build a parse tree from a mathematical expression

Node* build_parse_tree(const string& input) {
    stack<Node*> stack;
    for (int i = 0; i < input.size(); i++) {
      string token = input[i];
      Node* n = new Node(token);
      if (token == "+" || token == "-" || token == "*" || token == "/") {
         Node* right = stack.top();
         stack.pop();
         Node* left = stack.top();
         stack.pop();
         n->left = left;
         n->right = right;
         stack.push(n);
      } else {
        stack.push(n);
      }
    }

    return stack.top();
}