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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 Akra–Bazzi method ： ウィキペディア英語版 Akra–Bazzi method In computer science, the Akra–Bazzi method, or Akra–Bazzi theorem, is used to analyze the asymptotic behavior of the mathematical recurrences that appear in the analysis of divide and conquer algorithms where the sub-problems have substantially different sizes. It is a generalization of the well-known master theorem, which assumes that the sub-problems have equal size. == The formula == The Akra–Bazzi method applies to recurrence formulas of the form :$T(x)=g(x)\; +\; \backslash sum\_^k\; a\_i\; T(b\_i\; x\; +\; h\_i(x))\backslash qquad\; \backslash textx\; \backslash geq\; x\_0.$ The conditions for usage are: * sufficient base cases are provided * $a\_i$ and $b\_i$ are constants for all i * $a\_i\; >\; 0$ for all i * for all i * $\backslash left|g(x)\backslash right|\; \backslash in\; O(x^c)$, where ''c'' is a constant and ''O'' notates Big O notation * $\backslash left|\; h\_i(x)\; \backslash right|\; \backslash in\; O\backslash left(\backslash frac\backslash right)$ for all i * $x\_0$ is a constant The asymptotic behavior of T(x) is found by determining the value of p for which $\backslash sum\_^k\; a\_i\; b\_i^p\; =\; 1$ and plugging that value into the equation :$T(x)\; \backslash in\; \backslash Theta\; \backslash left(\; x^p\backslash left(\; 1+\backslash int\_1^x\; \backslash frac\; n\; \backslash right)$ and $T(n)\; =\; n\; +\; T\; \backslash left(\backslash left\backslash lfloor\; \backslash frac\; n\; \backslash right\backslash rfloor\; \backslash right)$ will, as per the Akra–Bazzi theorem, have the same asymptotic behavior. 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「Akra–Bazzi method」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.