Update app.py

app.py

@@ -279,6 +279,7 @@ def make_figure(d: int,
                 show_bits: bool,
                 show_ints: bool,
                 mark_negations: bool,
+                mark_distances: bool,
                 node_r: int,
                 edge_w: int,
                 path: List[int],
@@ -290,6 +291,26 @@ def make_figure(d: int,
     path = path or []
     in_path = set(path)
 
+    # ---------- Distances Logic (New) ----------
+    dist2_set = set()
+    if mark_distances and path:
+        # 1. Identify all nodes at distance 0 or 1 from the path
+        #    (We want strict distance 2)
+        forbidden = set()
+        for p_v in path:
+            forbidden.add(p_v)
+            for bit in range(d):
+                forbidden.add(p_v ^ (1 << bit))
+        
+        # 2. Identify neighbors of neighbors (potential dist 2)
+        #    and filter out those in forbidden set
+        for p_v in path:
+            for b1 in range(d):
+                for b2 in range(b1 + 1, d):
+                    neighbor2 = p_v ^ (1 << b1) ^ (1 << b2)
+                    if neighbor2 not in forbidden:
+                        dist2_set.add(neighbor2)
+    
     # ---------- negations (vertices + edges) ----------
     neg_set = set()
     neg_edges = set()
@@ -401,10 +422,23 @@ def make_figure(d: int,
         sizes.append(base_size * (3 if v in in_path else 1))
 
         if path and (v == path[0] or v == path[-1]):
-            colors.append("#111")          # endpoints
+            sizes.append(base_size * 3)
+            colors.append("#111")
+        elif v in in_path:
+            sizes.append(base_size * 3)
+            colors.append("#222")
+            
+        # --- INSERT THIS ELIF BLOCK ---
+        elif v in dist2_set:
+            sizes.append(base_size * 2.5) # Slightly larger
+            colors.append("#FFD700")      # Gold color
+        # ------------------------------
+        
         elif mark_negations and v in neg_set:
-            colors.append("red")           # negation vertices
+            sizes.append(base_size)
+            colors.append("red")
         else:
+            sizes.append(base_size)
             colors.append("#222")
 
     node_trace = go.Scatter(
@@ -498,7 +532,13 @@ app.layout = html.Div(
                         style={"marginTop": "0px"},
                     )
                 ]),
-                html.Div(),  # empty cell just to keep the grid tidy
+                html.Div([
+                    dcc.Checklist(
+                        id="mark_distances",
+                        options=[{"label": " Mark dist=2", "value": "dist2"}],
+                        value=[], style={"marginTop": "0px"},
+                    )
+                ]),
             ],
         ),
 
@@ -723,20 +763,19 @@ def update_path(clickData,
     Input("show_labels", "value"),
     Input("path_store", "data"),
     Input("mark_negations", "value"),
+    Input("mark_distances", "value"),
 )
-def render(d, show_labels_vals, path, mark_vals):
+def render(d, show_labels_vals, path, mark_vals, dist_vals): # <--- Add dist_vals
     labels_vals = show_labels_vals or []
-    show_bits = "bits" in labels_vals
-    show_ints = "ints" in labels_vals
-
     mark_vals = mark_vals or []
-    mark_negations = "neg" in mark_vals
-
+    dist_vals = dist_vals or []  # <--- Handle None case
+    
     fig = make_figure(
         d=int(d),
-        show_bits=show_bits,
-        show_ints=show_ints,
-        mark_negations=mark_negations,
+        show_bits=("bits" in labels_vals),
+        show_ints=("ints" in labels_vals),
+        mark_negations=("neg" in mark_vals),
+        mark_distances=("dist2" in dist_vals), # <--- Pass the boolean
         node_r=DEFAULTS["node_radius"],
         edge_w=DEFAULTS["edge_width"],
         path=path or [],