Condition on two and more subsequent pandas rows (not just grouped calculations)

I have df with student’s name, his/her score, class title, and date of exam.
I need to add a column as shown on the picture which will denote if a student’s grade improved or not (3-4 conditional marks like "score increased", "score decreased", "equal", or "initial grade").
I have sorted df according to this now need to compare some conditions in row and next one and if all true should return a mark.
Is there an effective way to do this (my actual table will consist of 1m rows that’s why it shouldn’t be memory consuming)?
Thank you in advance?

df=pd.DataFrame({"score":[10,20,15,10,20,30],
                   "student":['John', 'Alex', "John", "John", "Alex", "John"],
                   "class":['english', 'math', "english",'math','math', 'english'],
                 "date":['01/01/2022','02/01/2022', '05/01/2022', '17/02/2022', '02/01/2022', '03/01/2022']})

df=df.sort_values(['student','class', 'date'])

>Solution :

Get the change in scores using groupby and diff() and then assign the values using numpy.select:

import numpy as np

changes = df.groupby(["student","class"], sort=False)["score"].diff()
df["progress"] = np.select([changes.eq(0),changes.gt(0),changes.lt(0)],
                           ["equal score","score increased","score decreased"], 
                           "initial")

>>> df
   score student    class        date         progress
1     20    Alex     math  02/01/2022          initial
4     20    Alex     math  02/01/2022      equal score
0     10    John  english  01/01/2022          initial
5     30    John  english  03/01/2022  score increased
2     15    John  english  05/01/2022  score decreased
3     10    John     math  17/02/2022          initial