A Simple Gray Code to List All Minimal Signed Binary Representations
نویسنده
چکیده
Abstract. A signed binary representation (SBR) of an integer N is a string ab · · · a2a1a0 over the alphabet {−1, 0, 1} such that N = ∑b i=0 ai2 i. An SBR of an integer N is said to be minimal if the number of nonzero digits is minimum. In this paper, we describe a simple 3-close Gray code for listing all minimal SBRs of an integer N . The algorithm is implemented to run in constant amortized time. In addition, we identify the values for N that have the maximum number of minimal SBRs given the length of the binary representation of N .
منابع مشابه
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ورودعنوان ژورنال:
- SIAM J. Discrete Math.
دوره 21 شماره
صفحات -
تاریخ انتشار 2007