![]() The following snippet demonstrates how PriorityQueue can be used in simulating both MaxHeap and MinHeap. The priority queue is now ready for either the removal of its next highest priority item or the insertion of a new item.īelow is a partial implementation of a max heap that can serve as a priority queue, focusing on the removal of the maximum item in the heap (i.e. PriorityQueue class in JavaSE API can be used to implement heaps easily and efficiently. Inserting elements and removing one with the largest key in O(log2n) time. Seeing $K \gt H$, its only child, we know heap order has now been restored. In Scala, the PriorityQueue class uses max-heaps. & T & S & R & N & P & O & A & E & I & H & K\\\hlineĪs our first step, we exchange the item at index $1$ (which has highest priority) with the item at index $n$. We start with the heap of $n=11$ elements described by the following array,Ġ & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11\\\hline The poll () method returns and removes the value at the root node. We can use the peek () method to display the element from the root node in a heap. The class implements the min-heap by default, and we can use the reverseOrder () method from Collections to implement the max-heap. ![]() The corresponding changes made in the associated array are shown on the right. We can use the PriorityQueue class to implement the heaps in Java. The short description of sinking is this: as long as the item has a greater child, we exchange it with its greatest child.Īs a concrete example, consider the sequence of images shown below that describe the dequeuement of $T$ from a priority queue with the max heap representation given. Fortunately, we can restore the heap order through a process known as sinking the item. The only down side of doing this is that this item might be smaller than one or both of its children, in which case the heap order of the tree has been violated. If we move the last element in the array (the right-most leaf in the deepest level of the tree), the tree is again made complete. For example, doctors in a hospital emergency room often choose to see next the most critical patient rather than the one who arrived first. Of course, filling the hole made by our removal of the maximum element by moving another item in the heap to its location only serves to create a hole elsewhere - except in one case. Heaps and Priority Queues ¶ There are many situations, both in real life and in computing applications, where we wish to choose the next most important from a collection of people, tasks, or objects. We have to keep the heap in the form of a complete binary tree, so upon removal of this element we'll have to replace it with something. As such, every parent must be greater than or equal to its children.Ĭonsequently, the item with highest priority will thus be at index $1$ in the array. To keep things simple, let us assume the priority queue in question uses a max heap. Let us consider the case of dequeueing first. If we are to use a heap as a priority queue, then we need mechanisms for enqueueing (inserting) and dequeueing (removing) items from the collection.
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