Update app.py

app.py

@@ -126,6 +126,22 @@ def classify_path(path, d: int):
     return "snake", True
 
 
+def edge_dimension(a: int, b: int) -> int | None:
+    """
+    Return the dimension index of the edge (a,b) if they are adjacent,
+    otherwise return None.
+    """
+    x = a ^ b
+    if x == 0 or (x & (x - 1)) != 0:
+        # either same vertex or differ in more than one bit
+        return None
+    dim = 0
+    while x > 1:
+        x >>= 1
+        dim += 1
+    return dim
+
+
 def hamming_dist(a: int, b: int) -> int:
     x, c = a ^ b, 0
     while x:
@@ -793,10 +809,11 @@ def path_info(d, path):
     if not path:
         return html.Span("Path: (empty)")
 
+    # Vertex list
     path_str = ", ".join(str(v) for v in path)
 
+    # Classification
     label, valid = classify_path(path, d)
-
     color = {
         "snake": "green",
         "coil": "green",
@@ -804,9 +821,27 @@ def path_info(d, path):
         "not snake": "red",
     }[label]
 
-    return html.Span([
-        html.Span(f"Path: {path_str} "),
-        html.Span(f"[{label}]", style={"color": color, "fontWeight": "bold"}),
+    # Dimensions of consecutive edges
+    dims = []
+    for i in range(len(path) - 1):
+        dim = edge_dimension(path[i], path[i + 1])
+        if dim is not None:
+            dims.append(dim)
+        else:
+            # non adjacent step, keep something explicit
+            dims.append("?")
+
+    dims_str = ", ".join(str(x) for x in dims) if dims else "(none)"
+
+    return html.Div([
+        html.Div([
+            html.Span(f"Path: {path_str} "),
+            html.Span(f"[{label}]", style={"color": color, "fontWeight": "bold"}),
+        ]),
+        html.Div([
+            html.Span("Dimensions: "),
+            html.Span(dims_str, style={"fontFamily": "monospace"}),
+        ]),
     ])