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Classes of Algorithms

f(n) Name Example
1 Constant +
log(n) Logarithmic binary search
log2(n) Log-squared
n Linear max of array
n*log(n) Linearithmic quicksort
n2 Quadratic selection sort
n3 Cubic matrix multiply
nk Polynomial
2n Exponential knapsack problem

When we use log(n), we often mean log2(n); however, the base of the log(n) does not matter: logk(n) = log(n) / log(k) Thus, a log(n) is converted to another base by multiplying by a constant; but we eliminate constants when determining Big O.