Add adjacency representation generator for closed Hamiltonian tours

genetic_algorithm/adjacency_representation.py

@@ -0,0 +1,66 @@
+"""
+Closed Tour Adjacency Representation
+------------------------------------
+
+Converts a path representation (like A→L→G→C→...) into an adjacency
+vector form, where each position corresponds to a city in alphabetical
+order and the value indicates the next city in the tour.
+
+A closed tour means the last city connects back to the first.
+
+Reference:
+https://en.wikipedia.org/wiki/Adjacency_list
+"""
+
+
+def adjacency_vector_closed(path: list[str], nodes: list[str]) -> list[str]:
+    """
+    Generate adjacency vector for a closed tour.
+
+    Each position corresponds to a city (from `nodes`) and contains
+    the next city in the tour. The last city connects back to the first.
+
+    Parameters
+    ----------
+    path : list[str]
+        Ordered list of cities representing the tour.
+    nodes : list[str]
+        Fixed node order (e.g., ['A', 'B', 'C', ...]).
+
+    Returns
+    -------
+    list[str]
+        Adjacency vector aligned with the node order.
+
+    Examples
+    --------
+    >>> path = list("ALGCFJHEKIBD")
+    >>> nodes = sorted(set(path))
+    >>> adjacency_vector_closed(path, nodes)
+    ['L', 'D', 'F', 'A', 'K', 'J', 'C', 'E', 'B', 'H', 'I', 'G']
+
+    >>> adjacency_vector_closed(list("ABCD"), list("ABCD"))
+    ['B', 'C', 'D', 'A']
+    """
+
+    next_city_map: dict[str, str] = {}
+    total_cities = len(path)
+
+    for index, city in enumerate(path):
+        next_city = path[(index + 1) % total_cities]
+        next_city_map[city] = next_city
+
+    return [next_city_map.get(city, "-") for city in nodes]
+
+
+if __name__ == "__main__":
+    sample_path = list("ALGCFJHEKIBD")
+    ordered_nodes = sorted(set(sample_path))
+    adjacency = adjacency_vector_closed(sample_path, ordered_nodes)
+
+    print("Adjacency Representation (alphabetical order):")
+    for city, next_city in zip(ordered_nodes, adjacency):
+        print(f"{city} → {next_city}")
+
+    print("\nVector form:")
+    print(" ".join(adjacency))