• Min Heap Data Structure
• Min Max In C

A paper that no one seems to have mentioned is the original proposition for Min-Max-Heaps: I've implemented a min-max heap from this paper twice (not in C) and found it fairly trivial. An improvement, which I haven't ever implemented, is a Min-Max-Fine-Heap.

Example of a max-heap with node keys being integers from 1 to 100 In, a heap is a specialized -based that satisfies the heap property: if P is a parent of C, then the key (the value) of P is either greater than or equal to ( in a max heap) or less than or equal to ( in a min heap) the key of C. The node at the 'top' of the heap (with no parents) is called the root node. The heap is one maximally efficient implementation of an called a, and in fact priority queues are often referred to as 'heaps', regardless of how they may be implemented. A common implementation of a heap is the, in which the tree is a binary tree (see figure). The heap data structure, specifically the binary heap, was introduced by in 1964, as a data structure for the sorting algorithm.

Heaps are also crucial in several efficient such as. In a heap, the highest (or lowest) priority element is always stored at the root. A heap is not a sorted structure and can be regarded as partially ordered. As visible from the heap-diagram, there is no particular relationship among nodes on any given level, even among the siblings. When a heap is a complete binary tree, it has a smallest possible height—a heap with N nodes and for each node a branches always has log a N height.

A heap is a useful data structure when you need to remove the object with the highest (or lowest) priority. Note that, as shown in the graphic, there is no implied ordering between siblings or cousins and no implied sequence for an (as there would be in, e.g., a ). The heap relation mentioned above applies only between nodes and their parents, grandparents, etc. The maximum number of children each node can have depends on the type of heap, but in many types it is at most two, which is known as a binary heap.

Contents. Operations The common operations involving heaps are: Basic.

find-max or find-min: find a maximum item of a max-heap, or a minimum item of a min-heap, respectively (a.k.a. ). insert: adding a new key to the heap (a.k.a., push ). extract-max or extract-min: returns the node of maximum value from a max heap or minimum value from a min heap after removing it from the heap (a.k.a., pop ). delete-max or delete-min: removing the root node of a max heap or min heap, respectively. replace: pop root and push a new key.

More efficient than pop followed by push, since only need to balance once, not twice, and appropriate for fixed-size heaps. Creation. create-heap: create an empty heap. heapify: create a heap out of given array of elements. merge ( union): joining two heaps to form a valid new heap containing all the elements of both, preserving the original heaps. meld: joining two heaps to form a valid new heap containing all the elements of both, destroying the original heaps. Inspection.

size: return the number of items in the heap. is-empty: return true if the heap is empty, false otherwise. Internal. increase-key or decrease-key: updating a key within a max- or min-heap, respectively. delete: delete an arbitrary node (followed by moving last node and sifting to maintain heap). sift-up: move a node up in the tree, as long as needed; used to restore heap condition after insertion.

Called 'sift' because node moves up the tree until it reaches the correct level, as in a. sift-down: move a node down in the tree, similar to sift-up; used to restore heap condition after deletion or replacement. Implementation Heaps are usually implemented in an array (fixed size or ), and do not require pointers between elements.

After an element is inserted into or deleted from a heap, the heap property may be violated and the heap must be balanced by internal operations. Example of a complete binary max-heap with node keys being integers from 1 to 100 and how it would be stored in an array. May be represented in a very space-efficient way (as an ) using an alone. The first (or last) element will contain the root.

The next two elements of the array contain its children. The next four contain the four children of the two child nodes, etc. Thus the children of the node at position n would be at positions 2n and 2n + 1 in a one-based array, or 2n + 1 and 2n + 2 in a zero-based array. This allows moving up or down the tree by doing simple index computations.

Balancing a heap is done by sift-up or sift-down operations (swapping elements which are out of order). As we can build a heap from an array without requiring extra memory (for the nodes, for example), can be used to sort an array in-place. Different types of heaps implement the operations in different ways, but notably, insertion is often done by adding the new element at the end of the heap in the first available free space. This will generally violate the heap property, and so the elements are then sifted up until the heap property has been reestablished. Similarly, deleting the root is done by removing the root and then putting the last element in the root and sifting down to rebalance. Thus replacing is done by deleting the root and putting the new element in the root and sifting down, avoiding a sifting up step compared to pop (sift down of last element) followed by push (sift up of new element). Construction of a binary (or d-ary) heap out of a given array of elements may be performed in linear time using the classic, with the worst-case number of comparisons equal to 2 N − 2 s 2( N) − e 2( N) (for a binary heap), where s 2( N) is the sum of all digits of the binary representation of N and e 2( N) is the exponent of 2 in the prime factorization of N.

This is faster than a sequence of consecutive insertions into an originally empty heap, which is log-linear (or ). Variants. Comparison of theoretic bounds for variants In the following O( f) is an asymptotic upper bound and Θ( f) is an asymptotically tight bound (see ). Function names assume a min-heap.

Operation find-min Θ(1) Θ(1) Θ(log n) Θ(1) Θ(1) Θ(1) Θ(1) Θ(1) delete-min Θ(log n) Θ(log n) Θ(log n) O(log n) O(log n) O(log n) O(log n) O(log n) insert O(log n) Θ(log n) Θ(1) Θ(1) Θ(1) Θ(1) Θ(1) Θ(1) decrease-key Θ(log n) Θ( n) Θ(log n) Θ(1) o(log n) Θ(1) Θ(1) Θ(1) merge Θ( n) Θ(log n) O(log n) Θ(1) Θ(1) Θ(1) Θ(1) Θ(1). Black (ed.), Paul E. Entry for heap in.

Online version. U.S., 14 December 2004.

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FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science. Frederickson, Greg N. (1993), 'An Optimal Algorithm for Selection in a Min-Heap', (PDF), 104 (2), Academic Press, pp. 197–214,: External links Wikimedia Commons has media related to.

Min Heap Data Structure

The Wikibook has a page on the topic of:. at Wolfram MathWorld. of how the basic heap algorithms work.

Min Max In C

Hi, The std map is typically implemented as a binary search tree, the complexity of the construction is n.log(n), once constructed you basically have a sorted list, so finding the smallest C numbers means simply iterating from beginning C times. So total complexity is n.log(n) + C while the heap solution complexity is n + C.log(n). Please note that there is a heap like implementation in stl called: priorityqueue. This article point is to share my own implementation and explain the data structure and its complexity in general. Last Visit: 31-Dec-99 19:00 Last Update: 11-Feb-18 8:37 1 General News Suggestion Question Bug Answer Joke Praise Rant Admin Use Ctrl+Left/Right to switch messages, Ctrl+Up/Down to switch threads, Ctrl+Shift+Left/Right to switch pages.