add function to compute the max node depth of a DAG

pytato/analysis/__init__.py

@@ -48,6 +48,7 @@
 .. autofunction:: is_einsum_similar_to_subscript
 
 .. autofunction:: get_num_nodes
+.. autofunction:: get_max_node_depth
 
 .. autofunction:: get_num_call_sites
 
@@ -400,6 +401,53 @@ def get_num_nodes(outputs: Union[Array, DictOfNamedArrays]) -> int:
 # }}}
 
 
+# {{{ NodeMaxDepthMapper
+
+@optimize_mapper(drop_args=True, drop_kwargs=True, inline_get_cache_key=True)
+class NodeMaxDepthMapper(CachedWalkMapper):
+    """
+    Finds the maximum depth of a node in a DAG.
+
+    .. attribute:: max_depth
+
+       The depth of the deepest node.
+    """
+
+    def __init__(self) -> None:
+        super().__init__()
+        self.depth = 0
+        self.max_depth = 0
+
+    # FIXME: Do I need this?
+    # type-ignore-reason: dropped the extra `*args, **kwargs`.
+    def get_cache_key(self, expr: ArrayOrNames) -> int:  # type: ignore[override]
+        return id(expr)
+
+    def rec(self, expr: ArrayOrNames, *args: Any, **kwargs: Any) -> None:
+        """Call the mapper method of *expr* and return the result."""
+        self.depth += 1
+        self.max_depth = max(self.max_depth, self.depth)
+
+        try:
+            super().rec(expr, *args, **kwargs)
+        finally:
+            self.depth -= 1
+
+
+def get_max_node_depth(outputs: Union[Array, DictOfNamedArrays]) -> int:
+    """Finds the maximum depth of a node in *outputs*."""
+
+    from pytato.codegen import normalize_outputs
+    outputs = normalize_outputs(outputs)
+
+    nmdm = NodeMaxDepthMapper()
+    nmdm(outputs)
+
+    return nmdm.max_depth
+
+# }}}
+
+
 # {{{ CallSiteCountMapper
 
 @optimize_mapper(drop_args=True, drop_kwargs=True, inline_get_cache_key=True)