how to get a unique week number for start and end dates in multi years - Pandas

I have a dataframe where two of the columns represent the start and end date of the data record. There are multiple years. My goal is to assign a new column that represents the time step of the data record in each row. Since I have a location columns as well, some of these weeks will be repeating.

import pandas as pd


dates = pd.date_range(start='2021-11-11', periods=20, freq='W')


df = pd.DataFrame({
    'start_date': np.repeat(dates, 5),
    'end_date': np.repeat(dates + pd.DateOffset(days=6), 5),
    'country': ['USA', 'Canada', 'UK', 'Australia', 'Russia'] * 20
})

df = df.sort_values("start_date")


	start_date	end_date	country	
0	2021-11-14	2021-11-20	USA	
1	2021-11-14	2021-11-20	Canada
2	2021-11-14	2021-11-20	UK
3	2021-11-14	2021-11-20	Australia	
4	2021-11-14	2021-11-20	Russia	

I can get the week number using isocalendar().week, but it is giving the week number of the corresponding year. For instance, if 2021-11-14 and 2021-11-20 is the first week in the data frame, it should get 1. It may skip the next week, and have another record starting from 2021-11-27. Such time step should be the second week for me in the data frame.

IIUC, you can use groupby_ngroup:

df['week'] = df.groupby(df['start_date']).ngroup().add(1)
print(df)

# Output
   start_date   end_date    country  week
0  2021-11-14 2021-11-20        USA     1
1  2021-11-14 2021-11-20     Canada     1
2  2021-11-14 2021-11-20         UK     1
3  2021-11-14 2021-11-20  Australia     1
4  2021-11-14 2021-11-20     Russia     1
..        ...        ...        ...   ...
98 2022-03-27 2022-04-02  Australia    20
95 2022-03-27 2022-04-02        USA    20
96 2022-03-27 2022-04-02     Canada    20
97 2022-03-27 2022-04-02         UK    20
99 2022-03-27 2022-04-02     Russia    20

[100 rows x 4 columns]

Alternative with pd.factorize (IF the dataframe is already sorted by start_date value:

df['week'] = pd.factorize(df['start_date'])[0] + 1

You can use dt.week and subtract the minimum week from it. In order to ensure the first week is always labeled 1, you can add 1 to the subtraction.

df['start_date'] = pd.to_datetime(df['start_date'])
df['time_step'] = df['start_date'].dt.week - df['start_date'].dt.week.min() + 1