时空权衡——斐波那契数列(Time/Space Tradeoff - Fibonacci Sequence)

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于 2017-06-10 08:15:01 发布 · 817 阅读

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#时空权衡 #斐波那契额数列 #算法 #Java

本文介绍了斐波那契数列的概念，通过使用“时空权衡”的设计算法技巧，以线性时间O(n)复杂度求解第n个斐波那契数，同时需要额外的内存来存储中间结果。文中提供了伪代码和Java实现，并指出尽管这种方法比暴力求解更高效，但仍有额外的空间需求。

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时空权衡——斐波那契数列(Time/Space Tradeoff - Fibonacci Sequence)

斐波那契数列简介(Introduction)
In mathematics, the Fibonacci numbers are the numbers in the following integer sequence, called Fibonacci sequence, characterised by the fact that every number after first two is the sum of the two preceding ones:
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233…
The problem is finding the nth Fibonacci number.

算法(Algorithm)
We can use “time and space tradeoff” design algorithm technique, which is decreasing the time required to solve a problem by using additional memory in a clever way.

We use a table to tabulate the function FIB as we go: Once an intermediate result has been computed, it not only return the result to caller but also store it in the table. So each call to FIB first check if the needed value is there, if it is not, the usual recursive pro