// grammar:
// <letter> ::= a | b | ... | z | A | B | ... | Z
// <name> ::= { <letter> }+
// <digit> ::+ 0 | 1 | ... | 9
// <number> ::= { <digit> }+
// <subscript> ::= <name> [ <subscript> ] | <variable>
// <variable> ::= <name> | <name> [ <subscript> ]


class VarTreeNode{
public:

  // kinds of nodes which can occur.  the net effect of
  // this declaration is to define a bunch of constants.
  enum nodeType  { SUBSCRIPT = 0,
                   NAME = 1,
                   NUMBER = 2,
                   UNDEFINED = 3 };

  nodeType type;
  int value; // only used when "type" == NUMBER
  String2002 varname; // only used when "type" == NAME
  VarTreeNode *left, *right;

  // note: the second and third arguments are optional
  VarTreeNode (nodeType type, int value = 1, String2002 varname = "") {
    VarTreeNode::type = type;
    VarTreeNode::value = value; // harmless at worst
    VarTreeNode::varname = varname; // harmless at worst
    left = right = NULL; // guarantee reasonable values
  }

};


void deleteVarTree(VarTreeNode *root);

void outputVariable (VarTreeNode *root);

// outputs an error message and returns null if the string
// is not a valid expression
VarTreeNode *createVarTree (String2002 str);