Meaning of lg * N in Algorithmic Analysis

Question

I\'m currently reading about algorithmic analysis and I read that a certain algorithm (weighted quick union with path compression) is of order N + M lg * N. Apparently though th

Answer 1

lg n refers to log base n. It is the answer to the equation 2^x = n. In Big O complexity analysis, the base to log is irrelevant. Powers of 2 crop up in CS, so it is no surprise if we have to choose a base, it will be base 2.

A good example of where it crops up is a fully binary tree of height h, which has 2^h-1 nodes. If we let n be the number of nodes this relationship is the tree is height lg n with n nodes. The algorithm traversing this tree takes at most lg n to see if a value is stored in the tree.

As to be expected, wiki has great additional info.