What is the base of the logarithm for the purposes of Algorithms?

While cons开发者_开发百科idering O(log(N)) for time complexity, what is the base of log?

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All logarithms are related by some constant. (Hence the change-of-base formula). Because we generally disregard constants in complexity analysis, the base doesn't matter.

Usually, the base is considered to be 2, when deriving the algorithm. Consider a sort like merge sort. You can construct a tree out of it, and the tree has a height of log₂ n, because each node has two branches.

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It doesn't matter, the relative complexity is the same regardless of the base used.

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One way to think of it is that O(log₂X) = O(log₁₀X) = O(log_NX)