ADA算法知识（四）Divide-and-conquer algorithm

最新推荐文章于 2024-05-15 13:44:47 发布

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本文探讨了分治算法在解决复杂问题中的应用，以硬币伪造者问题为例，介绍了如何通过将问题分解为更小的子问题，然后逐一治理并最终合并解决方案来找到伪造硬币的方法。文章详细解释了在O(logn)次称重中找出伪造硬币的分治算法。

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分治算法

Divide the problem into smaller sub-problems.
Governance - breaking down these smaller sub-problems one by one;
Combination - merge the solved sub-problems and finally get the solution of the "mother" problem

Like this question:

[The Coin Counterfeiter]

Give a divide-and-conquer algorithm to find the counterfeit coin in O(logn) weighings. You may assume that n is a power of 2.

Like give n as 16

16 8 4 2 1

four progress

Through O (1) operation, the problem of size n into a n/2 problem

so T(n)=T(n/2)+O(1)

and divide and Conquer: by O (1) operation, the problem of size n into 2 n/2 problems.

so T(n)=2T(n/2)+O(1)

it is obvious that it is a binary search question

When solving the main problems, I will divide the main problems into two sub-problems, for example, dividing n piles of coins into two piles of 2/n piles. If the pile is lighter, the bad coins will be in that pile. After repeated operation, the light piles of coins will be picked out and divided into two piles of the same number of coins until the bad coins are found