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"The time complexity of a problem is the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm. To understand this intuitively, consider the example of an instance that is n bits long that can be solved in n² steps. In this example we say the problem has a time complexity of n². Of course, the exact number of steps will depend on exactly what machine or language is being used. To avoid that problem, the Big O notation is generally used (sometimes described as the ""order"" of the calculation, as in ""on the order of""). If a problem has time complexity O(n²) on one typical computer, then it will also have complexity O(n²) on most other computers, so this notation allows us to generalize away from the details of a particular computer. Example : Mowing grass has linear time complexity because it takes double the time to mow double the area. However, looking up something in a dictionary has only logarithmic time complexity because a double sized dictionary only has to be opened one time more (i.e. exactly in the middle, then the problem size is reduced by half). The space complexity of a problem is a related concept, that measures the amount of space, or memory required by the algorithm. An informal analogy would be the amount of scratch paper needed while working out a problem with pen and paper. Space complexity is also measured with Big O notation. Source: http://in.docsity.com/en-docs/Algorithms_and_Application_Programming__Lecture_notes__KUMAR"
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