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某种 找换硬币问题的贪心算法的正确性证明

代码星球阅读(1479)2020-04-04 收藏0次评论

一,问题介绍

最近一直在看贪心算法的正确性证明(如何证明贪心算法获得的解一定是最优解),感觉“剪枝”技巧用得比较多。再看了下《算法导论》中贪心算法一章里面的一个练习---找换硬币问题。这个问题对于某些 面值的硬币 是有最优解的,故记录下其中的一些证明思路。

考虑用最少的硬币数 来找 n 分钱的问题,假设每个硬币的值都是整数。

如果可换的硬币的单位是 c 的幂,也就是 c0,c1,... ,ck ,其中整数 c>1,k>=1

证明贪心算法总可以产生一个最优解。

 

二,找换硬币的贪心策略

这里的贪心策略很容易想到:总是优先选择 大面值的硬币 去找。比如,现有 1分、5分、25分的硬币可用来找钱,现在我们需要找 n=32分 的零钱,如何找?

优先选择大面值的嘛,那就是先选 25分;选完之后,还要找32-25=7,那就再选5分的,最终再先2个1分的。即可。

这里:32=25+5+1+1,一共用了4枚硬币。那么,问题来了!!!还有没有其他策略 只需要 3 枚硬币?或者更少的硬币?

这就需要证明贪心策略 有没有 最优解了?对于这个问题而言,如果用来找换的硬币的 面值 满足某种性质,该贪心策略是有最优解的。

这里说的某种性质就是:可换的硬币的单位(或者称 面值)是 c 的幂,也就是 c0,c1,... ,ck ,其中整数 c>1,k>=1

下面给出正确性证明。

这里需要强调一点: 硬币面值满足上面的性质时贪心算法一定能产生最优解,但是不满足时,也有可能有最优解。比如,面值为1,5,10,20,50,100时,贪心找零也一定有最优解。

 

三,找换硬币的贪心算法的正确性证明

在进行证明之前,先提一个性质:对于最优解而言,如果使用了面值为 ci 的硬币去找零,那么 ci 最多只能使用 c-1 个。

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" width="1014" height="179" />

因为我们的目标是使用 最少数目的硬币,对于最优解而言,如果使用了面值为 ci 的硬币去找零,那么 ci 最多只能使用 c-1 个。

why? 假设使用了 c 个(大于c个也一样)面值为 ci 的硬币去找零,那我为什么不用一个 面值为 ci+1 的硬币去找呢?

这样,我就可以用更少的硬币数啊(c>1)。所以说,在最优解里面,如果使用了面值为 ci 的硬币去找零,那么 面值为ci 的硬币 最多只能使用 c-1 个。

OK,下面再次用到剪枝的思想来证明贪心选择的正确性了。

总体思路是:先考察一个最优解,然后证明可对该解进行修改,使其采用贪心选择,这个选择将原问题变成一个相似的、但是“更小”的问题。(这里说的“更小”是一种抽象,并不是具体意义上的更小)

k 是可找换的硬币的种类数,n 是需要找换的价值,a(i)表示使用多少个 面值为 ci 的硬币。假设硬币已经按面值从小到大排序。

对于贪心选择而言,我们一定会选择面值为 c^j 的硬币,因为:我们的贪心策略就是总是优先选择 面值最大的硬币。

我们的目标是证明,对于所有的贪心选择而言,它们都不可能产生最优解。

对于非贪心选择,是不会选择 面值为 c^j (or higher)的硬币的。非贪心选择使用的硬币如下:

其中,a(i)表示使用了 a(i)个 面值为 ci 的硬币,总数之和是n。别忘了,n 就是需要找零的数目

而对于贪心选择而言,如果面值为 c^j 的硬币可用(当 n>=c^j 时),我们是优先使用 面值为 c^j 的硬币的。

因此有:

这说明,在面值为 c^j 的硬币 可用的情况下,换句话说:在 c^j <=n 的情况下,贪心选择没有使用 c^j 嘛。(选择了的话,那就是贪心选择了嘛...~)

 这里就会有矛盾了,根据前面提到的性质:有, a(i) <= c-1

 

 

从而,证明了贪心选择的正确性。

再来理解下它:总体思路是:先考察一个最优解,然后证明可对该解进行修改,使其采用贪心选择,这个选择将原问题变成一个相似的、但是“更小”的问题。(这里说的“更小”是一种抽象,并不是具体意义上的更小)

这里的最优解是:非贪心选择下的某个最优解,然后剪枝:将非贪心选择下的某个元素去掉,然后添入贪心选择的那个元素。其实就是下面的这个公式。

              从而得到了一个更优的问题。

 

四,参考资料

部分背包问题的贪心算法正确性证明

某种 找换硬币问题的贪心算法的正确性证明

从 活动选择问题 看动态规划和贪心算法的区别与联系

找换硬币问题的求解 以及与 0-1背包问题区别

 

以上就是某种 找换硬币问题的贪心算法的正确性证明的全部内容。