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Heap modeling: Run-time allocations may be abstracted by: their allocation sites (the statement or instruction that performs the allocation, e.g., a call to malloc or an object constructor), a more complex model based on a shape analysis, the type of the allocation, or; one single allocation (this is called heap-insensitivity).
Example of a binary max-heap with node keys being integers between 1 and 100. In computer science, a heap is a tree-based data structure that satisfies the heap property: In a max heap, for any given node C, if P is the parent node of C, then the key (the value) of P is greater than or equal to the key of C.
The interval scheduling problem is 1-dimensional – only the time dimension is relevant. The Maximum disjoint set problem is a generalization to 2 or more dimensions. This generalization, too, is NP-complete. Another variation is resource allocation, in which a set of intervals s are scheduled using resources k such that k is minimized. That ...
Memory allocation is dynamic – each process gets as much memory as it requests. Active pages are transferred into main memory for fast access; inactive pages are pushed out to secondary storage to make room, as needed. When a single process starts consuming a large amount of memory, it usually occupies more and more of main memory, pushing ...
The heapsort algorithm can be divided into two phases: heap construction, and heap extraction. The heap is an implicit data structure which takes no space beyond the array of objects to be sorted; the array is interpreted as a complete binary tree where each array element is a node and each node's parent and child links are defined by simple arithmetic on the array indexes.
Illustration of the table-heap compaction algorithm. Objects that the marking phase has determined to be reachable (live) are colored, free space is blank. A table-based algorithm was first described by Haddon and Waite in 1967. [1] It preserves the relative placement of the live objects in the heap, and requires only a constant amount of overhead.
This method of performing selection in a heap has been applied to problems of listing multiple solutions to combinatorial optimization problems, such as finding the k shortest paths in a weighted graph, by defining a state space of solutions in the form of an implicitly defined heap-ordered tree, and then applying this selection algorithm to ...
Basis: Heap's Algorithm trivially permutes an array A of size 1 as outputting A is the one and only permutation of A. Induction: Assume Heap's Algorithm permutes an array of size i . Using the results from the previous proof, every element of A will be in the "buffer" once when the first i elements are permuted.