feat: adding Apriori Algorithm (TheAlgorithms#10491)

* feat: adding Apriori Algorithm

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* fix: doctest, typo

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* fix: type error, code refactore

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* fix: refactore code

* fix: doctest

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* fix: typo

* fix: typo

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* Replace generate_candidates() with itertools.combinations()

* mypy

* Update apriori_algorithm.py

---------

Co-authored-by: Jeel Gajera <jeelgajera00@gmail.com>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Christian Clauss <cclauss@me.com>

Author: 4 people

DIRECTORY.md

@@ -554,6 +554,7 @@
   * [Word Frequency Functions](machine_learning/word_frequency_functions.py)
   * [Xgboost Classifier](machine_learning/xgboost_classifier.py)
   * [Xgboost Regressor](machine_learning/xgboost_regressor.py)
+  * [Apriori Algorithm](machine_learning/apriori_algorithm.py)
 
 ## Maths
   * [Abs](maths/abs.py)

machine_learning/apriori_algorithm.py

@@ -0,0 +1,112 @@
+"""
+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
+
+
+def load_data() -> list[list[str]]:
+    """
+    Returns a sample transaction dataset.
+
+    >>> load_data()
+    [['milk'], ['milk', 'butter'], ['milk', 'bread'], ['milk', 'bread', 'chips']]
+    """
+    return [["milk"], ["milk", "butter"], ["milk", "bread"], ["milk", "bread", "chips"]]
+
+
+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
+    frequent_itemsets = apriori(data=load_data(), min_support=2)
+    print("\n".join(f"{itemset}: {support}" for itemset, support in frequent_itemsets))