how to compare 2 dataframes and populate boolean value

check whether individual pattern from dict is present or whole string is present in second dataframe.

df1 = pl.DataFrame({
   "A": ["a", "b", "a", "c","a","c","a","b","b"], 
   "B": [23,45,60,50,56,44,34,30,97], 
   "C": [{'pattern1':['a','score1'],'pattern2':['df','text1']},
        {'pattern3':['abc','score1']},
        {'pattern1':['a','score2'],'pattern4':['df','text2']},
        {'pattern5':['a','score2'],'pattern6':['gh','text1'],'pattern7':['gh','text1']},
        {'pattern8':['a','score1']},
        {'pattern9':['a','score1'],'pattern10':['df','text1']},
        {'pattern11':['a','score1']},
        {'pattern12':['a','score1'],'pattern13':['df','text1']},
        {'pattern3':['a','score1'],'pattern5':['df','text1']}]
})
shape: (9, 3)
┌─────┬─────┬─────────────────────────────────────┐
│ A   ┆ B   ┆ C                                   │
│ --- ┆ --- ┆ ---                                 │
│ str ┆ i64 ┆ object                              │
╞═════╪═════╪═════════════════════════════════════╡
│ a   ┆ 23  ┆ {'pattern1': ['a', 'score1'], 'p... │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ b   ┆ 45  ┆ {'pattern3': ['abc', 'score1']}     │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ a   ┆ 60  ┆ {'pattern1': ['a', 'score2'], 'p... │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ c   ┆ 50  ┆ {'pattern5': ['a', 'score2'], 'p... │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ ... ┆ ... ┆ ...                                 │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ a   ┆ 56  ┆ {'pattern8': ['a', 'score1']}       │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ c   ┆ 44  ┆ {'pattern9': ['a', 'score1'], 'p... │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ a   ┆ 34  ┆ {'pattern11': ['a', 'score1']}      │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ b   ┆ 30  ┆ {'pattern12': ['a', 'score1'], '... │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ b   ┆ 97  ┆ {'pattern3': ['a', 'score1'], 'p... │
└─────┴─────┴─────────────────────────────────────┘

df2 = pl.DataFrame({
   "A": ["a", "a", "b", "b","a","c"], 
   "valid_patterns": ['pattern1',
       "{'pattern1': ['a', 'score2'], 'pattern4': ['df', 'text2']}",
        "{'pattern3':['abc','score1']}",
        'pattern3',
        "{'pattern11': ['a', 'score1']}",
        'pattern9']
})

┌─────┬─────────────────────────────────────┐
│ A   ┆ valid_patterns                      │
│ --- ┆ ---                                 │
│ str ┆ str                                 │
╞═════╪═════════════════════════════════════╡
│ a   ┆ pattern1                            │
├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ a   ┆ {'pattern1': ['a', 'score2'], 'p... │
├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ b   ┆ {'pattern3':['abc','score1']}       │
├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ b   ┆ pattern3                            │
├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ a   ┆ {'pattern11': ['a', 'score1']}      │
├╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┤
│ c   ┆ pattern9                            │
└─────┴─────────────────────────────────────┘

ouput:

Based on Column A , need to check column c values wither full dict or any one key in dict need to be present in second dataframe for column A.

shape: (9, 4)
┌─────┬─────┬─────────────────────────────────────┬───────┐
│ A   ┆ B   ┆ C                                   ┆ VALID │
│ --- ┆ --- ┆ ---                                 ┆ ---   │
│ str ┆ i64 ┆ object                              ┆ bool  │
╞═════╪═════╪═════════════════════════════════════╪═══════╡
│ a   ┆ 23  ┆ {'pattern1': ['a', 'score1'], 'p... ┆ true  │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ b   ┆ 45  ┆ {'pattern3': ['abc', 'score1']}     ┆ true  │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ a   ┆ 60  ┆ {'pattern1': ['a', 'score2'], 'p... ┆ true  │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ c   ┆ 50  ┆ {'pattern5': ['a', 'score2'], 'p... ┆ false │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ ... ┆ ... ┆ ...                                 ┆ ...   │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ a   ┆ 56  ┆ {'pattern8': ['a', 'score1']}       ┆ false │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ c   ┆ 44  ┆ {'pattern9': ['a', 'score1'], 'p... ┆ true  │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ a   ┆ 34  ┆ {'pattern11': ['a', 'score1']}      ┆ true  │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ b   ┆ 30  ┆ {'pattern12': ['a', 'score1'], '... ┆ false │
├╌╌╌╌╌┼╌╌╌╌╌┼╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌╌┼╌╌╌╌╌╌╌┤
│ b   ┆ 97  ┆ {'pattern3': ['a', 'score1'], 'p... ┆ false │
└─────┴─────┴─────────────────────────────────────┴───────┘