## complexity

<*algorithm*> The level in difficulty in solving mathematically
posed problems as measured by the time, number of steps or
arithmetic operations, or memory space required (called time
complexity, computational complexity, and space complexity,
respectively).

The interesting aspect is usually how complexity scales with the size of the input (the "scalability"), where the size of the input is described by some number N. Thus an algorithm may have computational complexity O(N^2) (of the order of the square of the size of the input), in which case if the input doubles in size, the computation will take four times as many steps. The ideal is a constant time algorithm (O(1)) or failing that, O(N).

See also NP-complete.

Last updated: 1994-10-20

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**complexity**» complexity analysis » complexity class » complexity measure