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In number theory, the Kempner function [1] is defined for a given positive integer to be the smallest number such that divides the factorial!. For example, the number 8 {\displaystyle 8} does not divide 1 ! {\displaystyle 1!} , 2 ! {\displaystyle 2!} , or 3 ! {\displaystyle 3!} , but does divide 4 ! {\displaystyle 4!} , so S ( 8 ) = 4 ...
LEMON has its own graph storing format, the so called Lemon Graph Format and includes general EPS drawing methods and special graph exporting tools. LEMON also includes several miscellaneous tools. For example, it provides simple tools for measuring the performance of algorithms, which can be used to compare different implementations of the ...
Its complexity can be expressed in an alternative way for very large graphs: when C * is the length of the shortest path from the start node to any node satisfying the "goal" predicate, each edge has cost at least ε, and the number of neighbors per node is bounded by b, then the algorithm's worst-case time and space complexity are both in O(b ...
isl (integer set library) is a portable C library for manipulating sets and relations of integer points bounded by linear constraints. [2] The following operations are supported: [3] intersection, union, set difference; emptiness check; convex hull (integer) affine hull; integer projection; computing the lexicographic minimum using parametric ...
_Bool functions similarly to a normal integer type, with one exception: any assignments to a _Bool that are not 0 (false) are stored as 1 (true). This behavior exists to avoid integer overflows in implicit narrowing conversions. For example, in the following code: In C23, the boolean type was moved to bool, making the <stdbool.h> header now ...
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). [1]
3. There is exactly one node with zero in-degree—the root node. The root node is either terminal or labelled by the smallest integer in the diagram. 4. If two nodes have the same label, then their LO or HI edges point to different nodes. In other words, there are no redundant nodes.
In graphs that have negative cycles, the set of shortest simple paths from v to all other vertices do not necessarily form a tree. For simple connected graphs, shortest-path trees can be used [1] to suggest a non-linear relationship between two network centrality measures, closeness and degree. By assuming that the branches of the shortest-path ...