Greedy Algorithm,也就是贪心算法,局部最优化的算法
虽然可以快速得到解,但是这个解往往不会是全局最优解。不过这个算法的思想倒是挺有趣的。
Requirement
Consider the following solitaire game: you are given a list of moves, x1, x2…xm, and their costs, y1, y2…ym. Moves and their costs both take the form of positive integers.
现在提到了代写服务,肯定很多人都不会觉得陌生,就算是国内也是有着专业代写作业的服务行业的,能够为有需求的学生提供很多的帮助,不过其实代写机构在国外会更获得学生的支持,这是因为国外的学校对于平时的作业要求比较严格,为了获得更高的分数顺利毕业,不少留学生就会让代写机构帮忙完成作业,比较常见的作业代写类型,就是计算机专业了,因为对于留学生来说这个技术对于Machine Learning或者AI的代码编程要求更高,所以找代写机构完成作业会简单轻松很多,那么代写机构的水平,要怎么选择才会比较高?
1、代写机构正规专业
不论是在什么情况下,选择正规合法经营的机构肯定是首要的操作,这也是为了避免自己在找机构的时候,出现上当受骗的现象,造成自己的经济出现损失,带来的影响还是非常大的,所以需要注意很多细节才可以,所以在这样的情况下,代写机构的选择,也要选择在经营方面属于正规合法的类型,这样才可以保证服务进行的时候,不会出现各种问题,也可以减少损失的出现,而且正规合法也是代写机构的合格基础。
2、代写机构编程能力
作业的难度相信很多人都很熟悉,特别是对于AI深度学习或者是人工神经网络这种算法来说,因为要对SVM、Design Tree、线性回归以及编程有很高的要求,可以说作业的完成要求非常高,因此才会带动代写机构的发展,找专业的代写机构,一般都是会有专业的人员帮忙进行作业的完成,因为这类型的作业对专业要求比较高,因此代写机构也要具备专业能力才可以,否则很容易导致作业的完成出现问题,出现低分的评价。
3、代写机构收费情况
现在有非常多的留学生,都很在意作业的完成度,为了保证作业可以顺利的被完成,要进行的相关操作可是非常多的,代写机构也是因为如此才会延伸出来的,在现在发展也很迅速,现在选择代写机构的时候,一定要重视收费情况的合理性,因为代写作业还是比较费精力的,而且对于专业能力要求也高,所以价格方面一般会收取几千元至万元左右的价格,但是比较简单的也只需要几百元价格。
4、代写机构完成速度
大部分人都很在意代写机构的专业能力,也会很关心要具备什么能力,才可以展现出稳定的代写能力,其实专业的代写机构,对于作业完成度、作业完成时间、作业专业性等方面,都是要有一定的能力的,特别是在完成的时间上,一定要做到可以根据客户规定的时间内完成的操作,才可以作为合格专业的代写机构存在,大众在选择的时候,也可以重视完成时间这一点来。
现在找专业的CS代写机构帮忙完成作业的代写,完全不是奇怪的事情了,而且专业性越强的作业,需要代写机构帮忙的几率就会越高,代写就发展很好,需求量还是非常高的,这也可以很好的说明了,这个专业的难度以及专业性要求,才可以增加代写机构的存在。
Such a list of moves and their costs is called an instance of the game.
To play the game, you start with a positive integer n. On each turn of the game you have two choices: subtract 1 from n incurring a cost of 1 or pick some move xi such that n is divisible by xi and divide n by xi incurring a cost of yi. The goal is to get to 0 while incurring the minimum possible cost.
For instance, suppose that the set of moves is 4, 5, 7 and the corresponding penalties are 1, 3, 4. If n is 20 then the optimal strategy is as follows:
- Divide 20 by 4 to get 5, incurring a cost of 1
- Subtract 1 from 5 to get 4 incurring a cost of 1
- Divide 4 by 4 to get 1, incurring a cost of 1
- Subtract 1 from 1 to get 0, incurring a cost of 1
So the final cost is 4. One suboptimal strategy for this game is as follows:
- Divide 20 by 5 to get 4, incurring a cost of 3
- Divide 4 by 4 to get 1, incurring a cost of 1
- Subtract 1 from 1 to get 0, incurring a cost of 1
which gives us a total cost of 5.
One possible greedy algorithm for this game is as follows: On each turn, simply divide the current number by the legal move x of cost y which maximizes x / y – the ratio of move to cost (and subtract 1 from the current number if it is not divisible by any move).
If two legal moves have the same ratio of move to cost then the greedy algorithm will take the larger move. Unfortunately, this greedy algorithm does not always give the optimal strategy. In this problem you will find counterexamples that show the greedy algorithm is not optimal in different instances of this game.
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Tips:
- To find instances where the greedy algorithm fails, you will probably need to be able to find the optimal strategy in all instances. What kind of algorithm can you use to do this?
- Most of the difficulty of this assignment is in coming up with the right approach. The code you write does not need to be especially long or complex to solve the problem.
- It may take some time for your code to find a counterexample, particularly for the last couple instances. But if it takes more than a couple of minutes, you probably need to rethink your approach.
- When searching for instances of where the greedy algorithm fails, it is useful to avoid redoing work.
- For reference, the optimal cost for the instance (3, 1), (2, 1) when n is 321 is 10, and the greedy algorithm gives 11. The smallest value of n for which the greedy algorithm fails on the instance (211, 2), (210, 1) is 4740960.
- Start early. You have two weeks to do this problem, so you shouldn’t try to do it all in the last day.
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LE PHUONG
在此对LE PHUONG对本文所作的贡献表示诚挚感谢,她在山东大学完成了计算机科学与技术专业的硕士学位,专注数据分析、数据可视化、数据采集等。擅长Python、SQL、C/C++、HTML、CSS、VSCode、Linux、Jupyter Notebook。