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In a 1977 review of permutation-generating algorithms, Robert Sedgewick concluded that it was at that time the most effective algorithm for generating permutations by computer. [2] The sequence of permutations of n objects generated by Heap's algorithm is the beginning of the sequence of permutations of n+1 objects.
However, for the special case in which the input is a permutation of the integers ,, …,, this approach can be made much more efficient, leading to time bounds of the form ( ). [4] The largest clique in a permutation graph corresponds to the longest decreasing subsequence of the permutation that defines the graph (assuming the original ...
The longest common substrings of a set of strings can be found by building a generalized suffix tree for the strings, and then finding the deepest internal nodes which have leaf nodes from all the strings in the subtree below it. The figure on the right is the suffix tree for the strings "ABAB", "BABA" and "ABBA", padded with unique string ...
In combinatorial mathematics and theoretical computer science, a (classical) permutation pattern is a sub-permutation of a longer permutation.Any permutation may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the sequence 123...; for instance the sequence 213 represents the permutation on three elements that swaps elements 1 and 2.
In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such games are used to pick out a person from a group, e.g. eeny, meeny, miny, moe. A drawing for the Josephus problem sequence for 500 people and skipping value of 6.
Suppose the initial iteration swapped the final element with the one at (non-final) position k, and that the subsequent permutation of first n − 1 elements then moved it to position l; we compare the permutation π of all n elements with that remaining permutation σ of the first n − 1 elements.
While tries commonly store character strings, they can be adapted to work with any ordered sequence of elements, such as permutations of digits or shapes. A notable variant is the bitwise trie , which uses individual bits from fixed-length binary data (such as integers or memory addresses ) as keys.
The sequence of permutations generated by the Steinhaus–Johnson–Trotter algorithm has a natural recursive structure, that can be generated by a recursive algorithm. . However the actual Steinhaus–Johnson–Trotter algorithm does not use recursion, instead computing the same sequence of permutations by a simple iterative me