Recently, neural network approaches for parsing have largely automated the combination of individual features, but still rely on (often a larger number of) atomic features created from human linguistic intuition, and potentially omitting important global context. To further reduce feature engineering to the bare minimum, we use bi-directional LSTM sentence representations to model a parser state with only three sentence positions, which automatically identifies important aspects of the entire sentence. This model achieves state-of-the-art results among greedy dependency parsers for English. We also introduce a novel transition system for constituency parsing which does not require binarization, and together with the above architecture, achieves state-of-the-art results among greedy parsers for both English and Chinese.