GENERATING THE FIBONACCI CHAIN IN O(log n) SPACE AND O(n) TIME
نویسنده
چکیده
On the example of the Fibonacci chain we show how to efˇciently generate inˇnite words deˇned by substitutions. We introduce substitution trees and we present an algorithm that uses them to generate such inˇnite words. We use a stack to generate the words in a completely different manner than in traditional breadth-ˇrst tree traversals. We show that the algorithm has O(logn) space complexity and O(n) time complexity, where n is the length of the generated word. The aperiodic Fibonacci chain is used for construction of aperiodic pseudorandom number generators.
منابع مشابه
Hyers-Ulam stability of K-Fibonacci functional equation
Let denote by Fk,n the nth k-Fibonacci number where Fk,n = kFk,n−1+Fk,n−2 for n 2 with initial conditions Fk,0 = 0, Fk,1 = 1, we may derive a functionalequation f(k, x) = kf(k, x − 1) + f(k, x − 2). In this paper, we solve thisequation and prove its Hyere-Ulam stability in the class of functions f : N×R ! X,where X is a real Banach space.
متن کاملFr{'e}chet and Hausdorff Queries on $x$-Monotone Trajectories
vspace{0.2cm}In this paper, we design a data structure for the following problem. Let $pi$ be an $x$-monotone trajectory with $n$ vertices in the plane and $epsilon >0$. We show how to preprocess $pi$ and $epsilon$ into a data structure such that for any horizontal query segment $Q$ in the plane, one can quickly determine the minimal continuous fraction of $pi$ whose Fr{'e}chet and Hausdo...
متن کاملFast Locating with the RLBWT
Indexing highly repetitive texts — such as genomic databases, software repositories and versioned text collections — has become an important problem since the turn of the millennium. A relevant compressibility measure for repetitive texts is r, the number of runs in their Burrows-Wheeler Transform (BWT). One of the earliest indexes for repetitive collections, the Run-Length FM-index, used O(r) ...
متن کاملTwo Dimensional Range Minimum Queries and Fibonacci Lattices
Given a matrix of size N , two dimensional range minimum queries (2D-RMQs) ask for the position of the minimum element in a rectangular range within the matrix. We study trade-offs between the query time and the additional space used by indexing data structures that support 2D-RMQs. Using a novel technique—the discrepancy properties of Fibonacci lattices—we give an indexing data structure for 2...
متن کاملRank-Relaxed Weak Queues: Faster than Pairing and Fibonacci Heaps?
A run-relaxed weak queue by Elmasry et al. (2005) is a priority queue data structure with insert and decrease-key in O(1) as well as delete and delete-min in O(log n) worst-case time. One further advantage is the small space consumption of 3n+O(log n) pointers. In this paper we propose rank-relaxed weak queues, reducing the number of rank violations nodes for each level to a constant, while pro...
متن کامل