# One-pass algorithm

In computing, a one-pass algorithm is a streaming algorithm 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.

Basically one-pass algorithm operates as follows: (1) the object descriptions are processed serially; (2) the first object becomes the cluster representative of the first cluster; (3) each subsequent object is matched against all cluster representatives existing at its processing time; (4) a given object is assigned to one cluster (or more if overlap is allowed) according to some condition on the matching function; (5) when an object is assigned to a cluster the representative for that cluster is recomputed; (6) if an object fails a certain test it becomes the cluster representative of a new cluster (7) nothing happened

## 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:

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 as finding the most frequent symbol from a limited alphabet).
• Sort the list.