Binary heapA binary heap is a heap data structure that takes the form of a binary tree. Binary heaps are a common way of implementing priority queues. The binary heap was introduced by J. W. J. Williams in 1964, as a data structure for heapsort. A binary heap is defined as a binary tree with two additional constraints: Shape property: a binary heap is a complete binary tree; that is, 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.
Heap (data structure)In computer science, a heap is a specialized tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is a parent node of C, then the key (the value) of P is greater than or equal to the key of C. In a min heap, the key of P is less than or equal to 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 abstract data type called a priority queue, and in fact, priority queues are often referred to as "heaps", regardless of how they may be implemented.
HeapsortIn computer science, heapsort is a comparison-based sorting algorithm. Heapsort can be thought of as an improved selection sort: like selection sort, heapsort divides its input into a sorted and an unsorted region, and it iteratively shrinks the unsorted region by extracting the largest element from it and inserting it into the sorted region. Unlike selection sort, heapsort does not waste time with a linear-time scan of the unsorted region; rather, heap sort maintains the unsorted region in a heap data structure to more quickly find the largest element in each step.
Weak heapIn computer science, a weak heap is a data structure for priority queues, combining features of the binary heap and binomial heap. It can be stored in an array as an implicit binary tree like a binary heap, and has the efficiency guarantees of binomial heaps. A sorting algorithm using weak heaps, weak-heapsort, uses a number of comparisons that is close to the theoretical lower bound on the number of comparisons required to sort a list, so is particularly useful when comparison is expensive, such as when comparing strings using the full Unicode collation algorithm.
Priority queueIn computer science, a priority queue is an abstract data-type similar to a regular queue or stack data structure. Each element in a priority queue has an associated priority. In a priority queue, elements with high priority are served before elements with low priority. In some implementations, if two elements have the same priority, they are served in the same order in which they were enqueued. In other implementations, the order of elements with the same priority is undefined.
