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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Longest alternating subsequence ： ウィキペディア英語版 Longest alternating subsequence In combinatorial mathematics, probability, and computer science, in the longest alternating subsequence problem, one wants to find a subsequence of a given sequence in which the elements are in alternating order, and in which the sequence is as long as possible. Formally, if $\backslash mathbf\; =\; \backslash$ is a sequence of distinct real numbers, then the subsequence $\backslash ,\; \backslash ldots,\; x\_\backslash \}$ is ''alternating''〔name="Stanleybook">〕 (or ''zigzag'' or ''down-up'')if : Similarly, $\backslash mathbf$ is ''reverse alternating'' (or ''up-down'') if : Let $\_n(\backslash mathbf)$ denote the length (number of terms) of the longest alternating subsequence of $\backslash mathbf$. For example, if we consider some of the permutations of the integers 1,2,3,4,5, we have that * $\_5(1,2,3,4,5)\; =\; 2$; because any sequence of 2 distinct digits are (by definition) alternating. (for example 1,2 or 1,4 or 3,5) * $\_5(1,5,3,2,4)\; =\; 4,$ because 1,5,3,4 and 1,5,2,4 and 1,3,2,4 are all alternating, and there is no alternating subsequence with more elements; * $\_5(5,3,4,1,2)\; =\; 5,$ because 5,3,4,1,2 is itself alternating. == Efficient algorithms == The longest alternating subsequence problem is solvable in time $O(n)$, where $n$ is the length of the original sequence. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Longest alternating subsequence」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.