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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.
More generally, combinatorial algorithms researchers have defined a Gray code for a set of combinatorial objects to be an ordering for the objects in which each two consecutive objects differ in the minimal possible way. In this generalized sense, the Steinhaus–Johnson–Trotter algorithm generates a Gray code for the permutations themselves ...
The algorithm generates a random permutations uniformly so long as the hardware operates in a fair manner. In 2015, Bacher et al. produced MERGESHUFFLE, an algorithm that divides the array into blocks of roughly equal size, uses Fisher—Yates to shuffle each block, and then uses a random merge recursively to give the shuffled array. [12]
The run time grows to O(nlog(n)) if all elements must be distinct. Bogosort has O(n) time when the elements are sorted on the first iteration. In each iteration all elements are checked if in order. There are n! possible permutations; with a balanced random number generator, almost each permutation of the array is yielded in n! iterations.
The algorithm generates a random permutation of its input using a quantum source of entropy, checks if the list is sorted, and, if it is not, destroys the universe. Assuming that the many-worlds interpretation holds, the use of this algorithm will result in at least one surviving universe where the input was successfully sorted in O( n ) time.
The basic form of the Bron–Kerbosch algorithm is a recursive backtracking algorithm that searches for all maximal cliques in a given graph G.More generally, given three disjoint sets of vertices R, P, and X, it finds the maximal cliques that include all of the vertices in R, some of the vertices in P, and none of the vertices in X.
In computational complexity theory, NP (nondeterministic polynomial time) is a complexity class used to classify decision problems. NP is the set of decision problems for which the problem instances , where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine , or alternatively the set of problems ...
Decision Tree Model. In computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree, i.e. a sequence of queries or tests that are done adaptively, so the outcome of previous tests can influence the tests performed next.