Parsing simple HTML into tree

I'd like to ask what is the best way to parse a simple html code into DOM Node tree like this one:

Here are some constraints I am facing:

• HTML code will have only pair tags, no attributes and I've to ignore spaces
• There can be Text between tags like <p>, <h1>, <a> etc.
• I can't use libraries

I was thinking about regex, but never tried it so.. Any ideas?

Every node in the tree is this struct:

  typedef struct tag
  {
      struct tag* parent;
      struct tag* nextSibling;
      struct tag* previousSibling;
      struct tag* firstChild;
      struct tag* lastChild;     
      char* name;
      char* text;     
  }node;