Add ordinal representation generator for closed Hamiltonian tours

genetic_algorithm/ordinal_representation.py

@@ -0,0 +1,60 @@
+"""
+Ordinal Representation of a Closed Tour
+---------------------------------------
+
+Converts a path (e.g., a Hamiltonian tour) into its ordinal
+representation based on a fixed alphabetical node reference.
+
+"""
+
+
+def ordinal_representation_closed(path: list[str], nodes: list[str]) -> list[int]:
+    """
+    Generate the ordinal representation for a closed path.
+
+    Each element in the result denotes the position (1-indexed)
+    of the corresponding city in the current reference list,
+    which shrinks as cities are removed.
+
+    Parameters
+    ----------
+    path : list[str]
+        Sequence of cities in the closed tour.
+    nodes : list[str]
+        Reference list of all nodes, in fixed order (e.g., A-Z).
+
+    Returns
+    -------
+    list[int]
+        Ordinal representation of the path.
+
+    Examples
+    --------
+    >>> path = list("GLADBIKEHJFC")
+    >>> nodes = list("ABCDEFGHIJKL")
+    >>> ordinal_representation_closed(path, nodes)
+    [7, 11, 1, 3, 1, 5, 6, 2, 3, 3, 2, 1]
+
+    >>> path = list("ALGC FJHEKIBD".replace(" ", ""))
+    >>> nodes = sorted(set(path))
+    >>> ordinal_representation_closed(path, nodes)
+    [1, 11, 6, 2, 4, 6, 4, 3, 4, 3, 1, 1]
+    """
+    reference = nodes.copy()
+    ordinal = []
+
+    for city in path:
+        index = reference.index(city) + 1  # 1-based index
+        ordinal.append(index)
+        reference.pop(index - 1)
+
+    return ordinal
+
+
+if __name__ == "__main__":
+    sample_path = list("ODGLAHKMBJFCNIE")
+    all_nodes = sorted(set(sample_path))
+    ordinal_values = ordinal_representation_closed(sample_path, all_nodes)
+
+    print("Ordinal Representation:")
+    print(" ".join(map(str, ordinal_values)))