Now, let’s apply to an example to understand how this process works. It keeps moving down the tree until the heap property is restored. Then, this item is compared with the child nodes and swap with the greater one. When removing the root node, we replace it with the last item of the priority queue. Next, we can remove the maximum element from the priority queue. As we know, the root node is the item with the highest priority in a max heap. If we add to the priority queue, we end up with: We notice that is greater than its parent, so we swap them: Then, is still greater than its new parent, so we swap them: Now, we notice that is smaller than its parent, so we stop and reach our priority queue: The following code shows the details of the insertion function: Let’s go through an example to understand the insertion process. This process continues until the new item is placed in the correct position. If it is found greater than its parent node, elements are swapped. At first, we insert the new item at the end of the priority queue. If we want to add a new node to a binary heap, we need to ensure that our two properties of the heap are maintained after the new node is added. The item at the root of the heap has the highest priority among all elements. We’ll use a binary heap to maintain a max-priority queue. The common operations that we can perform on a priority queue include insertion, deletion, and peek.
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