#### Apriori Algorithm

p
```"""
Apriori Algorithm is a Association rule mining technique, also known as market basket
analysis, aims to discover interesting relationships or associations among a set of
items in a transactional or relational database.

For example, Apriori Algorithm states: "If a customer buys item A and item B, then they
are likely to buy item C."  This rule suggests a relationship between items A, B, and C,
indicating that customers who purchased A and B are more likely to also purchase item C.

WIKI: https://en.wikipedia.org/wiki/Apriori_algorithm
Examples: https://www.kaggle.com/code/earthian/apriori-association-rules-mining
"""

from itertools import combinations

"""
Returns a sample transaction dataset.

"""

def prune(itemset: list, candidates: list, length: int) -> list:
"""
Prune candidate itemsets that are not frequent.
The goal of pruning is to filter out candidate itemsets that are not frequent.  This
is done by checking if all the (k-1) subsets of a candidate itemset are present in
the frequent itemsets of the previous iteration (valid subsequences of the frequent
itemsets from the previous iteration).

Prunes candidate itemsets that are not frequent.

>>> itemset = ['X', 'Y', 'Z']
>>> candidates = [['X', 'Y'], ['X', 'Z'], ['Y', 'Z']]
>>> prune(itemset, candidates, 2)
[['X', 'Y'], ['X', 'Z'], ['Y', 'Z']]

>>> itemset = ['1', '2', '3', '4']
>>> candidates = ['1', '2', '4']
>>> prune(itemset, candidates, 3)
[]
"""
pruned = []
for candidate in candidates:
is_subsequence = True
for item in candidate:
if item not in itemset or itemset.count(item) < length - 1:
is_subsequence = False
break
if is_subsequence:
pruned.append(candidate)
return pruned

def apriori(data: list[list[str]], min_support: int) -> list[tuple[list[str], int]]:
"""
Returns a list of frequent itemsets and their support counts.

>>> data = [['A', 'B', 'C'], ['A', 'B'], ['A', 'C'], ['A', 'D'], ['B', 'C']]
>>> apriori(data, 2)
[(['A', 'B'], 1), (['A', 'C'], 2), (['B', 'C'], 2)]

>>> data = [['1', '2', '3'], ['1', '2'], ['1', '3'], ['1', '4'], ['2', '3']]
>>> apriori(data, 3)
[]
"""
itemset = [list(transaction) for transaction in data]
frequent_itemsets = []
length = 1

while itemset:
# Count itemset support
counts = [0] * len(itemset)
for transaction in data:
for j, candidate in enumerate(itemset):
if all(item in transaction for item in candidate):
counts[j] += 1

# Prune infrequent itemsets
itemset = [item for i, item in enumerate(itemset) if counts[i] >= min_support]

# Append frequent itemsets (as a list to maintain order)
for i, item in enumerate(itemset):
frequent_itemsets.append((sorted(item), counts[i]))

length += 1
itemset = prune(itemset, list(combinations(itemset, length)), length)

return frequent_itemsets

if __name__ == "__main__":
"""
Apriori algorithm for finding frequent itemsets.

Args:
data: A list of transactions, where each transaction is a list of items.
min_support: The minimum support threshold for frequent itemsets.

Returns:
A list of frequent itemsets along with their support counts.
"""
import doctest

doctest.testmod()

# user-defined threshold or minimum support level