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The two most common representations are column-oriented (columnar format) and row-oriented (row format). [ 1 ] [ 2 ] The choice of data orientation is a trade-off and an architectural decision in databases , query engines, and numerical simulations. [ 1 ]
In the random-access machine commonly used in algorithm analysis, a simple algorithm that scans the indexes in input order and swaps whenever the scan encounters an index whose reversal is a larger number would perform a linear number of data moves. [10] However, computing the reversal of each index may take a non-constant number of steps.
In computing, natural sort order (or natural sorting) is the ordering of strings in alphabetical order, except that multi-digit numbers are treated atomically, i.e., as if they were a single character.
For example, the rational numbers Q have a gap at every irrational number. They also have a gap at infinity, i.e. the usual ordering. A cycle with no gaps is called complete. [15] [14] A cut with exactly one endpoint is called a principal or Dedekind cut. For example, every cut of the circle S 1 is a principal cut.