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Python priority queue heap10/2/2023 ![]() The rules being that all nodes have two children, unless they are the last node to have children in which case they may have one child instead. To iterate over the queue you need to know the rules about where children are stored in the list. They are also used in the Heapsort sorting algorithm and Huffman coding (A Data Compression technique).The PriorityQueue is implemented as binary heap, which is implemented using a list (array) in python. Heaps are crucial in several efficient graph algorithms, such as Dijkstra’s shortest path algorithm and Prim’s algorithm for minimum spanning tree. The following diagram illustrates the process: The idea is to add the new element to the heap’s bottom level and call heapify-up on the last node. Heapify-up is used in push() operation of the binary heap. The complexity of the heapify-up operation is O(log(n)). ![]() The process is repeated till the heap property is fixed. We then call heapify-up on the parent, i.e., heapify-up(PARENT(i)). It does so by comparing A with its parent and swapping the two if the heap property is violated. It converts the binary tree into a heap by moving A up the tree. Heapify-up(i) can be invoked if the parent of an element A violates the heap property. The idea is to replace the heap’s root with the last element on the last level and call heapify-down on the root. Heapify-down is used in pop() operation of the binary heap. The complexity of the heapify-down operation is O(log(n)). It does so by comparing A with its left & right child and swapping A with the smaller child for min-heaps & the larger child for max-heaps, and then calling heapify-down on the corresponding child, i.e., heapify-down(LEFT_CHILD(i)) or heapify-down(RIGHT_CHILD(i)). ![]() It converts the binary tree rooted at index i into a heap by moving A down the tree. Heapify-down(i) can be invoked if element A violates the heap property with its two direct children. It can be implemented as heapify-up and heapify-down. Heapify operation forms the crux of all major heap operations. If i is the index of the current node, then, For a zero-based array, the root node is stored at index 0. The index of the left or the right child of the parent node is simple expressions. The complete binary tree maps the binary tree structure into the array indices, where each array index represents a node. The following diagram shows an array representing a min-heap: We store keys in an array and use their relative positions within that array to represent child-parent relationships. Operations on HeapĪ binary heap is a complete binary tree, but we usually never use a binary tree for implementing heaps. Binary heaps have the smallest possible height of log(n), where n is the total number of nodes in a heap. The highest (or lowest) priority element is always stored at the root in the binary heap. ![]() In a min-heap, the keys of parent nodes are less than or equal to those of the children, and the lowest key is in the root node.In a max-heap, the keys of parent nodes are always greater than or equal to those of the children, and the highest key is in the root node.Heap Property: The key stored in each node is either “greater than or equal to” or “less than or equal to” the keys in the node’s children.Ī heap can be classified further as either a “max-heap” or a “min-heap”.Structural property: A binary heap is a complete binary tree, i.e., all levels of the tree, except possibly the last one (deepest) are fully filled, and, if the last level of the tree is not complete, the nodes of that level are filled from left to right.A common implementation of a heap is the binary heap, which is defined as a binary tree with two additional properties: A heap data structure should not be confused with the heap, a pool of memory used for dynamic memory allocation. Heap data structure can be used to implement a priority queue. pop(): returns and removes the element of S with highest (or lowest) priority – usually an O(log(n)) operation.top() or peek(): returns the element of S with highest (or lowest) priority (but does not modify the queue) – O(1) operation.push(x): inserts an element x in set S – usually an O(log(n)) operation.It basically supports the following operations: If two elements have the same priority, they are served according to their order in the queue. In a priority queue, an element with high priority is served before an element with low priority and vice versa. Priority QueueĪ priority queue is an ADT (Abstract Data Type) for maintaining a set S of elements, with each element having a “priority” associated with it. This article will introduce a significant data structure, priority queue, and discuss how we can implement them using (Binary) Heaps.
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