Create a separate class for spanning tree

Remarks:

1. Templates should be in header files only

2. Should pass in svector<_> instead of returning a local one

src/smt/spanning_tree.h

@@ -0,0 +1,63 @@
+/*++
+Copyright (c) 2013 Microsoft Corporation
+
+Module Name:
+
+    spanning_tree.h
+
+Abstract:
+
+    Represent spanning trees with needed operations for Network Simplex
+
+Author:
+
+    Anh-Dung Phan (t-anphan) 2013-11-06
+
+Notes:
+   
+--*/
+#ifndef _SPANNING_TREE_H_
+#define _SPANNING_TREE_H_
+
+#include "spanning_tree_base.h"
+
+namespace smt {
+
+
+    class thread_spanning_tree : virtual public spanning_tree_base {
+    private:        
+        // Store the parent of a node i in the spanning tree
+        svector<node> m_pred;
+        // Store the number of edge on the path from node i to the root
+        svector<int> m_depth;
+        // Store the pointer from node i to the next node in depth-first search order
+        svector<node> m_thread;
+
+        // m_upwards[i] is true if the corresponding edge 
+        // (i, m_pred[i]) points upwards (pointing toward the root node)
+        svector<bool> m_upwards;
+
+        void swap_order(node q, node v);
+        node find_rev_thread(node n) const;
+        void fix_depth(node start, node end);
+        node get_final(int start);
+        bool is_preorder_traversal(node start, node end);
+        bool is_ancestor_of(node ancestor, node child);
+
+    public:
+
+        void initialize(svector<bool> const & upwards, int num_nodes);
+        void get_descendants(node start, svector<node>& descendants);
+        void get_ancestors(node start, svector<node>& ancestors);
+        node get_common_ancestor(node u, node v);
+        void update(node p, node q, node u, node v);
+        bool check_well_formed();
+
+        // TODO: remove these two unnatural functions
+        bool get_arc_direction(node start) const;
+        node get_parent(node start);
+    };
+
+}
+
+#endif