Search results
Results from the WOW.Com Content Network
Then, each subsequent item of the collection may replace the largest or smallest element in the heap if it is smaller or larger than this element. The algorithm's memory usage is superior to heapselect (the former only holds elements in memory at a time while the latter requires manipulating the entire dataset into memory). Running time depends ...
Selection algorithms: A heap allows access to the min or max element in constant time, and other selections (such as median or kth-element) can be done in sub-linear time on data that is in a heap. [24] Graph algorithms: By using heaps as internal traversal data structures, run time will be reduced by polynomial order.
One of the two elements in the second level, which is a max (or odd) level, is the greatest element in the min-max heap Let x {\displaystyle x} be any node in a min-max heap. If x {\displaystyle x} is on a min (or even) level, then x . k e y {\displaystyle x.key} is the minimum key among all keys in the subtree with root x {\displaystyle x} .
The procedure for deleting the root from the heap (effectively extracting the maximum element in a max-heap or the minimum element in a min-heap) while retaining the heap property is as follows: Replace the root of the heap with the last element on the last level. Compare the new root with its children; if they are in the correct order, stop.
When it is removed and placed at the end of the list, the heap is rearranged so the largest element remaining moves to the root. Using the heap, finding the next largest element takes O(log n ) time, instead of O( n ) for a linear scan as in simple selection sort.
find-min: simply return the top element of the heap. meld: compare the two root elements, the smaller remains the root of the result, the larger element and its subtree is appended as a child of this root. insert: create a new heap for the inserted element and meld into the original heap.
I personally find the "create-heap" operation definition ("create-heap: create an empty heap") a bit useless, adding to the confusion around "heapify" ("create a heap out of given array of elements"). To me, "create-heap" (what I would call "build-heap") should use the current definition of "heapify" and a new one presented based on CLRS ...
Using pointers, an in-place heap algorithm [2] allocates a min-heap of pointers into the input arrays. Initially these pointers point to the smallest elements of the input array. The pointers are sorted by the value that they point to. In an O(k) preprocessing step the heap is created using the standard heapify procedure.