Texts: Hello, I'm studying algorithms and I found topics that make me confused. Growth Rate of functions. "Is it a running time?" Basic Efficiency Classes. "Does it also mean running time or what?" Because I have 2 slides, one of them talks about the growth rate of functions (log n, n, n^2, n^3, etc.) and another one talks about basic efficiency classes (which also contains log n, n, n^2, etc.) Also, in this slide, the comments of exponential, what is the meaning of all subsets of an n-item set?
Basic Efficiency Classes
Class Name Comments
1 constant Typically the result of cutting problem size by a constant factor on each iteration (Ch.4). Doesn't examine all/most of the input.
log n logarithmic
n linear Algorithms that scan all of the input, e.g. linear search.
n log n linearithmic log-linear Many divide and conquer algorithms (Ch.5) belong to this category, e.g. mergesort and quicksort. Characterizes the efficiency of algorithms with 2 embedded loops, e.g. simple sorting algorithms and operations on nxn matrices. Characterizes the efficiency of algorithms with 3 embedded loops, e.g. nontrivial algorithms from linear algebra.
n^2 quadratic
n^3 cubic
2^n exponential Typical for algorithms that generate all subsets of an n-item set.
n! factorial Typical for algorithms that generate all permutations of an n-item set.