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===Implementation=== | ===Implementation=== | ||
− | ''Implementation'' of an algorithm is the process by which it is translated from its abstract, newly designed form into machine language, which may be directly executed on a computer, and is, more or less, the proper name for what is often called simply ''programming'', although in actual fact a programmer cannot implement without also performing design. This tends to be the longest stage of the design-implementation-analysis process. The abstracted form of the algorithm must first be refined and carefully fleshed out; in particular, the programmer must decide which [[data | + | ''Implementation'' of an algorithm is the process by which it is translated from its abstract, newly designed form into machine language, which may be directly executed on a computer, and is, more or less, the proper name for what is often called simply ''programming'', although in actual fact a programmer cannot implement without also performing design. This tends to be the longest stage of the design-implementation-analysis process. The abstracted form of the algorithm must first be refined and carefully fleshed out; in particular, the programmer must decide which [[data structures]] to use, and this often determines the efficiency of the resulting implementation. The algorithm must then be converted into a form that is readable by both humans and computers, the ''syntax'' of a ''programming language''; the algorithm in this form is generally referred to as ''code'', and writing code is colloquially referred to as ''coding''. Finally, some combination of a ''compiler'', ''assembler'', and ''linker'' convert this syntax into a final concrete form, the ''machine code'', which may be directly executed by a computer (often simply called a ''program''). The ''testing'' phase follows; the code will be modified until the resulting program appears correct, sometimes using a tool called a ''debugger'' to help identify errors. The programmer may discover that the algorithm is incorrect and must be redesigned, or that the implementation does not accurately represent the algorithm and the code must be modified. |
===Analysis=== | ===Analysis=== | ||
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==Importance== | ==Importance== | ||
− | Among factors that determine a program's efficiency, the choice of the underlying algorithm and the data structures used to implement | + | Among factors that determine a program's efficiency, the choice of the underlying algorithm and the data structures used to implement stand out above all others in importance. In the early days of computing, the increase in speed and power of computing machines, exponential as it was, was vastly outpaced by the growth in knowledge of algorithms, allowing large problems to be solved quickly on modestly powered hardware. This trend continues to this day. |
Here is an example. Assume that the human genome numbers approximately 3.3×10<sup>9</sup> base pairs, and that the average gene contains 3×10<sup>4</sup> base pairs. Suppose that we wish to set up a web server that will allow biologists to search for genes in the human genome. Using a naive <math>O(nm)</math> time algorithm for [[string searching]], approximately 10<sup>14</sup> operations would be required to search for a gene inside the human genome. If our web server can execute 10<sup>9</sup> operations per second, it may take up to 10<sup>5</sup> seconds to answer a single query (that is, more than a day). On the other hand, if we use the <math>O(n+m)</math> [[Knuth–Morris–Pratt algorithm]], only about 3.3×10<sup>9</sup> operations will be required, so the biologist will have her result in about three seconds. | Here is an example. Assume that the human genome numbers approximately 3.3×10<sup>9</sup> base pairs, and that the average gene contains 3×10<sup>4</sup> base pairs. Suppose that we wish to set up a web server that will allow biologists to search for genes in the human genome. Using a naive <math>O(nm)</math> time algorithm for [[string searching]], approximately 10<sup>14</sup> operations would be required to search for a gene inside the human genome. If our web server can execute 10<sup>9</sup> operations per second, it may take up to 10<sup>5</sup> seconds to answer a single query (that is, more than a day). On the other hand, if we use the <math>O(n+m)</math> [[Knuth–Morris–Pratt algorithm]], only about 3.3×10<sup>9</sup> operations will be required, so the biologist will have her result in about three seconds. |