list下界

下界理論 (Lower Bound Theory)

Lower bound (L(n)) is a property of the specific problem i.e. the sorting problem, matrix multiplication not of any particular algorithm solving that problem.

下界(L(n))是特定問題(即排序問題)的矩陣，不是解決該問題的任何特定算法的矩陣乘法。

Lower bound theory says that no algorithm can do the job in fewer than that of (L (n)) times the units for arbitrary inputs i.e. that for every comparison based sorting algorithm must take at least L(n) time in the worst case.

下界理論說，沒有一種算法能以少于任意輸入的單位(L(n))倍的時間完成這項工作，也就是說，在最壞的情況下，每個基于比較的排序算法必須至少花費L(n)時間。

L(n) is the minimum over all possible algorithm which is maximum complete.

L(n)是所有可能算法中的最小值，而最大值是最大完成度。

Trivial lower bounds are used to yield the bound best option is to count the number of item in the problems input that must be processed and a number of output items that need to be produced.

瑣碎的下限用于產(chǎn)生綁定最佳選擇是計算問題輸入中必須處理的項目數(shù)和需要產(chǎn)生的輸出項數(shù)。

The lower bound theory is the technique that has been used to establish the given algorithm in the most efficient way which is possible. This is done by discovering a function g(n) that is a lower bound on the time that any algorithm must take to solve the given problem. Now if we have an algorithm whose computing time is the same order as g(n), then we know that asymptotically we cannot do better.

下限理論是一種已被用來以可能的最有效方式建立給定算法的技術(shù)。 這是通過發(fā)現(xiàn)一個函數(shù)g(n)來完成的，該函數(shù)在任何算法解決給定問題所需的時間上都有一個下限。 現(xiàn)在，如果我們有一種算法，其計算時間與g(n)相同 ，那么我們知道漸近地我們不能做得更好。

If f(n) is the time for some algorithm, then we write f(n) = Ω(g(n)) to mean that g(n) is the lower bound of f(n). This equation can be formally written, if there exists positive constants c and n0 such that |f(n)| >= c|g(n)| for all n > n0. In addition for developing lower bounds within the constant factor, we are more conscious of the fact to determine more exact bounds whenever this is possible.

如果f(n)是某種算法的時間，則我們將f(n)=Ω(g(n))表示為g(n)是f(n)的下限 。 如果存在正常數(shù)c和n0使得| f(n)|成立 ，則該方程式可以正式寫成。 > = c | g(n)| 對于所有n> n0 。 除了在恒定因子內(nèi)建立下界外，我們更意識到在可能的情況下確定更精確界限的事實。

Deriving good lower bounds is more difficult than devising efficient algorithms. This happens because a lower bound states a fact about all possible algorithms for solving a problem. Generally, we cannot enumerate and analyze all these algorithms, so lower bound proofs are often hard to obtain.

與設(shè)計有效的算法相比，得出良好的下界更加困難。 之所以會發(fā)生這種情況，是因為下限指出了所有可能解決問題的算法的事實。 通常，我們無法枚舉和分析所有這些算法，因此通常很難獲得下界證明。

The proofing techniques that are useful for obtaining lower bounds are:

對獲得下限有用的校對技術(shù)是：

Comparison trees:

比較樹：

Comparison trees are the computational model useful for determining lower bounds for sorting and searching problems.

比較樹是用于確定排序和搜索問題下限的計算模型。

Oracles and adversary arguments:

Oracle和對手的論點：

One of the techniques that are important for obtaining lower bounds consists of making the use of an oracle

獲得下界的重要技術(shù)之一是使用預(yù)言

Lower bounds through reduction:

通過縮減下界：

This is a very important technique of lower bound, This technique calls for reducing the given problem for which a lower bound is already known.

這是一個非常重要的下限技術(shù)。該技術(shù)要求減少已知下限的給定問題。

Techniques for the algebraic problem:

代數(shù)問題的技術(shù)：

Substitution and linear independence are two methods used for deriving lower bounds on algebraic and arithmetic problems. The algebraic problems are operation on integers, polynomials, and rational functions.

代換和線性獨立性是用于推導(dǎo)代數(shù)和算術(shù)問題下界的兩種方法。 代數(shù)問題是對整數(shù)，多項式和有理函數(shù)的運算。

翻譯自: https://www.includehelp.com/algorithms/lower-bound-theory.aspx

list下界

總結(jié)

以上是生活随笔為你收集整理的list下界_下界理论的全部內(nèi)容，希望文章能夠幫你解決所遇到的問題。

如果覺得生活随笔網(wǎng)站內(nèi)容還不錯，歡迎將生活随笔推薦給好友。