One-pass algorithm

In computing, a one-pass algorithm is one which reads its input exactly once, in order, without unbounded buffering. A one-pass algorithm generally requires O(n) (see 'big O' notation) time and less than O(n) storage (typically O(1)), where n is the size of the input.

Example problems solvable by one-pass algorithms

Given any list as an input:

• Count the number of elements.
• Find the nth element (or report that the list has fewer than n elements).
• Find the nth element from the end (or report that the list has fewer than n elements).

Given a list of numbers:

• Find the k largest or smallest elements, k given in advance.
• Find the sum, mean, variance and standard deviation of the elements of the list.

Given a list of symbols from an alphabet of k symbols, given in advance.

• Count the number of times each symbol appears in the input.
• Find the most or least frequent elements.
• Sort the list according to some order on the symbols (possible since the number of symbols is limited).
• Find the maximum gap between two appearances of a given symbol.

Example problems not solvable by one-pass algorithms

Given any list as an input:

• Find the middle element of the list.

Given a list of numbers:

• Find the median.
• Find the modes (This is not the same is finding the most frequent symbol from a limited alphabet).
• Sort the list.