A computationally expensive algorithm is one which, by its nature, requires a large number of processing cycles to complete. Units often displayed using Big O notation.

At times, there is a more elegant, less expensive solution. A traditional example where there are many algorithms to achieve a uniform end are the sorting algorithms used on a one-dimensional list. One of the simplest to implement is the Bubble Sort. It is, however, more computationally expensive than the Quick Sort. Quick Sort, however, is more difficult (relatively) to implement.

Often, the more general the solution, the more computationally expensive. For example, algorithms used for manipulating a generic matrix will work on a sparse matrix, but algorithms designed specifically for sparse matrices will be less expensive.