is somewhat different, as we discuss shortly Because the priority queue allows duplicates, it cannot be implemented by a setIt can be implemented by a multiset,but that turns out to be overkill because a multiset supports many more operations than required by a priority queue The penalty for the overkill is typically somewhat slower performance As the priority queue supports only the deleteMin and f indMin operations, we might expect performance that is a compromise between the constant-time queue and the logarithmic time set Indeed, this is the case: The basic priority queue supports all operations in logarithmic worst-case time, uses only an array, supports insertion in constant average time, and is simple to implement and is known as the binary heap This structure is one of the most elegant data structures known In 21 we provide details on the implementation of priority queues An important application of the priority queue is event-driven simulation Consider, for example, a system such as a bank in which customers arrive and wait in line until one of K tellers is available Customer arrival is governed by a probability distribution function, as is the service time (the amount of time it takes a teller to provide complete service to one customer) We are interested in statistics such as how long on average a customer has to wait or how long a line might be
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With certain probability distributions and values of K, we can compute these statistics exactly However, as K gets larger, the analysis becomes considerably more difficult so the use of a computer to simulate the operation of the bank is appealing In this way the bank's officers can determine how many tellers are needed to ensure reasonably smooth service An event-driven simulation consists of processing events The two events here are ( 1 ) a customer arriving and (2) a customer departing, thus freeing up a teller At any point we have a collection of events waiting to happen To run the simulation, we need to determine the next event, this is the event whose time of occurrence is minimum Hence we use a priority queue that extracts the event of minimum time to process the event list efficiently We present a complete discussion and implementation of event-driven simulation in Section 142 We close by mentioning that the STL priority queue uses different conventions than presented here First, a priority queue must be specified by several template parameters leading to an often tortuous declaration because default template parameters do not always work correctly Second, the priority queue does not use standard names such as insert, f indMin,and deleteMin Instead, it uses push,top,and pop and thus easily wins the award for worst method names in a widely used library Finally, it accesses the maximum, rather than the minimum, item The following is a summary of the operations