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insert path p s = {s} into B with cost 0 while B is not empty and count t < K: – let p u be the shortest cost path in B with cost C – B = B − {p u}, count u = count u + 1 – if u = t then P = P U {p u} – if count u ≤ K then for each vertex v adjacent to u: – let p v be a new path with cost C + w(u, v) formed by concatenating edge ...
Path consistency is a property similar to arc consistency, but considers pairs of variables instead of only one. A pair of variables is path-consistent with a third variable if each consistent evaluation of the pair can be extended to the other variable in such a way that all binary constraints are satisfied.
[7]: 196–206 It can be used to find the shortest path to a specific destination node, by terminating the algorithm after determining the shortest path to the destination node. For example, if the nodes of the graph represent cities, and the costs of edges represent the average distances between pairs of cities connected by a direct road, then ...
The binary Golay code, G 23 is a perfect code. That is, the spheres of radius three around code words form a partition of the vector space. G 23 is a 12-dimensional subspace of the space F 23 2. The automorphism group of the perfect binary Golay code G 23 (meaning the subgroup of the group S 23 of permutations of the coordinates of F 23
The path from the root 1 to a number q in the Stern–Brocot tree may be found by a binary search algorithm, which may be expressed in a simple way using mediants. Augment the non-negative rational numbers to including a value 1 / 0 (representing +∞) that is by definition greater than all other rationals.
It is the first self-balancing binary search tree data structure to be invented. [ 3 ] AVL trees are often compared with red–black trees because both support the same set of operations and take O ( log n ) {\displaystyle {\text{O}}(\log n)} time for the basic operations.
On the right Nicomachus's example with numbers 49 and 21 resulting in their GCD of 7 (derived from Heath 1908:300). In mathematics , the Euclidean algorithm , [ note 1 ] or Euclid's algorithm , is an efficient method for computing the greatest common divisor (GCD) of two integers , the largest number that divides them both without a remainder .
In graph theory and theoretical computer science, the longest path problem is the problem of finding a simple path of maximum length in a given graph.A path is called simple if it does not have any repeated vertices; the length of a path may either be measured by its number of edges, or (in weighted graphs) by the sum of the weights of its edges.