Update app.py

app.py

@@ -605,7 +605,7 @@ app.layout = html.Div(
                 html.Div(
                     style={"display": "flex", "gap": "8px", "alignItems": "center", "marginBottom": "8px"},
                     children=[
-                        html.Button("Flip subpath (2 clicks)", id="btn_flip_subpath", n_clicks=0,
+                        html.Button("Flip subpath", id="btn_flip_subpath", n_clicks=0,
                                     style={"background": "#2563EB", "color": "white"}),
                         dcc.Input(
                             id="subpath_dim",
@@ -834,16 +834,16 @@ def update_path(clickData,
             return path, {"active": False, "start_idx": None, "end_idx": None}
 
         # subpath is path[s:e+1] = (v1,...,vk)
-        # requirement: remove v2..vk and replace them with flipped(v2..vk)
-        # so v1 stays as-is, and we replace the tail of the selected subpath.
-        head = path[:s + 1]
-        tail_selected = path[s + 1:e + 1]  # v2..vk
-        flipped_tail = [flip_dim_vertex(v, i) for v in tail_selected]
-        rest = path[e + 1:]
-        new_path = head + flipped_tail + rest
+        # desired: keep prefix (..., v1), keep suffix (vk, ...),
+        # and insert flipped(v1..vk) between them.
+        head = path[:s + 1]                 # includes v1
+        flipped_subpath = [flip_dim_vertex(v, i) for v in path[s:e + 1]]
+        rest = path[e:]                     # starts at vk
+        new_path = head + flipped_subpath + rest
 
         return new_path, {"active": False, "start_idx": None, "end_idx": None}
 
+
     # 7) Figure clicks
     if trigger == "fig" and clickData and clickData.get("points"):
         p = clickData["points"][0]