منابع مشابه
Trimming and gluing Gray codes
We consider the algorithmic problem of generating each subset of [n] := {1, 2, . . . , n} whose size is in some interval [k, l], 0 ≤ k ≤ l ≤ n, exactly once (cyclically) by repeatedly adding or removing a single element, or by exchanging a single element. For k = 0 and l = n this is the classical problem of generating all 2 subsets of [n] by element additions/removals, and for k = l this is the...
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We consider the problem of constructing a cyclic listing of all bitstrings of length 2n+1 with Hamming weights in the interval [n+1−`, n+`], where 1 ≤ ` ≤ n+1, by flipping a single bit in each step. This is a far-ranging generalization of the wellknown middle two levels problem (the case ` = 1). We provide a solution for the case ` = 2 and solve a relaxed version of the problem for general valu...
متن کاملAntipodal Gray codes
An n-bit Gray code is a circular listing of the 2 n-bit strings so that successive strings differ only in one bit position. An n-bit antipodal Gray code has the additional property that the complement of any string appears exactly n steps away in the list. The problem of determining for which values of n antipodal Gray codes can exist was posed by Hunter Snevily, who showed them to be possible ...
متن کاملTransition Restricted Gray Codes
A Gray code is a Hamilton path H on the n-cube, Q n. By labeling each edge of Q n with the dimension that changes between its incident vertices, a Gray code can be thought of as a sequence H = t 1 ; t 2 ; : : : ; t N-1 (with N = 2 n and each t i satisfying 1 t i n). The sequence H deenes an (undirected) graph of transitions, G H , whose vertex set is f1; 2; : : : ; ng and whose edge set E(G H) ...
متن کاملBalanced Gray Codes
It is shown that balanced n-bit Gray codes can be constructed for all positive integers n. A balanced Gray code is one in which the bit changes are distributed as equally as possible among the bit positions. The strategy used is to prove the existence of a certain subsequence which will allow successful use of the construction proposed by Robinson and Cohn in 1981. Although Wagner and West prov...
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ژورنال
عنوان ژورنال: Theoretical Computer Science
سال: 2018
ISSN: 0304-3975
DOI: 10.1016/j.tcs.2017.12.003