which one is best for parsing between Left corner Parsing algorithm and CYK parsing algorithm ? and Why ?
Generally speaking, CYK is a maximum-likelihood parse tree. It never gives you the best performance because of this reason and the fact that it ignores contextual information when assigns the probabilities. You need to modify it to consider more contexts, or integrate it into something else. For example, Left-Corner parser can use a CYK procedure, inside. So the answer to your question is, LC is more powerful than CYK, though it's computationally more expensive. Have a look at Mark Johnson's paper.