refactor core a bit, prep for better algo

src/cgi/script.py

@@ -13,7 +13,7 @@ sys.path.insert(0,
         )
     )
 )
-from smithy import smith_set
+from smithy import smith_set_from_rcv
 
 print("Content-Type: text/html\n")
 message = ""
@@ -75,7 +75,7 @@ if spreadsheet is not None:
                     ]
                 )
 
-                smiths = smith_set(df) # Solve!
+                smiths = smith_set_from_rcv(df) # Solve!
 
                 message = f"""
                 <h1>The Smith set winners are:</h1>

src/smithy/__init__.py

@@ -1 +1,74 @@
-from .rcv import smith_set
+import polars as pl
+from itertools import combinations
+
+from .rcv import pairmaj_from_rcv
+
+
+def smith_set_brutefrom_pairmaj(pairmaj_graph: dict[str, set[str]]) -> list:
+    """
+    Brute-force the Smith set from a pairwise majority winner graph.
+
+    parameters
+    ---
+    pairmaj_graph: dict[str, set[str]]
+        A graph whose nodes correspond to candidates and (directed) edges show
+        which candidates they beat pairwise.
+
+    returns
+    ---
+    smith_set: list
+        A list of the Smith set candidates - all are equally good winners; 
+        ordering is determined lexicographically. If there is a Condorcet winner 
+        (single Majority winner), the Smith set will contain that single candidate.
+    """
+
+    candidates = set(pairmaj_graph.keys())
+    size = len(candidates)
+
+    for size in range(1, len(candidates) + 1):
+        for sub in combinations(candidates, size):
+            subset = set(sub)
+            out = set(candidates) - subset
+
+            dom = True
+
+            for member in subset:
+                if not out.issubset(pairmaj_graph[member]):
+                    dom = False
+                    break
+
+            if dom:
+                return sorted(subset)
+
+    return []
+
+def smith_set_from_rcv(rcv_ballots: pl.DataFrame) -> list:
+    """
+    Compute the Smith set from a Ranked-Choice ballot.
+
+    The Smith set is the minimal set of candidates which can beat all others pairwise - 
+    if there is a single winner in the set they are guaranteed the Condorcet i.e. Majority winner.
+
+    parameters
+    ---
+    df : pl.DataFrame
+        A Polars DataFrame representing ballots. Each column is a candidate and each
+        row is is a voter's ranking of the candidates. Lower numbers indicate higher
+        preference (1 = top-choice).
+
+    returns
+    ---
+    smith_set : list
+        A list of the Smith set candidates - all are equally good winners; 
+        ordering is determined lexicographically. If there is a Condorcet winner 
+        (single Majority winner), the Smith set will contain that single candidate.
+
+    """
+
+    return smith_set_brutefrom_pairmaj(pairmaj_from_rcv(rcv_ballots))
+
+def smith_set(df: pl.DataFrame, ballotkind="rcv") -> list:
+    if ballotkind == "rcv":
+        return smith_set_from_rcv(df)
+    else:
+        raise NotImplementedError(f"`smith_set` ballotkind={ballotkind} is not implemented.")

src/smithy/rcv.py

@@ -1,36 +1,29 @@
 import polars as pl
 from itertools import combinations
 
-def smith_set(df: pl.DataFrame) -> list:
+def pairmaj_from_rcv(rcv_ballots: pl.DataFrame) -> dict[str, set[str]]:
     """
-    Compute the Smith set from a Ranked-Choice ballot.
+    Build a pairwise majority winner graph from a box of Ranked-Choice Ballots.
-
-    The Smith set is the minimal set of candidates which can beat all others pairwise - if there is a single winner
-    in the set they are guaranteed the Condorcet i.e. Majority winner.
 
     parameters
     ---
-    df : pl.DataFrame
+    rcv_ballots : pl.DataFrame
         A Polars DataFrame representing ballots. Each column is a candidate and each
         row is is a voter's ranking of the candidates. Lower numbers indicate higher
         preference (1 = top-choice).
 
     returns
     ---
-    smith_set : list
+    pairmaj_graph: dict[str, set[str]]
-        A list of the Smith set candidates - all are equally good winners; ordering is determined lexicographically.
+        A pairwise majority winner graph whose nodes correspond to candidates and 
-        If there is a Condorcet winner (single Majority winner), the Smith set will contain that single candidate.
+        (directed) edges show which candidates they beat pairwise.
-
-
     """
+    candidates = rcv_ballots.columns
 
-    candidates = df.columns
+    pairmaj_graph: dict[str, set[str]] = {c: set() for c in candidates}
-
-    # Build pairwise majority graph
-    graph: dict[str, set[str]] = {c: set() for c in candidates}
 
     for a, b in combinations(candidates, 2):
-        result = df.select(
+        result = rcv_ballots.select(
             [
                 (pl.col(a) < pl.col(b)).sum().alias("a_wins"),
                 (pl.col(b) < pl.col(a)).sum().alias("b_wins"),
@@ -40,24 +33,14 @@ def smith_set(df: pl.DataFrame) -> list:
         a_wins, b_wins = result
 
         if a_wins > b_wins:
-            graph[a].add(b)
+            pairmaj_graph[a].add(b)
         elif b_wins > a_wins:
-            graph[b].add(a)
+            pairmaj_graph[b].add(a)
+
+    return pairmaj_graph
+
 
-    # Find Smith set
-    for size in range(1, len(candidates) + 1):
-        for sub in combinations(candidates, size):
-            subset = set(sub)
-            out = set(candidates) - subset
 
-            dom = True
 
-            for member in subset:
-                if not out.issubset(graph[member]):
-                    dom = False
-                    break
 
-            if dom:
-                return sorted(subset)
 
-    return []