[WIP][tracing] Add memory dump provider for sync Directory

sync/syncable/parent_child_index.h

Index: sync/syncable/parent_child_index.h
diff --git a/sync/syncable/parent_child_index.h b/sync/syncable/parent_child_index.h
index 540234c62b29e81b16557739a626dad8a7a06e14..fad40fdde59fba6d4655cd553013c65f24f9de8a 100644
--- a/sync/syncable/parent_child_index.h
+++ b/sync/syncable/parent_child_index.h
@@ -60,6 +60,9 @@ class SYNC_EXPORT ParentChildIndex {
   // Returns all siblings of the entry.
   const OrderedChildSet* GetSiblings(EntryKernel* e) const;
 
+  // Returns the memory usage of the index.
+  size_t bytes_used() const { return bytes_used_; }
+
  private:
   friend class ParentChildIndexTest;
 
@@ -95,6 +98,9 @@ class SYNC_EXPORT ParentChildIndex {
   // with implicit parent.
   TypeRootChildSets type_root_child_sets_;
 
+  // Stores the current memory usage of the objects.
+  size_t bytes_used_;
+
   DISALLOW_COPY_AND_ASSIGN(ParentChildIndex);
 };