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Movie Title Year Distributor Notes Rev Formats Adult Video News Awards 1992 1992 VCA American Buttman in London 1991 Evil Angel LezOnly 2 DRO Ben Dover's Alley Cats 1996 VCA Facial GS 2 Fiona Cooper V403 1990 Fiona Cooper Girl on Girl 1 2007 Viv Thomas LezOnly DRO Hot Wet Sex 2000 Big Top Video LezOnly DRO Kerry's Foot Fantasies 1999 Big Top Video O Leg Sex Dream 1998 Viv Thomas LezOnly 1 DRO Leg Sex Spy 1998 Big Top Video NonSex Maximum Perversum 29: Gierige Spalten 1992 Videorama Selen: dalla testa ai piedi 1998 Rabbit Digital Video MastOnly O Sex Club Holiday 1992 Videorama Slutty English Housewives 1996 Xcel Facial 1
than a total function. A notable failure due to exceptions is the Ariane 5 Flight 501 rocket failure (June 4, 1996). Proof of program correctness by use of mathematical induction: Knuth demonstrates the application of mathematical induction to an "extended" version of Euclid's algorithm, and he proposes "a general method applicable to proving the validity of any algorithm".[66] Tausworthe proposes that a measure of the complexity of a program be the length of its correctness proof.[67] Measuring and improving the Euclid algorithms Elegance (compactness) versus goodness (speed): With only six core instructions, "Elegant" is the clear winner, compared to "Inelegant" at thirteen instructions. However, "Inelegant" is faster (it arrives at HALT in fewer steps). Algorithm analysis[68] indicates why this is the case: "Elegant" does two conditional tests in every subtraction loop, whereas "Inelegant" only does one. As the algorithm (usually) requires many loop-throughs, on average much time is wasted doing a "B = 0?" test that is needed only after the remainder is computed. Can the algorithms be improved?: Once the programmer judges a program "fit" and "effective"—that is, it computes the function intended by its author—then the question becomes, can it be improved?



The compactness of "Inelegant" can be improved by the elimination of five steps. But Chaitin proved that compacting an algorithm cannot be automated by a generalized algorithm;[69] rather, it can only be done heuristically; i.e., by exhaustive search (examples to be found at Busy beaver), trial and error, cleverness, insight, application of inductive reasoning, etc. Observe that steps 4, 5 and 6 are repeated in steps 11, 12 and 13. Comparison with "Elegant" provides a hint that these steps, together with steps 2 and 3, can be eliminated. This reduces the number of core instructions from thirteen to eight, which makes it "more elegant" than "Elegant", at nine steps. The speed of "Elegant" can be improved by moving the "B=0?" test outside of the two subtraction loops. This change calls for the addition of three instructions (B = 0?, A = 0?, GOTO). Now "Elegant" computes the example-numbers faster; whether this is always the case for any given A, B, and R, S would require a detailed analysis. Algorithmic analysis Main article: Analysis of algorithms It is frequently important to know how much of a particular resource (such as time or storage) is theoretically required for a given algorithm. Methods have been developed for the analysis of algorithms to obtain such quantitative answers (estimates); for example, the sorting algorithm above has a time requirement of O(n), using the big O notation with n as the length of the list. At all times the algorithm only needs to remember two values: the largest number found so far, and its current position in the input list. Therefore, it is said to have a space requirement of O(1), if the space required to store the input numbers is not counted, or O(n) if it is counted. Different algorithms may complete the same task with a different set of instructions in less or more time, space, or 'effort' than others. For example, a binary search algorithm (with cost O(log n) ) outperforms a sequential search (cost O(n) ) when used for table lookups on sorted lists or arrays. Formal versus empirical Main articles: Empirical algorithmics, Profiling (computer programming), and Program optimization The analysis, and study of algorithms is a discipline of computer science, and is often practiced abstractly without the use of a specific programming language or implementation. In this sense, algorithm analysis resembles other mathematical disciplines in that it focuses on the underlying properties of the algorithm and not on the specifics of any particular implementation. Usually pseudocode is used for analysis as it is the simplest and most general representation. However, ultimately, most algorithms are usually implemented on particular hardware/software platforms and their algorithmic efficiency is eventually put to the test using real code. For the solution of a "one off" problem, the efficiency of a particular algorithm may not have significant consequences (unless n is extremely large) but for algorithms designed for fast interactive, commercial or long life scientific usage it may be critical. Scaling from small n to large n frequently exposes inefficient algorithms that are otherwise benign. Empirical testing is useful because it may uncover unexpected interactions that affect performance. Benchmarks may be used to compare before/after potential improvements to an algorithm after program optimization. Empirical tests cannot replace formal analysis, though, and are not trivial to perform in a fair manner.[70] Execution efficiency Main article: Algorithmic efficiency To illustrate the potential improvements possible even in well-established algorithms, a recent significant innovation, relating to FFT algorithms (used heavily in the field of image processing), can decrease processing time up to 1,000 times for applications like medical imaging.[71] In general, speed improvements depend on special properties of the problem, which are very common in practical applications.[72] Speedups of this magnitude enable computing devices that make extensive use of image processing (like digital cameras and medical equipment) to consume less power. Classification There are various ways to classify algorithms, each with its own merits. By implementation One way to classify algorithms is by implementation means. int gcd(int A, int B) { if (B == 0) return A; else if (A > B) return gcd(A-B,B); else return gcd(A,B-A); } Recursive C implementation of Euclid's algorithm from the above flowchart Recursion A recursive algorithm is one that invokes (makes reference to) itself repeatedly until a certain condition (also known as termination condition) matches, which is a method common to functional programming. Iterative algorithms use repetitive constructs like loops and sometimes additional data structures like stacks to solve the given problems. Some problems are naturally suited for one implementation or the other. For example, towers of Hanoi is well understood using recursive implementation. Every recursive version has an equivalent (but possibly more or less complex) iterative version, and vice versa. Logical An algorithm may be viewed as controlled logical deduction. This notion may be expressed as: Algorithm = logic + control.[73] The logic component expresses the axioms that may be used in the computation and the control component determines the way in which deduction is applied to the axioms. This is the basis for the logic programming paradigm. In pure logic programming languages, the control component is fixed and algorithms are specified by supplying only the logic component. The appeal of this approach is the elegant semantics: a change in the axioms produces a well-defined change in the algorithm. Serial, parallel or distributed Algorithms are usually discussed with the assumption that computers execute one instruction of an algorithm at a time. Those computers are sometimes called serial computers. An algorithm designed for such an environment is called a serial algorithm, as opposed to parallel algorithms or distributed algorithms. Parallel algorithms take advantage of computer architectures where several processors can work on a problem at the same time, whereas distributed algorithms utilize multiple machines connected with a computer network. Parallel or distributed algorithms divide the problem into more symmetrical or asymmetrical subproblems and collect the results back together. The resource consumption in such algorithms is not only processor cycles on each processor but also the communication overhead between the processors. Some sorting algorithms can be parallelized efficiently, but their communication overhead is expensive. Iterative algorithms are generally parallelizable. Some problems have no parallel algorithms and are called inherently serial problems. Deterministic or non-deterministic Deterministic algorithms solve the problem with exact decision at every step of the algorithm whereas non-deterministic algorithms solve problems via guessing although typical guesses are made more accurate through the use of heuristics. Exact or approximate While many algorithms reach an exact solution, approximation algorithms seek an approximation that is closer to the true solution. The approximation can be reached by either using a deterministic or a random strategy. Such algorithms have practical value for many hard problems. One of the examples of an approximate algorithm is the Knapsack problem, where there is a set of given items. Its goal is to pack the knapsack to get the maximum total value. Each item has some weight and some value. Total weight that can be carried is no more than some fixed number X. So, the solution must consider weights of items as well as their value.[74] Quantum algorithm They run on a realistic model of quantum computation. The term is usually used for those algorithms which seem inherently quantum, or use some essential feature of Quantum computing such as quantum superposition or quantum entanglement. By design paradigm Another way of classifying algorithms is by their design methodology or paradigm. There is a certain number of paradigms, each different from the other. Furthermore, each of these categories includes many different types of algorithms. Some common paradigms are: Brute-force or exhaustive search This is the naive method of trying every possible solution to see which is best.[75] Divide and conquer A divide and conquer algorithm repeatedly reduces an instance of a problem to one or more smaller instances of the same problem (usually recursively) until the instances are small enough to solve easily. One such example of divide and conquer is merge sorting. Sorting can be done on each segment of data after dividing data into segments and sorting of entire data can be obtained in the conquer phase by merging the segments. A simpler variant of divide and conquer is called a decrease and conquer algorithm, that solves an identical subproblem and uses the solution of this subproblem to solve the bigger problem. Divide and conquer divides the problem into multiple subproblems and so the conquer stage is more complex than decrease and conquer algorithms. An example of a decrease and conquer algorithm is the binary search algorithm. Search and enumeration Many problems (such as playing chess) can be modeled


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