منابع مشابه
Gray code for derangements
We give a Gray code and constant average time generating algorithm for derangements, i.e., permutations with no 0xed points. In our Gray code, each derangement is transformed into its successor either via one or two transpositions or a rotation of three elements. We generalize these results to permutations with number of 0xed points bounded between two constants. ? 2003 Elsevier B.V. All rights...
متن کاملGray Code for Cayley Permutations
A length-n Cayley permutation p of a total ordered set S is a length-n sequence of elements from S, subject to the condition that if an element x appears in p then all elements y < x also appear in p. In this paper, we give a Gray code list for the set of length-n Cayley permutations. Two successive permutations in this list di er at most in two positions.
متن کاملLogic for Gray Code Computation
Gray code is a well-known binary number system such that neighboring values differ in one digit only. Tsuiki (2002) has introduced Gray code to the field of real number computation. He assigns to each number a unique 1⊥-sequence, i.e., a (possibly infinite) sequence of {−1, 1,⊥} such that at most one copy of ⊥ (meaning undefinedness) is contained in the sequence not as the last character. In th...
متن کاملGray Code Compression
An n-bit (cyclic) Gray code is a (cyclic) sequence of all n-bit strings such that consecutive strings differ in a single bit. We describe an algorithm which for every positive integer n constructs an n-bit cyclic Gray code whose graph of transitions is the d-dimensional hypercube Qd if n = 2, or a subgraph of Qd if 2 d−1 < n < 2. This allows to compress sequences that follow this code so that o...
متن کاملThe Gray Code
Here we summarise the properties and algorithms of the Gray code. Descriptions are given of the Gray code definition, algorithms and circuits for generating the code and for conversion between binary and Gray code, for incrementing, counting, and adding Gray code words. Some interesting applications of the code are also treated. Java implementations of the algorithms in this paper are available...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2004
ISSN: 0166-218X
DOI: 10.1016/j.dam.2003.06.002