Broadly speaking, algorithms can be classified into two categories:

• “Polynomial time”: O(1), O(n), O(n^2), O(n*log(n)), O(n^3), …
• “Exponential time”: O(2^n), O(3^n), O(n^n), O(n!)

There is also factorial time, but let’s lump it in together with exponential.

An algorithm runs in “Polynomial time” if its runtime does not grow faster than n^k, where k is any constant and n is the size of the input.

To put it simply, polynomial time algorithms can be useful. Exponential time algorithms are almost always too slow to ever be practical.

References

• binary-search-algorithm

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