Priority Queue

Priority queues are useful data structures in simulations particularly for maintaining a set of future events ordered by time so that we can quickly retrieve what the next thing to happen as They are called "priority" queues because they enable you to retrieve items not by the insertion time (as in stack or queue), nor by a key match (as in a dictionary), but by which item has the highest priority of retrieval

If your application performs no insertions after the first query, there is no need for an explicit priority queue. Simply sort the records by priority and precede from top to bottom, maintaining a pointer to the last record deleted. We have the following basic priority queue choices;

(1)   Sorted array or list. In a sorted array, it is very efficient to find and delete the smallest element. However maintaining sortedness makes the insertion of new elements slow. Sorted arrays are suitable where there will be a few insertions into the priority queue.

(2)   Binary heaps. This simple elegant data structure supports both insertion and extract min in O (log n) time each. Heaps maintain an implicit binary free structure in an array, such that the key of the root of any sub tree is less than that of all its descendents. Thus the minimum key is always at the root of the heap. New keys can be inserted by placing them at an open leaf and relocating the elements whenever until it sits at its proper place them at an open leaf and relocation the elements upwards until it sits at its proper place in the partial order. Binary heaps are the right answer whenever you know an upper bound on the number of items in your priority queue, since you must specify the array size at creation time.

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