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After this pre-computing step, a query RMQ A (l,r) can now be answered in constant time by splitting it into two separate queries: one is the pre-computed query with range from l to the largest memoized value smaller than r. The other is the query of an interval of the same length that has r as its right boundary. These intervals may overlap ...
Factor () Multiple Value Item 0 0 0 Singularity: 10 −35: 1 Planck length: 0.0000162 qm Planck length; typical scale of hypothetical loop quantum gravity or size of a hypothetical string and of branes; according to string theory, lengths smaller than this do not make any physical sense. [1]
For every long enough string in a regular language, there must be a middle section (y) that can be repeated (or pumped) any number of times to produce a string still in the language. In the theory of formal languages, the pumping lemma for regular languages is a lemma that describes an essential property of all regular languages.
The smallest meaningful increment of time is the Planck time―the time light takes to traverse the Planck distance, many decimal orders of magnitude smaller than a second. [ 1 ] The largest realized amount of time, based on known scientific data, is the age of the universe , about 13.8 billion years—the time since the Big Bang as measured in ...
If values differ by two orders of magnitude, they differ by a factor of about 100. Two numbers of the same order of magnitude have roughly the same scale: the larger value is less than ten times the smaller value. The growing amounts of Internet data have led to addition of new SI prefixes over time, most recently in 2022. [6]
This definition implies that a string of length is a Lyndon word if and only if there exist Lyndon words and such that < and =. [4] Although there may be more than one choice of u {\displaystyle u} and v {\displaystyle v} with this property, there is a particular choice, called the standard factorization , in which v {\displaystyle v} is as ...
In mathematics, and particularly in the theory of formal languages, shortlex is a total ordering for finite sequences of objects that can themselves be totally ordered. In the shortlex ordering, sequences are primarily sorted by cardinality (length) with the shortest sequences first, and sequences of the same length are sorted into lexicographical order. [1]
The length of a string can also be stored explicitly, for example by prefixing the string with the length as a byte value. This convention is used in many Pascal dialects; as a consequence, some people call such a string a Pascal string or P-string. Storing the string length as byte limits the maximum string length to 255.