clusterlin: add algorithms for connectedness/connected components

Add utility functions to DepGraph for finding connected components.

src/cluster_linearize.h

@@ -171,6 +171,50 @@ public:
         return ret;
     }
 
+    /** Find some connected component within the subset "todo" of this graph.
+     *
+     * Specifically, this finds the connected component which contains the first transaction of
+     * todo (if any).
+     *
+     * Two transactions are considered connected if they are both in `todo`, and one is an ancestor
+     * of the other in the entire graph (so not just within `todo`), or transitively there is a
+     * path of transactions connecting them. This does mean that if `todo` contains a transaction
+     * and a grandparent, but misses the parent, they will still be part of the same component.
+     *
+     * Complexity: O(ret.Count()).
+     */
+    SetType FindConnectedComponent(const SetType& todo) const noexcept
+    {
+        if (todo.None()) return todo;
+        auto to_add = SetType::Singleton(todo.First());
+        SetType ret;
+        do {
+            SetType old = ret;
+            for (auto add : to_add) {
+                ret |= Descendants(add);
+                ret |= Ancestors(add);
+            }
+            ret &= todo;
+            to_add = ret - old;
+        } while (to_add.Any());
+        return ret;
+    }
+
+    /** Determine if a subset is connected.
+     *
+     * Complexity: O(subset.Count()).
+     */
+    bool IsConnected(const SetType& subset) const noexcept
+    {
+        return FindConnectedComponent(subset) == subset;
+    }
+
+    /** Determine if this entire graph is connected.
+     *
+     * Complexity: O(TxCount()).
+     */
+    bool IsConnected() const noexcept { return IsConnected(SetType::Fill(TxCount())); }
+
     /** Append the entries of select to list in a topologically valid order.
      *
      * Complexity: O(select.Count() * log(select.Count())).