• pandas 基础


    import pandas as pd
    import numpy as np
    
    import matplotlib.pyplot as plt
    

    创建一个Series ,同时让pandas自动生成索引列

    s = pd.Series([1,3,5,np.nan,6,8])
    
    # 查看s
    s
    
    0    1.0
    1    3.0
    2    5.0
    3    NaN
    4    6.0
    5    8.0
    dtype: float64
    

    创建一个DataFrame数据框

    ### 创建一个DataFrame ,可以传入一个numpy array 可以自己构建索引以及列标
    dates = pd.date_range('2018-11-01',periods=7)
    #### 比如说生成一个时间序列,以20181101 为起始位置的,7个日期组成的时间序列,数据的类型为datetime64[ns]
    
    dates
    
    DatetimeIndex(['2018-11-01', '2018-11-02', '2018-11-03', '2018-11-04',
                   '2018-11-05', '2018-11-06', '2018-11-07'],
                  dtype='datetime64[ns]', freq='D')
    
    df = pd.DataFrame(np.random.randn(7,4),index= dates,columns=list('ABCD'))
    df
    # 产生随机正态分布的数据,7行4列,分别对应的index的长度以及column的长度
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    2018-11-06 -0.691073 0.933016 1.857647 0.775526
    2018-11-07 0.467075 0.362407 2.319375 -0.721314
    ### 同时用可以使用dict的实行创建DataFrame
    df2 = pd.DataFrame({"A":1,
                       "B":"20181101",
                       'C':np.array([3]*4,dtype='int32'),
                       'D':pd.Categorical(['test','train','test','train']),
                       "E":1.5},
                      )
    df2
    
    A B C D E
    0 1 20181101 3 test 1.5
    1 1 20181101 3 train 1.5
    2 1 20181101 3 test 1.5
    3 1 20181101 3 train 1.5
    df2.dtypes
    ### 查看数据框中的数据类型,常见的数据类型还有时间类型以及float类型
    
    A       int64
    B      object
    C       int32
    D    category
    E     float64
    dtype: object
    

    查看数据

    
    # 比如说看前5行
    df.head()
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    # 后4行
    df.tail(4)
    
    A B C D
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    2018-11-06 -0.691073 0.933016 1.857647 0.775526
    2018-11-07 0.467075 0.362407 2.319375 -0.721314
    # 查看DataFrame的索引
    df.index
    
    DatetimeIndex(['2018-11-01', '2018-11-02', '2018-11-03', '2018-11-04',
                   '2018-11-05', '2018-11-06', '2018-11-07'],
                  dtype='datetime64[ns]', freq='D')
    
    # 查看DataFrame的列索引
    df.columns
    
    
    Index(['A', 'B', 'C', 'D'], dtype='object')
    
    # 查看DataFrame的数据,将DataFrame转化为numpy array 的数据形式
    df.values
    
    array([[ 2.19709382,  0.90891281, -0.64802911, -1.32554721],
           [ 0.35466158, -1.22424591, -0.50120854, -1.49017025],
           [-0.24583358, -1.04959585,  2.36622453,  0.6373212 ],
           [-0.6899396 ,  0.47128154, -1.41740143,  0.26890482],
           [-0.54804068, -0.84193368,  0.57312781, -1.05517487],
           [-0.6910726 ,  0.93301611,  1.85764662,  0.77552552],
           [ 0.46707509,  0.36240665,  2.31937488, -0.721314  ]])
    

    数据的简单统计

    # 可以使用describe函数对DataFrame中的数值型数据进行统计
    df.describe()
    
    A B C D
    count 7.000000 7.000000 7.000000 7.000000
    mean 0.120563 -0.062880 0.649962 -0.415779
    std 1.031487 0.942664 1.553537 0.955789
    min -0.691073 -1.224246 -1.417401 -1.490170
    25% -0.618990 -0.945765 -0.574619 -1.190361
    50% -0.245834 0.362407 0.573128 -0.721314
    75% 0.410868 0.690097 2.088511 0.453113
    max 2.197094 0.933016 2.366225 0.775526
    df2.describe()
    ### 对于其他的数据类型的数据describe函数会自动过滤掉
    
    A C E
    count 4.0 4.0 4.0
    mean 1.0 3.0 1.5
    std 0.0 0.0 0.0
    min 1.0 3.0 1.5
    25% 1.0 3.0 1.5
    50% 1.0 3.0 1.5
    75% 1.0 3.0 1.5
    max 1.0 3.0 1.5
    ### DataFrame 的转置,将列索引与行索引进行调换,行数据与列数进行调换
    df.T
    
    2018-11-01 00:00:00 2018-11-02 00:00:00 2018-11-03 00:00:00 2018-11-04 00:00:00 2018-11-05 00:00:00 2018-11-06 00:00:00 2018-11-07 00:00:00
    A 2.197094 0.354662 -0.245834 -0.689940 -0.548041 -0.691073 0.467075
    B 0.908913 -1.224246 -1.049596 0.471282 -0.841934 0.933016 0.362407
    C -0.648029 -0.501209 2.366225 -1.417401 0.573128 1.857647 2.319375
    D -1.325547 -1.490170 0.637321 0.268905 -1.055175 0.775526 -0.721314
    df
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    2018-11-06 -0.691073 0.933016 1.857647 0.775526
    2018-11-07 0.467075 0.362407 2.319375 -0.721314

    数据的排序

    df.sort_index(ascending=False)
    ### 降序,按照列进行降序,通过该索引列
    
    A B C D
    2018-11-07 0.467075 0.362407 2.319375 -0.721314
    2018-11-06 -0.691073 0.933016 1.857647 0.775526
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    
    print(df.sort_values(by=['B','A']))
    #  默认是升序,可以选择多指排序,先照B,后排A,如果B中的数据一样,则按照A中的大小进行排序
    df.sort_values(by='B')
    
                       A         B         C         D
    2018-11-02  0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596  2.366225  0.637321
    2018-11-05 -0.548041 -0.841934  0.573128 -1.055175
    2018-11-07  0.467075  0.362407  2.319375 -0.721314
    2018-11-04 -0.689940  0.471282 -1.417401  0.268905
    2018-11-01  2.197094  0.908913 -0.648029 -1.325547
    2018-11-06 -0.691073  0.933016  1.857647  0.775526
    
    A B C D
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175
    2018-11-07 0.467075 0.362407 2.319375 -0.721314
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-06 -0.691073 0.933016 1.857647 0.775526

    选择数据(类似于数据库中sql语句)

    df['A']
    # 取出单独的一列数据,等价于df.A
    
    2018-11-01    2.197094
    2018-11-02    0.354662
    2018-11-03   -0.245834
    2018-11-04   -0.689940
    2018-11-05   -0.548041
    2018-11-06   -0.691073
    2018-11-07    0.467075
    Freq: D, Name: A, dtype: float64
    
    # 通过[]进行行选择切片
    df[0:3]
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    # 同时对于时间索引而言,可以直接使用比如
    df['2018-11-01':'2018-11-04']
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905

    另外可以使用标签来选择

    
    df.loc['2018-11-01']
    
    A    2.197094
    B    0.908913
    C   -0.648029
    D   -1.325547
    Name: 2018-11-01 00:00:00, dtype: float64
    
    #### 通过标签来进行多个轴上的进行选择
    df.loc[:,["A","B"]] # 等价于df[["A","B"]]
    
    A B
    2018-11-01 2.197094 0.908913
    2018-11-02 0.354662 -1.224246
    2018-11-03 -0.245834 -1.049596
    2018-11-04 -0.689940 0.471282
    2018-11-05 -0.548041 -0.841934
    2018-11-06 -0.691073 0.933016
    2018-11-07 0.467075 0.362407
    df.loc["2018-11-01":"2018-11-03",["A","B"]]
    
    A B
    2018-11-01 2.197094 0.908913
    2018-11-02 0.354662 -1.224246
    2018-11-03 -0.245834 -1.049596
    #### 获得一个标量数据
    df.loc['2018-11-01','A']
    
    2.1970938156943904
    

    通过位置获取数据

    df.iloc[3]  # 获得第四行的数据
    
    A   -0.689940
    B    0.471282
    C   -1.417401
    D    0.268905
    Name: 2018-11-04 00:00:00, dtype: float64
    
    df.iloc[1:3,1:4]  #  与numpy中的ndarray类似
    
    B C D
    2018-11-02 -1.224246 -0.501209 -1.490170
    2018-11-03 -1.049596 2.366225 0.637321
    # 可以选取不连续的行或者列进行取值
    df.iloc[[1,3],[1,3]]
    
    B D
    2018-11-02 -1.224246 -1.490170
    2018-11-04 0.471282 0.268905
    #  对行进行切片处理
    df.iloc[1:3,:]
    
    A B C D
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321
    # 对列进行切片
    df.iloc[:,1:4]
    
    B C D
    2018-11-01 0.908913 -0.648029 -1.325547
    2018-11-02 -1.224246 -0.501209 -1.490170
    2018-11-03 -1.049596 2.366225 0.637321
    2018-11-04 0.471282 -1.417401 0.268905
    2018-11-05 -0.841934 0.573128 -1.055175
    2018-11-06 0.933016 1.857647 0.775526
    2018-11-07 0.362407 2.319375 -0.721314
    # 获取特定的值
    df.iloc[1,3]
    
    -1.4901702546027098
    

    布尔值索引

    # 使用单列的数据作为条件进行筛选
    df[df.A>0]
    
    A B C D
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170
    2018-11-07 0.467075 0.362407 2.319375 -0.721314
     #很少用到,很少使用这种大范围的条件进行筛选
    df[df>0] 
    
    A B C D
    2018-11-01 2.197094 0.908913 NaN NaN
    2018-11-02 0.354662 NaN NaN NaN
    2018-11-03 NaN NaN 2.366225 0.637321
    2018-11-04 NaN 0.471282 NaN 0.268905
    2018-11-05 NaN NaN 0.573128 NaN
    2018-11-06 NaN 0.933016 1.857647 0.775526
    2018-11-07 0.467075 0.362407 2.319375 NaN
    # 使用isin()方法过滤
    df2.head()
    
    A B C D E
    0 1 20181101 3 test 1.5
    1 1 20181101 3 train 1.5
    2 1 20181101 3 test 1.5
    3 1 20181101 3 train 1.5
    df2[df2['D'].isin(['test'])]
    
    A B C D E
    0 1 20181101 3 test 1.5
    2 1 20181101 3 test 1.5

    设定数值(类似于sql update 或者add)

    • 设定一个新的列
    df['E'] = [1,2,3,4,5,6,7]
    
    df
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547 1
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170 2
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321 3
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 4
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 5
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 6
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 7
    • 通过标签设定新的值
    df.loc['2018-11-01','E']= 10  # 第一行,E列的数据修改为10
    
    df
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547 10
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170 2
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321 3
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 4
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 5
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 6
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 7
    df.iloc[1,4]=5000  # 第二行第五列数据修改为5000
    
    df
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547 10
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170 5000
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321 3
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 4
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 5
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 6
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 7
    df3 =df.copy()
    df3[df3<0]= -df3
    df3  # 都变成非负数
    
    A B C D E
    2018-11-01 2.197094 0.908913 0.648029 1.325547 10
    2018-11-02 0.354662 1.224246 0.501209 1.490170 5000
    2018-11-03 0.245834 1.049596 2.366225 0.637321 3
    2018-11-04 0.689940 0.471282 1.417401 0.268905 4
    2018-11-05 0.548041 0.841934 0.573128 1.055175 5
    2018-11-06 0.691073 0.933016 1.857647 0.775526 6
    2018-11-07 0.467075 0.362407 2.319375 0.721314 7

    缺失值处理

    df
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 -1.325547 10
    2018-11-02 0.354662 -1.224246 -0.501209 -1.490170 5000
    2018-11-03 -0.245834 -1.049596 2.366225 0.637321 3
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 4
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 5
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 6
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 7
    df['E']=[1,np.nan,2,np.nan,4,np.nan,6]
    
    df.loc['2018-11-01':'2018-11-03','D']=np.nan
    
    df
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 NaN 1.0
    2018-11-02 0.354662 -1.224246 -0.501209 NaN NaN
    2018-11-03 -0.245834 -1.049596 2.366225 NaN 2.0
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 NaN
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 4.0
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 NaN
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 6.0
    • 去掉缺失值的行
    df4 = df.copy()
    
    df4.dropna(how='any')
    
    A B C D E
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 4.0
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 6.0
    df4.dropna(how='all')
    # """DataFrame.dropna(axis=0, how='any', thresh=None, subset=None, inplace=False)""" 
    # aixs 轴0或者1 index或者columns
    # how 方式
    # thresh 超过阈值个数的缺失值
    # subset 那些字段的处理
    # inplace 是否直接在原数据框中的替换
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 NaN 1.0
    2018-11-02 0.354662 -1.224246 -0.501209 NaN NaN
    2018-11-03 -0.245834 -1.049596 2.366225 NaN 2.0
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 NaN
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 4.0
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 NaN
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 6.0
    • 对缺失值就行填充
    df4.fillna(1000)
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 1000.000000 1.0
    2018-11-02 0.354662 -1.224246 -0.501209 1000.000000 1000.0
    2018-11-03 -0.245834 -1.049596 2.366225 1000.000000 2.0
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 1000.0
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 4.0
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 1000.0
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 6.0
    • 对数据进行布尔值进行填充
    pd.isnull(df4)
    
    A B C D E
    2018-11-01 False False False True False
    2018-11-02 False False False True True
    2018-11-03 False False False True False
    2018-11-04 False False False False True
    2018-11-05 False False False False False
    2018-11-06 False False False False True
    2018-11-07 False False False False False

    数据操作

    #统计的工作一般情况下都不包含缺失值,
    df4.mean() 
    #  默认是对列进行求平均,沿着行方向也就是axis=0
    
    A    0.120563
    B   -0.062880
    C    0.649962
    D   -0.183015
    E    3.250000
    dtype: float64
    
    df4.mean(axis=1)
    #  沿着列方向求每行的平均
    
    2018-11-01    0.864494
    2018-11-02   -0.456931
    2018-11-03    0.767699
    2018-11-04   -0.341789
    2018-11-05    0.425596
    2018-11-06    0.718779
    2018-11-07    1.685509
    Freq: D, dtype: float64
    
     # 对于拥有不同维度,需要对齐的对象进行操作。Pandas会自动的沿着指定的维度进行广播:
    s = pd.Series([1,3,4,np.nan,6,7,8],index=dates)
    s
    
    2018-11-01    1.0
    2018-11-02    3.0
    2018-11-03    4.0
    2018-11-04    NaN
    2018-11-05    6.0
    2018-11-06    7.0
    2018-11-07    8.0
    Freq: D, dtype: float64
    
    df4.sub(s,axis='index')
    
    A B C D E
    2018-11-01 1.197094 -0.091087 -1.648029 NaN 0.0
    2018-11-02 -2.645338 -4.224246 -3.501209 NaN NaN
    2018-11-03 -4.245834 -5.049596 -1.633775 NaN -2.0
    2018-11-04 NaN NaN NaN NaN NaN
    2018-11-05 -6.548041 -6.841934 -5.426872 -7.055175 -2.0
    2018-11-06 -7.691073 -6.066984 -5.142353 -6.224474 NaN
    2018-11-07 -7.532925 -7.637593 -5.680625 -8.721314 -2.0
    df4
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 NaN 1.0
    2018-11-02 0.354662 -1.224246 -0.501209 NaN NaN
    2018-11-03 -0.245834 -1.049596 2.366225 NaN 2.0
    2018-11-04 -0.689940 0.471282 -1.417401 0.268905 NaN
    2018-11-05 -0.548041 -0.841934 0.573128 -1.055175 4.0
    2018-11-06 -0.691073 0.933016 1.857647 0.775526 NaN
    2018-11-07 0.467075 0.362407 2.319375 -0.721314 6.0
    df4.apply(np.cumsum)
    
    A B C D E
    2018-11-01 2.197094 0.908913 -0.648029 NaN 1.0
    2018-11-02 2.551755 -0.315333 -1.149238 NaN NaN
    2018-11-03 2.305922 -1.364929 1.216987 NaN 3.0
    2018-11-04 1.615982 -0.893647 -0.200415 0.268905 NaN
    2018-11-05 1.067942 -1.735581 0.372713 -0.786270 7.0
    2018-11-06 0.376869 -0.802565 2.230360 -0.010745 NaN
    2018-11-07 0.843944 -0.440158 4.549735 -0.732059 13.0
    df4.apply(lambda x: x.max()-x.min())
    
    A    2.888166
    B    2.157262
    C    3.783626
    D    1.830700
    E    5.000000
    dtype: float64
    

    统计个数与离散化

    s = pd.Series(np.random.randint(0,7,size=15))
    s
    
    0     1
    1     6
    2     3
    3     1
    4     1
    5     0
    6     4
    7     1
    8     3
    9     4
    10    6
    11    1
    12    4
    13    3
    14    5
    dtype: int32
    
    s.value_counts()
    # 统计元素的个数,并按照元素统计量进行排序,未出现的元素不会显示出来
    
    1    5
    4    3
    3    3
    6    2
    5    1
    0    1
    dtype: int64
    
    s.reindex(range(0,7))
    # 按照固定的顺序输出元素的个数统计
    
    0    1
    1    6
    2    3
    3    1
    4    1
    5    0
    6    4
    dtype: int32
    
    s.mode()
    #  众数 
    
    0    1
    dtype: int32
    
    • 离散化
    # 连续值转化为离散值,可以使用cut函数进行操作(bins based on vlaues) qcut (bins based on sample
    # quantiles) 函数
    arr = np.random.randint(0,20,size=15)  # 正态分布
    arr
    
    array([ 3, 14, 10,  2,  2,  0, 17, 13,  7,  0, 15, 14,  4, 19,  9])
    
    factor = pd.cut(arr,3)
    factor
    
    [(-0.019, 6.333], (12.667, 19.0], (6.333, 12.667], (-0.019, 6.333], (-0.019, 6.333], ..., (12.667, 19.0], (12.667, 19.0], (-0.019, 6.333], (12.667, 19.0], (6.333, 12.667]]
    Length: 15
    Categories (3, interval[float64]): [(-0.019, 6.333] < (6.333, 12.667] < (12.667, 19.0]]
    
    pd.value_counts(factor)
    
    (12.667, 19.0]     6
    (-0.019, 6.333]    6
    (6.333, 12.667]    3
    dtype: int64
    
    factor1 = pd.cut(arr,[-1,5,10,15,20])
    
    pd.value_counts(factor1)
    
    (-1, 5]     6
    (10, 15]    4
    (5, 10]     3
    (15, 20]    2
    dtype: int64
    
    factor2 = pd.qcut(arr,[0,0.25,0.5,0.75,1])
    
    pd.value_counts(factor2)
    
    (9.0, 14.0]      4
    (2.5, 9.0]       4
    (-0.001, 2.5]    4
    (14.0, 19.0]     3
    dtype: int64
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  • 原文地址:https://www.cnblogs.com/onemorepoint/p/9979725.html
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