How do I translate LR(1) Parse into a Abstract syntax tree?

Question

I have coded a table driven LR(1) parser and it is working very well however I am having a bit of a disconnect on the stage of turing a parse into a syntax tree/abstract syntax tree. This is a project that I m very passionate about but I have really just hit a dead end here. Thank you for your help in advance.

Edit: Also my parser just uses a 2d array and an action object that tells it where to go next or if its a reduction where to go and how many items to pop. I noticed that many people use the visitor pattern. Im not sure how they know what type of node to make.

Here is the pushdown automata for context

 while (lexer.hasNext() || parseStack.size() > 0) {
        Action topOfStack = parseStack.peek();
        token = parseStack.size() > 0 ? lexer.nextToken() : new Token(TokenType.EOF, "EOF");
        topOfStack.setToken(token);

        int row = topOfStack.getTransitionIndex();
        int column = getTerminalIndex(token.getLexeme());

        column = token.getType() == TokenType.IDENTIFIER
                && !terminalsContain(token.getLexeme()) ? 0 : column;

        Action action = actionTable[row][column];

        if (action instanceof Accept) {
            System.out.println("valid parse!!!!!!");
        } else if (action instanceof Reduction) {
            Reduction reduction = (Reduction) action;

            popStack(parseStack, reduction.getNumberOfItemsToPop());
            column = reduction.getTransitionIndex();
            row = parseStack.peek().getTransitionIndex();

            parseStack.push(new Action(gotoTable[row][column]));
            lexer.backupTokenStream();
        } else if (action != null) {
            parseStack.push(actionTable[row][column]);
        } else {
            System.out.println("Parse error");
            System.out.println("On token: " + token.getLexeme());
            break;
        }

Answer 1

Each reduction in the LR parsing process corresponds to an internal node in the parse tree. The rule being reduced is the internal AST node, and the items popped off the stack correspond to the children of that internal node. The item pushed for the goto corresponds to the internal node, while those pushed by shift actions correspond to leaves (tokens) of the AST.

Putting all that together, you can easily build an AST by createing a new internal node every time you do a reduction and wiring everything together appropriately.