267:, designed for practical implementation). In this sense, it resembles other mathematical disciplines in that the analysis focuses on the underlying principles driving the algorithm, and not it's particular implementation. The 'coding' (more properly 'codifying' though this terminology is seldom, if ever, used) of algorithms in such an abstract manner is termed 'writing
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Correctly performing an algorithm will not solve a problem if the algorithm is flawed, or not appropriate to the problem. For example, performing the potato salad algorithm will fail if there are no potatoes present, even if all the motions of preparing the salad are performed as if the potatoes were
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Because an algorithm is a precise list of precise steps, the order of computation will almost always be critical to the functioning of the algorithm. Instructions are usually assumed to be listed explicitly, and are described as starting 'from the top' and going 'down to the bottom', an idea that is
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Different algorithms may complete the same task with a different set of instructions in more or less time, space, or effort than others. A cooking recipe is an example of an algorithm. Given two different recipes for making potato salad, one may have "peel the potato" before "boil the potato" while
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Imagine you have an unsorted list of random numbers. Our goal is to find the highest number in this list. Upon first thinking about the solution, you will realize that you must look at every number in the list. Upon further thinking, you will realize that you need to look at each number only once.
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For any such computational process, the algorithm must be rigorously defined: specified in the way it applies in all possible circumstances that could arise. That is, any conditional steps must be systematically dealt with, case-by-case; the criteria for each case must be clear (and computable).
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to procedures that eventually finish. Others include procedures that could run forever without stopping, arguing that a computer may be required to carry out an ongoing task. Other requirements beside having an ending state, then, are used to determine if the algorithm successfully completes a
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Algorithms are usually discussed with the assumption that computers execute each 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
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is essentially an algorithm that tells the computer what specific steps to perform (in what specific order) in order to carry out a specified task, such as calculating employees' paychecks or printing students' report cards.
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Typically, when an algorithm is associated with processing information, data is read from an input source or device, written to an output sink or device, and/or stored for further use. Stored data is regarded as part of the
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is an interpretable, finite set of instructions for dealing with contingencies and accomplishing some task which can be anything that has a recognizable end-state, end-point, or result for all inputs. (contrast with
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works bottom-up by building progressively larger solutions to subproblems arising from the original problem, and then uses those solutions to obtain the final result. Many problems (such as playing
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As it happens, most people who implement algorithms want to know how much of a particular resource (such as time or storage) a given algorithm requires. Methods have been developed for the
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as used here indicates assignment. That is, the value on the right-hand side of the expression is assigned to the container (or variable) on the left-hand side of the expression.
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the other presents the steps in the reverse order, yet they both call for these steps to be repeated for all potatoes and end when the potato salad is ready to be eaten.
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processes, with a cycle of random mutations yielding successive generations of 'solutions'. Thus, they emulate reproduction and "survival of the fittest". In
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reduces an instance of a problem to one or more smaller instances of the same problem, until the instances are small enough to be directly expressible in the
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Nowadays, a formal criterion for an algorithm is that it is a procedure implementable on a completely-specified Turing machine or one of the equivalent
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counter = 1
largest = List
while counter <= Length:
if List > largest:
largest = List
counter = counter + 1
print largest
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to obtain such quantitative answers, and after reading that section, you will determine that this algorithm has a time requirement of O(
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The lack of mathematical rigor in the "well-defined procedure" definition of algorithms posed some difficulties for mathematicians and
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is one that invokes (makes reference to) itself repeatedly until a certain condition matches, which is a method common to
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In formal mathematical terms, an algorithm is considered to be any sequence of operations which can be performed by a
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as used here indicates the counter element of the list. For example: if the value of
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Algorithms and Data
Structures: Growing work on algorithms and data structures
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works by making a series of simple decisions that are never reconsidered. A
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matters more: it includes the puzzling problem of the algorithms called
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Code and documentation for algorithms and data structure, under
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Gaston H. Gonnet and
Ricardo Baeza-Yates: Example programs from
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Repeat steps 2 and 3 until you have gone through the whole list.
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Look at the next number, and compare it with this largest number
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