![]() ![]() They are also used in the Heapsort sorting algorithm and Huffman coding (A Data Compression technique).When using a min/max-heap algorithm, priorities may change. 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.
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