Cohesion degree is an important feature in differentiating ambiguous Chinese phrases. At the present time, there are no module in computer-oriented linguistic theories to represent this information and it is represented by additional statistical modules. The Binary Combinatorial Grammar (BCG) is based on arithmetic computing and integrates the cohesion degree as the priorities between operators. In order to resolve the share space problem and to improve the efficiency of operator-precedence shift-reduce parsing algorithm, the notion of precedence is introduced to the CYK algorithm to determine the combinatorial direction and to prune a portion of unnecessary subtrees during the parsing process. In the experiment of Chinese BCG parsing, all of the spent time, produced edges and result trees in the precedence based CYK algorithm are much less than that of the traditional CYK algorithm and the operator precedence based shift-reduce algorithm.