知行编程网知行编程网  2022-05-21 06:00 知行编程网 |  隐藏边栏 |   抢沙发 |  1 
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菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

在浩瀚无垠的东方玄域有无数的大大小小的门派，分布在丛山峻岭之间。其中位列顶尖有A门派，T门派，B门派，H门派，M门派，Z门派这6大势力最强，受众最广。每年都会通过笔试面试，挑选码农入门派内修炼。而码农在修炼的过程中有三大神器必看：

  • 写代码无论是遇到任何问题上，只要上Stackoveflow都能查到答案；
  • 查看源码，无论是复杂的框架还是小的脚本，都可以在GitHub上搜索查到；
  • 学会精妙的算法尤其是面试大门派之前，必刷LeetCode ；
小编周末在家，也开始静心的修炼起来，今天来刷一道在LeetCode上非常有名的题目CoinChange，据说这道面试题有师兄在阿里被面过，来一起挑战一下。


菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

1.题目：零钱兑换

给你不同面额的硬币coins和一个总金额amount。需要你来写一个函数来计算可以凑成总金额所需的最少的硬币个数。如果没有任何一种硬币组合能组成总金额，返回 -1。

示例：

输入: coins = [1, 2, 5], amount = 11

输出: 3 

解释: 11 = 5 + 5 + 1


示例：

输入: coins = [2], amount = 3

输出: -1 

2.菜鸟解法：暴力求解

如果不太动脑子不考虑效率的话，抱着不管三七二十一先做出来再说的话，肯定是暴力遍历比较容易想到。其实就是一个很简单的数学公式11=x1* 1+x2*2+x3*5,我们直接三层循环即可。

面值为1的钱币最大11张，x1的搜索空间为0-11

面值为2的钱币最大5张，x2的搜索空间为0-5

面值为5的钱币最大2张，x3的搜索空间为0-2

1).第一步算出每一张币种的最大张数

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

如果我们的输入的coins=[1,2,5],target =11 ，那么每一种币种的最大张数为11,5,2
2).进行空间搜索，凑到面值为11的组合

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

通过暴力的循环迭代，把凑到的钱币为11的组合用yield记录下来。
得到的组合示例为：
(4, [0, 3, 1])  
4是使用钱币的张数，0表示0张1元面，3表示3张2元面，1表示1张5元面值
(3, [1, 0, 2])  
3是使用钱币的张数，1表示1张1元面，0表示0张2元面，2表示1张5元面值

3).对组合的结果进行排序

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！


4).运行看一下结果

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

最后的结果就是{1: 1, 2: 0, 5: 2} ,最少用3张：1元面值*1，5元面值*2


3.优化：进阶解法

上面的解法平铺直叙，但是很明显有致命的缺陷，因为c1,c2,c3都是写死的，这样的话肯定不行，如果我们的币种的数目变化的不是3种，那上面的代码就直接挂了。

因为我们代码里写死了循环3层，其实每一个币种的面值也不一定是1，2，5，所以我们需要换一个思路来处理，代码优化如下：

三个币种【1，2，5】，每一种币种若要凑11元的最多使用张数为【11，5，2】，那么对于每一个面值的来说组合为：

  • 1元：[(0,1),(1,1),(2,1),(3,1)...(11,1)] 即为0张1元，1张1元，2张1元，3张1元

  • 2元:  [(0,2),(1,2),(2,2),(3,2)...(5,2)]即为0张2元，1张2元，2张2元，3张2元

  • 5元：[(0,5),(1,5),(2,5)]即为0张5元，1张5元，2张5元

然后我们把所有的币种的组合进行全排列即可

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

我们先得出币种和最大的张数的一个mapping,就是[(11, 1), (5, 2), (2, 5)]
接着进行把币种的单一面值的组合都列出来，就是:
[[0, 1], [1, 1], ... [11, 1], [0, 2], [1, 2],... [5, 2], [0, 5], [1, 5], [2, 5]]
最后用itertools里面的permutations进行全排列，剩下的其实就是对全排列的组合进行排序，就很简单了。

4. 王者：大神解法

上面的解法时间复杂度很高，而且效率很低，完全没有美感可言，非常简单粗暴。在真正的生成环境是不能这样使用的，很明显我们需要另辟蹊径。这个问题是一个很明显的动态规划问题。
动态规划算是算法里面比较难理解的一个概念，每个动态规划都是从网格开始。

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

对于面值1元，2元，5元，要凑11元，我们从0开始最大使用11张。
每一个等级的钱数我们通过网格画出使用最少的钱数，那么这个问题就分解为1+10: 寻找满足1元使用最少的钱数 和10元使用最少的钱数
2+9: 寻找满足2元使用的最少的钱数，寻找满足9使用最少的钱数
3+8: 寻找满足3元使用的最少的钱数，寻找满足8元使用最少的钱数
以此类推。。。

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

设计一个dp容器，进行存储每一个面值需要的最少的张数，一开始设置为正无穷大；

用2层循环去搜索这个网格，把每一个面值的使用的最少张数存进网格

我们输入几个测试用例看一下结果：

菜鸟刷题记！一道阿里算法面试题 ，来挑战不！

测试用例全部通过，懂点算法还是很有用点，尤其是面试招聘，行走江湖还是需要几把刷子呢！有的同学说面试的时候严格的像造火箭，招进去干活的活就是每天拧螺丝。

确实现实很骨干，但是拧螺丝也得有本书先混进大厂才行啊。好了，不啰嗦啦，小伙伴赶紧Python学起来！


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data-darkmode-original-bgcolor-15882396318564="rgb(255, 255, 255)" data-darkmode-color-15882396318564="rgb(230, 230, 230)" data-darkmode-original-color-15882396318564="rgb(0, 0, 0)" data-darkmode-bgcolor-15900529136199="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15900529136199="rgb(255, 255, 255)" data-darkmode-color-15900529136199="rgb(230, 230, 230)" data-darkmode-original-color-15900529136199="rgb(0, 0, 0)" style="display: inline-block;clear: both;"><section data-brushtype="text" data-darkmode-bgcolor-15860613985508="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15860613985508="rgb(255, 255, 255)" data-darkmode-color-15860613985508="rgb(230, 230, 230)" data-darkmode-original-color-15860613985508="rgb(0, 0, 0)" data-darkmode-bgimage-15860613985508="1" data-style="padding: 18px 15px 20px 10px; color: rgb(86, 146, 214); text-align: center; letter-spacing: 1.5px; background-image: url('https://www.zkxjob.com/wp-content/uploads/2022/05/wxsync-2022-05-a2a8a5e1e58f30392066a170034ee027.png'); background-size: 100% 100%; background-repeat: no-repeat; overflow-wrap: break-word !important;" data-darkmode-bgcolor-15870356070738="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356070738="rgb(255, 255, 255)" data-darkmode-color-15870356070738="rgb(230, 230, 230)" data-darkmode-original-color-15870356070738="rgb(0, 0, 0)" data-darkmode-bgimage-15870356070738="1" data-darkmode-bgcolor-15870356071023="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356071023="rgb(255, 255, 255)" data-darkmode-color-15870356071023="rgb(230, 230, 230)" data-darkmode-original-color-15870356071023="rgb(0, 0, 0)" data-darkmode-bgimage-15870356071023="1" data-darkmode-bgcolor-15882384789136="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882384789136="rgb(255, 255, 255)" data-darkmode-color-15882384789136="rgb(230, 230, 230)" data-darkmode-original-color-15882384789136="rgb(0, 0, 0)" data-darkmode-bgimage-15882384789136="1" data-darkmode-bgcolor-15882396318564="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882396318564="rgb(255, 255, 255)" data-darkmode-color-15882396318564="rgb(230, 230, 230)" data-darkmode-original-color-15882396318564="rgb(0, 0, 0)" data-darkmode-bgimage-15882396318564="1" data-darkmode-bgcolor-15900529136199="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15900529136199="rgb(255, 255, 255)" data-darkmode-color-15900529136199="rgb(230, 230, 230)" data-darkmode-original-color-15900529136199="rgb(0, 0, 0)" data-darkmode-bgimage-15900529136199="1" class="js_darkmode__bg__0 js_darkmode__8" style="padding: 18px 15px 20px 10px;background-size: 100% 100%;background-image: url('https://www.zkxjob.com/wp-content/uploads/2022/05/wxsync-2022-05-a2a8a5e1e58f30392066a170034ee027.png');color: rgb(86, 146, 214);letter-spacing: 1.5px;background-repeat: no-repeat;"><section data-darkmode-bgcolor-15860613985508="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15860613985508="rgb(255, 255, 255)" data-darkmode-color-15860613985508="rgb(230, 230, 230)" data-darkmode-original-color-15860613985508="rgb(0, 0, 0)" data-darkmode-bgimage-15860613985508="1" data-darkmode-bgcolor-15870356070738="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356070738="rgb(255, 255, 255)" data-darkmode-color-15870356070738="rgb(230, 230, 230)" data-darkmode-original-color-15870356070738="rgb(0, 0, 0)" data-darkmode-bgimage-15870356070738="1" data-darkmode-bgcolor-15870356071023="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356071023="rgb(255, 255, 255)" data-darkmode-color-15870356071023="rgb(230, 230, 230)" data-darkmode-original-color-15870356071023="rgb(0, 0, 0)" data-darkmode-bgimage-15870356071023="1" data-darkmode-bgcolor-15882384789136="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882384789136="rgb(255, 255, 255)" data-darkmode-color-15882384789136="rgb(230, 230, 230)" data-darkmode-original-color-15882384789136="rgb(0, 0, 0)" data-darkmode-bgimage-15882384789136="1" data-darkmode-bgcolor-15882396318564="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882396318564="rgb(255, 255, 255)" data-darkmode-color-15882396318564="rgb(230, 230, 230)" data-darkmode-original-color-15882396318564="rgb(0, 0, 0)" data-darkmode-bgimage-15882396318564="1" data-darkmode-bgcolor-15900529136199="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15900529136199="rgb(255, 255, 255)" data-darkmode-color-15900529136199="rgb(230, 230, 230)" data-darkmode-original-color-15900529136199="rgb(0, 0, 0)" data-darkmode-bgimage-15900529136199="1" style="display: flex;justify-content: center;align-items: center;"><section data-darkmode-bgcolor-15860613985508="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15860613985508="rgb(255, 255, 255)" data-darkmode-color-15860613985508="rgb(230, 230, 230)" data-darkmode-original-color-15860613985508="rgb(0, 0, 0)" data-darkmode-bgimage-15860613985508="1" data-darkmode-bgcolor-15870356070738="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356070738="rgb(255, 255, 255)" data-darkmode-color-15870356070738="rgb(230, 230, 230)" data-darkmode-original-color-15870356070738="rgb(0, 0, 0)" data-darkmode-bgimage-15870356070738="1" data-darkmode-bgcolor-15870356071023="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356071023="rgb(255, 255, 255)" data-darkmode-color-15870356071023="rgb(230, 230, 230)" data-darkmode-original-color-15870356071023="rgb(0, 0, 0)" data-darkmode-bgimage-15870356071023="1" data-darkmode-bgcolor-15882384789136="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882384789136="rgb(255, 255, 255)" data-darkmode-color-15882384789136="rgb(230, 230, 230)" data-darkmode-original-color-15882384789136="rgb(0, 0, 0)" data-darkmode-bgimage-15882384789136="1" data-darkmode-bgcolor-15882396318564="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882396318564="rgb(255, 255, 255)" data-darkmode-color-15882396318564="rgb(230, 230, 230)" data-darkmode-original-color-15882396318564="rgb(0, 0, 0)" data-darkmode-bgimage-15882396318564="1" data-darkmode-bgcolor-15900529136199="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15900529136199="rgb(255, 255, 255)" data-darkmode-color-15900529136199="rgb(230, 230, 230)" data-darkmode-original-color-15900529136199="rgb(0, 0, 0)" data-darkmode-bgimage-15900529136199="1" style="margin-left: 2px;width: 20px;"></section><section data-brushtype="text" data-darkmode-bgcolor-15860613985508="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15860613985508="rgb(255, 255, 255)" data-darkmode-color-15860613985508="rgb(51, 51, 51)" data-darkmode-original-color-15860613985508="rgb(51, 51, 51)" data-darkmode-bgimage-15860613985508="1" data-darkmode-bgcolor-15870356070738="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356070738="rgb(255, 255, 255)" data-darkmode-color-15870356070738="rgb(51, 51, 51)" data-darkmode-original-color-15870356070738="rgb(51, 51, 51)" data-darkmode-bgimage-15870356070738="1" data-darkmode-bgcolor-15870356071023="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15870356071023="rgb(255, 255, 255)" data-darkmode-color-15870356071023="rgb(51, 51, 51)" data-darkmode-original-color-15870356071023="rgb(51, 51, 51)" data-darkmode-bgimage-15870356071023="1" data-darkmode-bgcolor-15882384789136="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882384789136="rgb(255, 255, 255)" data-darkmode-color-15882384789136="rgb(51, 51, 51)" data-darkmode-original-color-15882384789136="rgb(51, 51, 51)" data-darkmode-bgimage-15882384789136="1" data-darkmode-bgcolor-15882396318564="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15882396318564="rgb(255, 255, 255)" data-darkmode-color-15882396318564="rgb(51, 51, 51)" data-darkmode-original-color-15882396318564="rgb(51, 51, 51)" data-darkmode-bgimage-15882396318564="1" data-darkmode-bgcolor-15900529136199="rgb(36, 36, 36)" data-darkmode-original-bgcolor-15900529136199="rgb(255, 255, 255)" data-darkmode-color-15900529136199="rgb(51, 51, 51)" data-darkmode-original-color-15900529136199="rgb(51, 51, 51)" data-darkmode-bgimage-15900529136199="1" style="font-size: 14px;color: rgb(51, 51, 51);text-align: left;"><span style="font-family: 楷体, 楷体_GB2312, SimKai;font-size: 15px;">点这里，领取新手福利</span></section></section></section></section></section></section></section>

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