[+] A3 Starter Files

assignments/A3/a3_part3.py

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+"""CSC111 Winter 2022 Assignment 3: Graphs, Recommender Systems, and Clustering (Part 3)
+
+Instructions (READ THIS FIRST!)
+===============================
+
+This Python module contains the functions you'll write for determining *clusters* of vertices
+in a graph.
+
+Copyright and Usage Information
+===============================
+
+This file is provided solely for the personal and private use of students
+taking CSC111 at the University of Toronto St. George campus. All forms of
+distribution of this code, whether as given or with any changes, are
+expressly prohibited. For more information on copyright for CSC111 materials,
+please consult our Course Syllabus.
+
+This file is Copyright (c) 2022 Mario Badr, David Liu, and Isaac Waller.
+"""
+import random
+
+from a3_part2_recommendations import WeightedGraph, load_weighted_review_graph
+
+
+################################################################################
+# Part 3, Q1
+################################################################################
+def create_book_graph(review_graph: WeightedGraph,
+                      threshold: float = 0.05,
+                      score_type: str = 'unweighted') -> WeightedGraph:
+    """Return a book graph based on the given review_graph.
+
+    The score_type parameter plays the same role as in WeightedGraph.get_similarity_score.
+
+    The returned book graph has the following properties:
+        1. Its vertex set is exactly the set of book vertices in review_graph
+            (items are book titles).
+        2. For every two distinct books b1 and b2, let s(b1, b2) be their similarity score,
+            where score_type specifies which similarity score to use.
+
+            - If s(b1, b2) > threshold, there is an edge between b1 and b2 in the book graph
+              with weight equal to s(b1, b2). Unlike Part 2, these weights will be floats,
+              not ints!
+            - Otherwise, there is no edge between b1 and b2.
+
+    Preconditions:
+        - score_type in {'unweighted', 'strict'}
+    """
+
+
+################################################################################
+# Part 3, Q2
+################################################################################
+def cross_cluster_weight(book_graph: WeightedGraph, cluster1: set, cluster2: set) -> float:
+    """Return the cross-cluster weight between cluster1 and cluster2.
+
+    See assignment handout for the definition of cross-cluster weight.
+
+    Preconditions:
+        - cluster1 != set() and cluster2 != set()
+        - cluster1.isdisjoint(cluster2)
+        - Every item in cluster1 and cluster2 is a vertex in book_graph
+    """
+
+
+################################################################################
+# Part 3, Q3 (don't modify this code)
+################################################################################
+def find_clusters_random(graph: WeightedGraph, num_clusters: int) -> list[set]:
+    """Return a list of <num_clusters> vertex clusters for the given graph.
+
+    At each iteration, this algorithm first chooses a random cluster, and then chooses
+    the cluster that has the highest cross-cluster weight to the randomly-chose cluster
+    to merge.
+
+    Preconditions:
+        - num_clusters >= 1
+    """
+    # Each book starts in its own cluster
+    clusters = [{book} for book in graph.get_all_vertices()]
+
+    for _ in range(0, len(clusters) - num_clusters):
+        print(f'{len(clusters)} clusters')
+
+        c1 = random.choice(clusters)
+        # Pick the best cluster to merge c1 into.
+        best = -1
+        best_c2 = None
+
+        for c2 in clusters:
+            if c1 is not c2:
+                score = cross_cluster_weight(graph, c1, c2)
+                if score > best:
+                    best = score
+                    best_c2 = c2
+
+        best_c2.update(c1)
+        clusters.remove(c1)
+
+    return clusters
+
+
+def find_clusters_greedy(graph: WeightedGraph, num_clusters: int) -> list[set]:
+    """Return a list of <num_clusters> vertex clusters for the given graph.
+
+    At each iteration, this algorithm chooses the pair of clusters with the highest
+    cross-cluster weight to merge.
+
+    Preconditions:
+        - num_clusters >= 1
+    """
+    # Each book starts in its own cluster
+    clusters = [{book} for book in graph.get_all_vertices()]
+
+    for _ in range(0, len(clusters) - num_clusters):
+        print(f'{len(clusters)} clusters')
+
+        # Merge the two communities with the most links
+        best = -1
+        best_c1, best_c2 = None, None
+
+        for i1 in range(0, len(clusters)):
+            for i2 in range(i1 + 1, len(clusters)):
+                c1, c2 = clusters[i1], clusters[i2]
+                score = cross_cluster_weight(graph, c1, c2)
+                if score > best:
+                    best, best_c1, best_c2 = score, c1, c2
+
+        best_c2.update(best_c1)
+        clusters.remove(best_c1)
+
+    return clusters
+
+
+if __name__ == '__main__':
+    # You can uncomment the following lines for code checking/debugging purposes.
+    # However, we recommend commenting out these lines when working with the large
+    # datasets, as checking representation invariants and preconditions greatly
+    # increases the running time of the functions/methods.
+    # import python_ta.contracts
+    # python_ta.contracts.check_all_contracts()
+
+    import doctest
+    doctest.testmod()
+
+    import python_ta
+    python_ta.check_all(config={
+        'max-line-length': 1000,
+        'disable': ['E1136'],
+        'extra-imports': ['random', 'a3_part2_recommendations'],
+        'allowed-io': ['find_clusters_greedy', 'find_clusters_random'],
+        'max-nested-blocks': 4
+    })