解题思路

本题要求使用$KNN$算法对待分类的手写数字进行识别，并且题目已经规定：

• $K=3$
• 距离度量使用欧式距离
• 如果最近的$3$个样本中，类别投票数相同，则选择“距离之和更小”的类别

核心做法如下：

题目内容

电商系统中验证码校对经常需要使用手写数字识别功能。写数字识别是机器学习领域中的经典问题。手写数字的形式有很多，有基于文本的手写数字识别和基于图像的手写数字识别。本题中结合 KNN 算法，实现手写数字的识别。请根据输出描述完成代码补全的部分。

输入描述

第一个输入是一个二维list，用于表示训练数据;

第二个输入是一个一维list，表示训练样本的对应 label，

第三个输入是一个一维list，是用于决策的手写数据。

输出描述

要求给出使用$KNN$算法计算后待决策数据对应的分类数字结果，以整形数据进行返回。

说明:因为$K=3$，根据$KNN$进行计算得到待决策数据最近的$3$个向量的索引为$1、2、4$，类别分别为$1、2、4$，最大数量类别存在相等的情况，将距离之和最小的类别$1$作为输出结果.

补充说明

(1)使用$python$中的$eval$函数可以很方便地还原输入内容;

(2)待决策的$K$值大小统一规定为$3$，如果类别投票数量相等，选择距离之和最小的类别;

(3)为了结果的唯一性，使用欧式距离作为度量依据，且所有数据均不需要进行归一化;

(4)$python$中可以使用第三方的库有:$numpy、scipy、pandas、scikit-learn$。

示例1

输入

[[0.0,0.0,5.0,13.0,9.0,1.0,0.0,0.0,0.0,0.0,13.0,15.0,10.0,15.0,5.0,0.0,0.0,3.0,15.0,2.0,0.0,11.0,8.0,0.0.0.0,4.0,12.0,0.0,0.0,8.0,8.0,0.0,0.0,5.0,8.0,0.0,0.0,9.0,8.0,0.0,0.0,4.0,11.0,0.0,1.0,12.0,7.0,0.0,0.0,2.0,14.0,5.0,10.0,12.0,0.0,0.0,0.0,0.0,6.0,13.0,10.0,0.0,0.0,0.0],[0.0,0.0,0.0,12.0,13.0,5.0,0.0,0.0,0.0,0.0,0.0,11.0,16.0,9.0,0.0,0.0,0.0,0.0,3.0,15.0,16.0,6.0,0.0,0.0,0.0,7.0,15.0,16.0,16.0,2.0,0.0,0.0,0.0,0.0,1.0,16.0,16.0,3.0,0.0,0.0,0.0,0.0,1.0,16.0,16.0,6.0,0.0,0.0,1.0,0.0,1.0,16.0,16.0,6.0,0.0,0.0,0.0,0.0,0.0,11.0,16.0,10.0,0.0,0.0],[0.0,0.0,0.0,4.0,15.0,12.0,0.0,0.0,0.0,0.0,3.0,16.0,15.0,14.0,0.0,0.0,0.0,0.0,8.0,13.0,8.0,16.0,0.0,0.0,0.0,0.0,1.0,6.0,15.0,11.0,0.0,0.0,0.0,1.0,8.0,13.0,15.0,1.0,0.0,0.0,0.0,9.0,16.0,16.0,5.0,0.0,0.0,0.0,0.0,3.0,13.0,16.0,16.0,11.0,5.0,0.0,0.0,0.0,0.0,3.0,11.0,16.0,9.0,0.0],[0.0,0.0,7.0,15.0,13.0,1.0,0.0,0.0,0.0,8.0,13.0,6.0,15.0,4.0,0.0,0.0,0.0,2.0,1.0,13.0,13.0,0.0,0.0,0.0,0.0,0.0,2.0,15.0,11.0.1.0,0.0,0.0,0.0,0.0,0.0,1.0,12.0,12.0,1.0,0.0,0.0,0.0.0.0,0.0,1.0.10.0,8.0,0.0,0.0,0.0,8.0,4.0,5.0,14.0,9.0,0.0,0.0,0.07.0,13.0,13.0,9.0,0.0,0.0],[0.0,0.0,0.0,1.0,11.0,0.0,0.0,0.0,0.0,0.0,0.0,7.0,8.0,0.0,0.0,0.0,0.0,0.0,1.0.13.0,6.0,2.0,2.0,0.0,0.0,0.0,7.0,15.0,0.0,9.0,8.0,0.0,0.0,5.0,16.0,10.0,0.0,16.0,6.0,0.0,0.0,4.0,15.0,16.0,13.0,16.0,1.0,0.0,0.0,0.0,0.0,3.0,15.0,10.0,0.0,0.00.0,0.0,0.0,2.0,16.0,4.0,0.0,0.0],[0.0,0.0,12.0,10.00.0,0.0,0.0,0.0,0.0,0.0,14.0,16.0,16.0,14.0,0.0,0.0,0.0,0.0,13.0,16.0,15.0,10.0,1.0,0.0,0.0,0.0,11.0,16.0,16.0,7.0,0.0,0.0,0.0,0.0,0.0,4.0,7.0,16.0,7.0,0.0,0.0,0.0,0.0,0.0,4.0,16.0,9.0,0.0,0.0,0.0,5.0,4.0,12.0,16.0,4.0,0.0,0.0,0.0,9.0,16.0,16.0,10.0,0.0,0.0], [0.0,0.0.0.0,12.0,13.0,0.0,0.0,0.0,0.0,0.0,5.0,16.0,8.0,0.0,0.0,0.0,0.0,0.0,13.0,16.0,3.0,0.0,0.0,0.0,0.0,0.0,14.0,13.0,0.0,0.0,0.0,0.0,0.0,0.0,15.0,12.0,7.0,2.0,0.0,0.0,0.0,0.0,13.0,16.0,13.0,16.0,3.0,0.0,0.0,0.0,7.0,16.0,11.0,15.0,8.0,0.0,0.0,0.0,1.0,9.0,15.0,11.0,3.0,0.0],[0.0,0.0,7.0,8.0,13.0,16.0,15.0,1.0,0.0,0.0,7.0,7.0,4.0,11.0,12.0,0.0,0.0,0.0,0.0,0.0,8.0,13.0,1.0,0.0,0.0,4.0,8.0,8.0,15.0,15.0,6.0,0.0,0.0,2.0,11.0,15.0,15.0,4.0,0.0,0.0,0.0,0.0,0.0,16.0,5.0,0.0,0.0,0.0,0.0,0.0,9.0,15.0,1.0,0.0,0.0,0.0,0.0,0.0,13.0,5.0,0.0,0.0,0.0,0.0][0.0,0.0,9.0,14.0,8.0,1.0,0.0,0.0,0.0,0.0,12.0,14.0,14.0,12.0,0.0,0.0,0.0,0.0,9.0,10.0,0.0,15.0,4.0,0.0,0.0,0.0,3.0,16.0,12.0,14.0,2.0,0.0,0.0,0.0,4.0,16.0,16.0,2.0,0.0,0.0,0.0,3.0,16.0,8.0,10.0,13.0,2.0,0.0,0.0,1.0,15.0,1.0,3.0,16.0,8.0,0.0,0.0,0.0,11.0,16.0,15.0,11.0,1.0,0.0][0.0,0.0,11.0,12.0,0.0,0.0,0.0,0.0,0.0,2.0,16.0,16.0,16.0,13.0,0.0,0.0,0.0,3.0,16.0,12.0,10.0,14.0,0.0,0.0,0.0,10,16.0,1.0,12.0,15.0,0.0,0.0,0.0,0.0,13.0,16.0,9.0,15.0,2.0,0.0,0.0,0.0,0.0,3.0,0.0,9.0,11.0,0.0,0.0,0.0,0.0,0.0,9.0,15.0,4.0,0.0,0.0,0.0,9.0,12.0,13.0,3.0,0.0,0.0]]
[0,1,2,3,4,5,6,7,8,9]
[0.0,0.0,0.0,0.0,14.0,13.0,1.0,0.0,0.0,0.0,0.0,5.0,16.0,16.0,2.0,0.0,0.0,0.0,0.0,14.0,16.0,12.0,0.0,0.00.0,1.0,10.0,16.0,16.0,12.0,0.0,0.0,0.0,3.0,12.0,14.0,16.0,9.0,0.0,0.0,0.0,0.0,0.0,5.0,16.0,15.0,0.0,0.0,0.0,0.0,0.0,4.0,16.0,14.0,0.0,0.0,0.0,0.0,0.0,1.0,13.0,16.0,1.0,0.0]

输出

1

说明

使用$KNN$进行计算得到待决策数据的样本分类应为数字$1$,所以返回值是$1$。