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Time complexity

In [computer science] , the ** time complexity ** of an [algorithm] quantifies the amount of time taken by an algorithm to run as a function of the size of the input to the problem. The time complexity of an algorithm is commonly expressed using the [big O notation] , which suppresses multiplicative constants and lower order terms. When expressed this way, the time complexity is said to be described * asymptotically * , i.e., as the input size goes to infinity. For example, if the time required by an algorithm on all inputs of size * n * is at most 5 * n * 3 3 * n * , the asymptotic time complexity is O( * n * 3).

Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation takes a fixed amount of time to perform. Thus the amount of time taken and the number of elementary operations performed by the algorithm differ by at most a constant factor.

Since an algorithm may take a different amount of time even on inputs of the same size, the most commonly used measure of time complexity, the worst-case time complexity of an algorithm, denoted as ** T ** ** ( **

The following table summarises some classes of commonly encountered time complexities. In the table, poly(

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