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題名 | Generalized Gray Codes with Applications=Gray Code的推廣與其應用 |
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作者 | 官大智; | 書刊名 | Proceedings of the National Science Council : Part A, Physical Science and Engineering |
卷期 | 22:6 1998.11[民87.11] |
頁次 | 頁841-848 |
分類號 | 319.9 |
關鍵詞 | 群碼; 權重多項式; 非遞回; 演算法; (n,k)-gray code; Weight polynomial; Tower of hanoi; Hamiltonian path; Hypercube network; |
語文 | 英文(English) |
中文摘要 | 我們提出一個依特定順序產生 (Z�a)�滫漫狾酗葛尷犖t算法。此序列稱為 (n,k)-Gray 碼。在此序列中,每一對相鄰的元素僅差一個位元,且其差值為 +1 或 -1。此 序列可以應用於群碼 (group code) 權重多項式 (weight polynomial) 的計算, 以減少計 算時間。 此演算法為非遞回 (nonrecursive),且產生下一個元素時只和上一個元素有關。 因此可以將計算量大的工作分段來做。此演算法所產生之序列亦可用來解一種 Hanoi Tower 問題,在此問題中,圓盤僅能移到鄰的柱子上。此問題的解恰好是 (3,k)-Gray 碼,其中 k 為圓盤的個數。 最後, 我們證明 (n, k) -Gray 碼也是推廣高次立方體 (generalized hypercube) 中一個 Hamiltonian path。 |
英文摘要 | An efficient algorithm for enumerating a sequence of all elements in (Z�a)�� in a special order is presented. The seguence enumerated is called the (n,k) -Gray code. It has the property that each pair of adjacent elements differs in only one digit and the difference is either +1 or -1. This sequence can be efficiently applied to calculation of the weight polynomial of a group code. We also show that the Tower of Hanoi problem, in which disks can only be moved to the adjacent pegs, can be solved by enumerating the (3,k)-Gray code, where k is the number of disks to be moved. Finally, we show that the enumeration of the (n,k)-Gray code can also be regarded as a Hamiltonian path in a generalized hypercube network. |
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