What is Big O notation ....? Calculating the exact runtime of an algorithm is difficult because it depends on the machine, the programming language, and the implementation of the algorithm. Instead of calculating the exact runtime or number of operations, we can estimate the runtime using big O notation, which ignores constant factors. We associate with each algorithm a function f(n), which is the number of operations performed for input size n. We say that f(n) is O(g(n)) if for some positive constants c and n0, f(n) ≤ cg(n) for all n ≥ n0 For example, if an algorithm's runtime is O(n), then the runtime is ≤ c * n for all sufficiently large n. We can also use big O notation to describe how much space an algorithm uses. Sometimes space is described in terms of extra space (not including the space used by the input). Example 3n2 100n is O(n2). A simple way to find the big O is by looking at the largest exponent. As n becomes large, the 100n becomes insignificant. * Basic operations such as comparison or arithmetic take constant time. * A loop that repeats n times, with a constant number of operations per loop, takes O(n) time. * A nested loop where each loop repeats n times takes O(n2) time. * A loop that repeatedly halves n takes O(logn) time. - Study24x7
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What is Big O notation ....? Calculating the exact runtime of an algorithm is difficult because it depends on the machine, the programming language, and the implementation of the algorithm. Instead of calculating the exact runtime or number of operations, we can estimate the ru...

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