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Excel maintains 15 figures in its numbers, but they are not always accurate; mathematically, the bottom line should be the same as the top line, in 'fp-math' the step '1 + 1/9000' leads to a rounding up as the first bit of the 14 bit tail '10111000110010' of the mantissa falling off the table when adding 1 is a '1', this up-rounding is not undone when subtracting the 1 again, since there is no ...
Maximum subarray problems arise in many fields, such as genomic sequence analysis and computer vision.. Genomic sequence analysis employs maximum subarray algorithms to identify important biological segments of protein sequences that have unusual properties, by assigning scores to points within the sequence that are positive when a motif to be recognized is present, and negative when it is not ...
It is possible to find the maximum clique, or the clique number, of an arbitrary n-vertex graph in time O (3 n/3) = O (1.4422 n) by using one of the algorithms described above to list all maximal cliques in the graph and returning the largest one. However, for this variant of the clique problem better worst-case time bounds are possible.
Numbers p and q like this can be computed with the extended Euclidean algorithm. gcd(a, 0) = | a |, for a ≠ 0, since any number is a divisor of 0, and the greatest divisor of a is | a |. [2] [5] This is usually used as the base case in the Euclidean algorithm. If a divides the product b⋅c, and gcd(a, b) = d, then a/d divides c.
In mathematics, the floor function is the function that takes as input a real number x, and gives as output the greatest integer less than or equal to x, denoted ⌊x⌋ or floor(x). Similarly, the ceiling function maps x to the least integer greater than or equal to x , denoted ⌈ x ⌉ or ceil( x ) .
When data is already organized into a data structure, it may be possible to perform selection in an amount of time that is sublinear in the number of values. As a simple case of this, for data already sorted into an array, selecting the k {\displaystyle k} th element may be performed by a single array lookup, in constant time. [ 27 ]
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The number of points (n), chords (c) and regions (r G) for first 6 terms of Moser's circle problem. In geometry, the problem of dividing a circle into areas by means of an inscribed polygon with n sides in such a way as to maximise the number of areas created by the edges and diagonals, sometimes called Moser's circle problem (named after Leo Moser), has a solution by an inductive method.