bottom-up heap construction
Bottom-up heap construction is a technique used to build a heap data structure from a given array of elements. In this approach, the elements are initially treated as individual heaps of size one. Then, pairs of heaps are merged together and further merged until a single heap is formed. This method starts by dividing the array into subarrays of size one, each representing a heap by itself. The adjacent pairs of heaps are then merged together to form larger heaps. This process continues iteratively, merging adjacent pairs of heaps until only one heap remains, which is the desired heap. The merging of two heaps involves comparing their root elements and rearranging them to satisfy the heap property, which ensures that every parent node is greater (or smaller) than its children. This process is repeated until all elements are merged into a single heap, resulting in an efficient bottom-up heap construction. The bottom-up approach saves time by directly constructing a proper heap structure, as opposed to the traditional top-down approach that inserts elements one-by-one into an initially empty heap.
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