Python 如何根据日期范围合并两个字符串

我有两个DataFrame:df1和df2

import pandas as pd 

df1 = pd.DataFrame(
    {
        'a': ['2024-01-01 04:00:00', '2023-02-02 20:00:00'],
        'id':['a_1', 'a_2']

    }
)

df2 = pd.DataFrame(
    {
        'a': [
            '2024-01-01 4:00:00', '2024-01-01 05:00:00',
            '2024-01-01 06:00:00', '2024-01-01 07:00:00',
            '2024-01-01 08:00:00', '2024-01-01 09:00:00',
            '2023-02-02 21:00:00', '2023-02-02 23:00:00',
         ]
    }
)

这是预期的输出.我想把id从df1合并到df2:

                    a  id
0 2024-01-01 04:00:00  a_1  
1 2024-01-01 05:00:00  a_1
2 2024-01-01 06:00:00  a_1
3 2024-01-01 07:00:00  a_1
4 2024-01-01 08:00:00  NaN
5 2024-01-01 09:00:00  NaN
6 2023-02-02 21:00:00  a_2
7 2023-02-02 23:00:00  a_2

如果你熟悉烛台，df1.a就是4小时的烛台.例如df1.a.iloc[0]为:

2024-01-01 04:00:00

2024-01-01 05:00:00

2024-01-01 06:00:00

2024-01-01 07:00:00

基本上它的范围是从df1.a.iloc[0]到df1.a.iloc[0] + pd.Timedelta(hours=3).我想根据这些身份证覆盖的时间范围对其进行merge次查验.

这是我的try ，但我不知道如何通过日期范围merge:

df1['a'] = pd.to_datetime(df1.a)
df2['a'] = pd.to_datetime(df2.a)
df1['b'] = df1.a + pd.Timedelta(hours=3)