A mesh strainer known as sift known as sieve, is a device for separating wanted elements from unwanted material or for characterizing the particle size distribution of a sample using a woven screen such as a mesh or net or metal. The word "sift" derives from "sieve". In cooking, a sifter is used to separate and break up clumps in dry ingredients such as flour, as well as to aerate and combine them. A strainer is a form of sieve used to separate solids from liquid; some industrial strainers available are simplex basket strainers, duplex basket strainers, Y strainers. Simple basket strainers are used to protect valuable or sensitive equipment in systems that are meant to be shut down temporarily; some used strainers are bell mouth strainers, foot valve strainers, basket strainers. Most processing industries will opt for a self-cleaning strainer instead of a basket strainer or a simplex strainer due to limitations of simple filtration systems; the self-cleaning strainers or filters are more efficient and provide an automatic filtration solution.
Sieving is a simple technique for separating particles of different sizes. A sieve such as used for sifting flour has small holes. Coarse particles are separated or broken up by grinding against screen openings. Depending upon the types of particles to be separated, sieves with different types of holes are used. Sieves are used to separate stones from sand. Sieving plays an important role in food industries where sieves are used to prevent the contamination of the product by foreign bodies; the design of the industrial sieve is here of primary importance. Triage sieving refers to grouping people according to their severity of injury; the mesh in a wooden sieve might be made from wicker. Use of wood to avoid contamination is important. Henry Stephens, in his Book of the Farm, advised that the withes of a wooden riddle or sieve be made from fir or willow with American elm being best; the rims would be made of fir, oak or beech. A sieve analysis is a practice or procedure used to assess the particle size distribution of a granular material.
Sieve sizes used in combinations of four to eight sieves. Designations and Nominal Sieve Openings Chinois, or conical sieve used as a strainer sometimes used like a food mill Cocktail strainer, a bar accessory Colander, a bowl-shaped sieve used as a strainer in cooking Flour sifter or bolter, used in flour production and baking Graduated sieves, used to separate varying small sizes of material soil, rock or minerals Mesh strainer, or just "strainer" consisting of a fine metal mesh screen on a metal frame Riddle, used for soil Spider, used in Chinese cooking Tamis known as a drum sieve Tea strainer intended for use when making tea Zaru, or bamboo sieve, used in Japanese cooking Cheesecloth Cloth filter Gold panning Gyratory equipment Mechanical screening Molecular sieve Separation process Sieve analysis Soil gradation Filter
In computer science, a binary tree is a tree data structure in which each node has at most two children, which are referred to as the left child and the right child. A recursive definition using just set theory notions is that a binary tree is a tuple, where L and R are binary trees or the empty set and S is a singleton set; some authors allow the binary tree to be the empty set as well. From a graph theory perspective, binary trees as defined here are arborescences. A binary tree may thus be called a bifurcating arborescence—a term which appears in some old programming books, before the modern computer science terminology prevailed, it is possible to interpret a binary tree as an undirected, rather than a directed graph, in which case a binary tree is an ordered, rooted tree. Some authors use rooted binary tree instead of binary tree to emphasize the fact that the tree is rooted, but as defined above, a binary tree is always rooted. A binary tree is a special case of an ordered K-ary tree, where k is 2.
In mathematics, what is termed binary tree can vary from author to author. Some use the definition used in computer science, but others define it as every non-leaf having two children and don't order the children either. In computing, binary trees are used in two different ways: First, as a means of accessing nodes based on some value or label associated with each node. Binary trees labelled this way are used to implement binary search trees and binary heaps, are used for efficient searching and sorting; the designation of non-root nodes as left or right child when there is only one child present matters in some of these applications, in particular it is significant in binary search trees. However, the arrangement of particular nodes into the tree is not part of the conceptual information. For example, in a normal binary search tree the placement of nodes depends entirely on the order in which they were added, can be re-arranged without changing the meaning. Second, as a representation of data with a relevant bifurcating structure.
In such cases the particular arrangement of nodes under and/or to the left or right of other nodes is part of the information. Common examples occur with Huffman coding and cladograms; the everyday division of documents into chapters, paragraphs, so on is an analogous example with n-ary rather than binary trees. To define a binary tree in general, we must allow for the possibility that only one of the children may be empty. An artifact, which in some textbooks is called an extended binary tree is needed for that purpose. An extended binary tree is thus recursively defined as: the empty set is an extended binary tree if T1 and T2 are extended binary trees denote by T1 • T2 the extended binary tree obtained by adding a root r connected to the left to T1 and to the right to T2 by adding edges when these sub-trees are non-empty. Another way of imagining this construction is to consider instead of the empty set a different type of node—for instance square nodes if the regular ones are circles. A binary tree is a rooted tree, an ordered tree in which every node has at most two children.
A rooted tree imparts a notion of levels, thus for every node a notion of children may be defined as the nodes connected to it a level below. Ordering of these children makes possible to distinguish left child from right child, but this still doesn't distinguish between a node with left but not a right child from a one with right but no left child. The necessary distinction can be made by first partitioning the edges, i.e. defining the binary tree as triplet, where is a rooted tree and E1 ∩ E2 is empty, requiring that for all j ∈ every node has at most one Ej child. A more informal way of making the distinction is to say, quoting the Encyclopedia of Mathematics, that "every node has a left child, a right child, neither, or both" and to specify that these "are all different" binary trees. Tree terminology so varies in the literature. A rooted binary tree has a root node and every node has at most two children. A full binary tree is a tree in which every node has 2 children. Another way of defining a full binary tree is a recursive definition.
A full binary tree is either:A single vertex. A tree whose root note has two subtrees. In a complete binary tree every level, except the last, is filled, all nodes in the last level are as far left as possible, it can have between 2h nodes at the last level h. An alternative definition is a perfect tree; some authors use the term complete to refer instead to a perfect binary tree as defined above, in which case they call this type of tree an complete binary tree or nearly complete binary tree. A complete binary tree can be efficiently represented using an array. A perfect binary tree is a binary tree in which all interior nodes have two children and all leaves have the same depth or same level. An example of a perfect binary tree is the ancestry chart of a person to a given depth, as each person has two biological parents. In the infinite complete binary tree, every node has two children; the set of all nodes is countably infinite, but the set of all infinite paths from the root
In computer science, a leftist tree or leftist heap is a priority queue implemented with a variant of a binary heap. Every node has an s-value, the distance to the nearest leaf. In contrast to a binary heap, a leftist tree attempts to be unbalanced. In addition to the heap property, leftist trees are maintained so the right descendant of each node has the lower s-value; the height-biased leftist tree was invented by Clark Allan Crane. The name comes from the fact that the left subtree is taller than the right subtree. A leftist tree is a mergeable heap; when inserting a new node into a tree, a new one-node tree is created and merged into the existing tree. To delete an item, it is replaced by the merge of its right sub-trees. Both these operations take O time. For insertions, this is slower than Fibonacci heaps, which support insertion in O amortized time, O worst-case. Leftist trees are advantageous because of their ability to merge compared to binary heaps which take Θ. In all cases, the merging of skew heaps has better performance.
However merging leftist heaps has worst-case O complexity while merging skew heaps has only amortized O complexity. The usual leftist tree is a height-biased leftist tree. However, other biases can exist, such as in the weight-biased leftist tree; the s-value of a node is the distance from that node to the nearest missing leaf. Put another way, the s-value of a null child is implicitly zero. Other nodes have an s-value equal to one more the minimum of their children's s-values. Thus, in the example at right, all nodes with at least one missing child have an s-value of 1, while node 4 has an s-value of 2, since its right child has an s-value of 1. Assuming a min-heap, choose the lower-valued node as the root, merge the higher-valued node into the new root's right subtree. After merging, compare the s-values of the resultant children. Swap them, if necessary, so the left child's s-value. Update the s-value of the root to be one more than its right child's. Several variations on the basic leftist tree exist, which make only minor changes top the basic algorithm: The choice of the left child as the taller one is arbitrary.
It is possible to avoid swapping children, but instead record which child is the tallest and use that in the merge operation. The s-value used to decide which side to merge with could use a metric other than height. For example, weight could be used. Initializing a height biased leftist tree is done in one of two ways; the first is to merge each node one at a time into one HBLT. This process takes O time; the other approach is to use a queue to store resulting tree. The first two items in the queue are removed and placed back into the queue; this can initialize a HBLT in O time. This approach is detailed in the three diagrams supplied. A min height biased leftist tree is shown. To initialize a min HBLT, place each element to be added to the tree into a queue. In the example, the set of numbers are initialized; each line of the diagram represents another cycle of the algorithm, depicting the contents of the queue. The first five steps are easy to follow. Notice that the freshly created HBLT is added to the end of the queue.
In the fifth step, the first occurrence of an s-value greater than 1 occurs. The sixth step shows two trees merged with each other, with predictable results. In part 2 a more complex merge happens; the tree with the lower value has a right child, so merge must be called again on the subtree rooted by tree x's right child and the other tree. After the merge with the subtree, the resulting tree is put back into tree x; the s-value of the right child is now greater than the s-value of the left child, so they must be swapped. The s-value of the root node 4 is now 2. Part 3 is the most complex. Here, we recursively call merge twice; this uses the same process described for part 2. Leftist Trees, Sartaj Sahni Robert E. Tarjan. Data Structures and Network Algorithms. SIAM. pp. 38–42. ISBN 978-0-89871-187-5. Dinesh P. Mehta. "Chapter 5: Leftist trees". Handbook of Data Structures and Applications. CRC Press. ISBN 978-1-4200-3517-9
A beap, or bi-parental heap, is a data structure where a node has two parents and two children. Unlike a heap, a beap allows sublinear search; the beap was introduced by Hendra Suwanda. A related data structure is the Young tableau; the height of the structure is n. Assuming the last level is full, the number of elements on that level is n. In fact, because of these properties all basic operations run in O time on average. Find operations in the heap can be O in the worst case. Removal and insertion of new elements involves propagation of elements up or down in order to restore the beap invariant. An additional perk is that beap provides constant time access to the smallest element and O time for the maximum element. A O find operation can be implemented if parent pointers at each node are maintained. You would start at the absolute bottom-most element of the top node and move either up or right to find the element of interest. Munro, J. Ian. "Implicit data structures for fast search and update". Journal of Computer and System Sciences.
21: 236–250. Doi:10.1016/0022-000090037-9. Williams, J. W. J.. "Algorithm 232 - Heapsort". Communications of the ACM. 7: 347–348. Doi:10.1145/512274.512284
A 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 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. Heap property: the key stored in each node is either greater than or equal to or less than or equal to the keys in the node's children, according to some total order. Heaps where the parent key is greater than or equal to the child keys are called max-heaps. Efficient algorithms are known for the two operations needed to implement a priority queue on a binary heap: inserting an element, removing the smallest or largest element from a min-heap or max-heap, respectively. Binary heaps are commonly employed in the heapsort sorting algorithm, an in-place algorithm because binary heaps can be implemented as an implicit data structure, storing keys in an array and using their relative positions within that array to represent child-parent relationships.
Both the insert and remove operations modify the heap to conform to the shape property first, by adding or removing from the end of the heap. The heap property is restored by traversing up or down the heap. Both operations take O time. To add an element to a heap we must perform an up-heap operation, by following this algorithm: Add the element to the bottom level of the heap. Compare the added element with its parent. If not, swap the element with its parent and return to the previous step; the number of operations required depends only on the number of levels the new element must rise to satisfy the heap property, thus the insertion operation has a worst-case time complexity of O but an average-case complexity of O. As an example of binary heap insertion, say we have a max-heap and we want to add the number 15 to the heap. We first place the 15 in the position marked by the X. However, the heap property is violated since 15 > 8, so we need to swap the 15 and the 8. So, we have the heap looking as follows after the first swap: However the heap property is still violated since 15 > 11, so we need to swap again:, a valid max-heap.
There is no need to check the left child after this final step: at the start, the max-heap was valid, meaning 11 > 5. The procedure for deleting the root from the heap and restoring the properties is called down-heap. Replace the root of the heap with the last element on the last level. Compare the new root with its children. If not, swap the element with one of its children and return to the previous step. So, if we have the same max-heap as before We remove the 11 and replace it with the 4. Now the heap property is violated since 8 is greater than 4. In this case, swapping the two elements, 4 and 8, is enough to restore the heap property and we need not swap elements further: The downward-moving node is swapped with the larger of its children in a max-heap, until it satisfies the heap property in its new position; this functionality is achieved by the Max-Heapify function as defined below in pseudocode for an array-backed heap A of length heap_length. Note that "A" is indexed starting at 1. Max-Heapify: left ← 2×i // ← means "assignment" right ← 2×i + 1 largest ← i if left ≤ heap_length and A > A then: largest ← left if right ≤ heap_length and A > A then: largest ← right if largest ≠ i then: swap A and A Max-Heapify For the above algorithm to re-heapify the array, the node at index i and its two direct children must violate the heap property.
If they do not, the algorithm will fall through with no change to the array. The down-heap operation can be used to modify the value of the root when an element is not being deleted. In the pseudocode above, what starts. Note that A is an array that starts being indexed from 1 up to length, according to the pseudocode. In the worst case, the new root has to be swapped with its child on each level until it reaches the bottom level of the heap, meaning that the delete operation has a time complexity relative to the height of the tree, or O. Building a heap from an array of n input elements can be done by starting with an empty heap successively inserting each element; this approach, called Williams’ method after the inventor of binary heaps, is seen to run in O time: it performs n insertions at O cost each. However, Williams’ method is suboptimal. A faster method starts by arbitrarily putting the elements on a binary tree, respecting the shape property. Starting from the lowest level and moving upwards, sift the root of each subtree downward as in the deletion algorithm
Computer science is the study of processes that interact with data and that can be represented as data in the form of programs. It enables the use of algorithms to manipulate and communicate digital information. A computer scientist studies the theory of computation and the practice of designing software systems, its fields can be divided into practical disciplines. Computational complexity theory is abstract, while computer graphics emphasizes real-world applications. Programming language theory considers approaches to the description of computational processes, while computer programming itself involves the use of programming languages and complex systems. Human–computer interaction considers the challenges in making computers useful and accessible; the earliest foundations of what would become computer science predate the invention of the modern digital computer. Machines for calculating fixed numerical tasks such as the abacus have existed since antiquity, aiding in computations such as multiplication and division.
Algorithms for performing computations have existed since antiquity before the development of sophisticated computing equipment. Wilhelm Schickard designed and constructed the first working mechanical calculator in 1623. In 1673, Gottfried Leibniz demonstrated a digital mechanical calculator, called the Stepped Reckoner, he may be considered the first computer scientist and information theorist, among other reasons, documenting the binary number system. In 1820, Thomas de Colmar launched the mechanical calculator industry when he released his simplified arithmometer, the first calculating machine strong enough and reliable enough to be used daily in an office environment. Charles Babbage started the design of the first automatic mechanical calculator, his Difference Engine, in 1822, which gave him the idea of the first programmable mechanical calculator, his Analytical Engine, he started developing this machine in 1834, "in less than two years, he had sketched out many of the salient features of the modern computer".
"A crucial step was the adoption of a punched card system derived from the Jacquard loom" making it infinitely programmable. In 1843, during the translation of a French article on the Analytical Engine, Ada Lovelace wrote, in one of the many notes she included, an algorithm to compute the Bernoulli numbers, considered to be the first computer program. Around 1885, Herman Hollerith invented the tabulator, which used punched cards to process statistical information. In 1937, one hundred years after Babbage's impossible dream, Howard Aiken convinced IBM, making all kinds of punched card equipment and was in the calculator business to develop his giant programmable calculator, the ASCC/Harvard Mark I, based on Babbage's Analytical Engine, which itself used cards and a central computing unit; when the machine was finished, some hailed it as "Babbage's dream come true". During the 1940s, as new and more powerful computing machines were developed, the term computer came to refer to the machines rather than their human predecessors.
As it became clear that computers could be used for more than just mathematical calculations, the field of computer science broadened to study computation in general. In 1945, IBM founded the Watson Scientific Computing Laboratory at Columbia University in New York City; the renovated fraternity house on Manhattan's West Side was IBM's first laboratory devoted to pure science. The lab is the forerunner of IBM's Research Division, which today operates research facilities around the world; the close relationship between IBM and the university was instrumental in the emergence of a new scientific discipline, with Columbia offering one of the first academic-credit courses in computer science in 1946. Computer science began to be established as a distinct academic discipline in the 1950s and early 1960s; the world's first computer science degree program, the Cambridge Diploma in Computer Science, began at the University of Cambridge Computer Laboratory in 1953. The first computer science degree program in the United States was formed at Purdue University in 1962.
Since practical computers became available, many applications of computing have become distinct areas of study in their own rights. Although many believed it was impossible that computers themselves could be a scientific field of study, in the late fifties it became accepted among the greater academic population, it is the now well-known IBM brand that formed part of the computer science revolution during this time. IBM released the IBM 704 and the IBM 709 computers, which were used during the exploration period of such devices. "Still, working with the IBM was frustrating if you had misplaced as much as one letter in one instruction, the program would crash, you would have to start the whole process over again". During the late 1950s, the computer science discipline was much in its developmental stages, such issues were commonplace. Time has seen significant improvements in the effectiveness of computing technology. Modern society has seen a significant shift in the users of computer technology, from usage only by experts and professionals, to a near-ubiquitous user base.
Computers were quite costly, some degree of humanitarian aid was needed for efficient use—in part from professional computer operators. As computer adoption became more widespread and affordable, less human assistance was needed for common usage. Despite its short history as a formal academic discipline, computer science has made a number of fundamental contributions to science and society—in fact, along with electronics, it is
C++ is a general-purpose programming language, developed by Bjarne Stroustrup as an extension of the C language, or "C with Classes". It has imperative, object-oriented and generic programming features, while providing facilities for low-level memory manipulation, it is always implemented as a compiled language, many vendors provide C++ compilers, including the Free Software Foundation, Intel, IBM, so it is available on many platforms. C++ was designed with a bias toward system programming and embedded, resource-constrained software and large systems, with performance and flexibility of use as its design highlights. C++ has been found useful in many other contexts, with key strengths being software infrastructure and resource-constrained applications, including desktop applications and performance-critical applications. C++ is standardized by the International Organization for Standardization, with the latest standard version ratified and published by ISO in December 2017 as ISO/IEC 14882:2017.
The C++ programming language was standardized in 1998 as ISO/IEC 14882:1998, amended by the C++03, C++11 and C++14 standards. The current C++ 17 standard supersedes these with an enlarged standard library. Before the initial standardization in 1998, C++ was developed by Danish computer scientist Bjarne Stroustrup at Bell Labs since 1979 as an extension of the C language. C++20 is the next planned standard, keeping with the current trend of a new version every three years. In 1979, Bjarne Stroustrup, a Danish computer scientist, began work on "C with Classes", the predecessor to C++; the motivation for creating a new language originated from Stroustrup's experience in programming for his Ph. D. thesis. Stroustrup found that Simula had features that were helpful for large software development, but the language was too slow for practical use, while BCPL was fast but too low-level to be suitable for large software development; when Stroustrup started working in AT&T Bell Labs, he had the problem of analyzing the UNIX kernel with respect to distributed computing.
Remembering his Ph. D. experience, Stroustrup set out to enhance the C language with Simula-like features. C was chosen because it was general-purpose, fast and used; as well as C and Simula's influences, other languages influenced C++, including ALGOL 68, Ada, CLU and ML. Stroustrup's "C with Classes" added features to the C compiler, including classes, derived classes, strong typing and default arguments. In 1983, "C with Classes" was renamed to "C++", adding new features that included virtual functions, function name and operator overloading, constants, type-safe free-store memory allocation, improved type checking, BCPL style single-line comments with two forward slashes. Furthermore, it included the development of a standalone compiler for Cfront. In 1985, the first edition of The C++ Programming Language was released, which became the definitive reference for the language, as there was not yet an official standard; the first commercial implementation of C++ was released in October of the same year.
In 1989, C++ 2.0 was released, followed by the updated second edition of The C++ Programming Language in 1991. New features in 2.0 included multiple inheritance, abstract classes, static member functions, const member functions, protected members. In 1990, The Annotated C++ Reference Manual was published; this work became the basis for the future standard. Feature additions included templates, namespaces, new casts, a boolean type. After the 2.0 update, C++ evolved slowly until, in 2011, the C++11 standard was released, adding numerous new features, enlarging the standard library further, providing more facilities to C++ programmers. After a minor C++14 update released in December 2014, various new additions were introduced in C++17, further changes planned for 2020; as of 2017, C++ remains the third most popular programming language, behind Java and C. On January 3, 2018, Stroustrup was announced as the 2018 winner of the Charles Stark Draper Prize for Engineering, "for conceptualizing and developing the C++ programming language".
According to Stroustrup: "the name signifies the evolutionary nature of the changes from C". This name is credited to Rick Mascitti and was first used in December 1983; when Mascitti was questioned informally in 1992 about the naming, he indicated that it was given in a tongue-in-cheek spirit. The name comes from C's ++ operator and a common naming convention of using "+" to indicate an enhanced computer program. During C++'s development period, the language had been referred to as "new C" and "C with Classes" before acquiring its final name. Throughout C++'s life, its development and evolution has been guided by a set of principles: It must be driven by actual problems and its features should be useful in real world programs; every feature should be implementable. Programmers should be free to pick their own programming style, that style should be supported by C++. Allowing a useful feature is more important than preventing every possible misuse of C++, it should provide facilities for organising programs into separate, well-defined parts, provide facilities for combining separately developed parts.
No implicit violations of the type system (but allow explicit violations.