Abstract: It exists a lot of problems to place balls using artificial method in billiards sports, such as time-consuming, labor-intensive, placed unreasonable, increasing the cost of service and so on. The paper puts forward an optimization algorithm of placement for Chinese billiards. The algorithm defines inside triangle and outside triangle. The locations of the sub-balls are numbered. It constructs a mathematical model, gives a formal description, uses binary tree structure to organize all the possible layout schemes, and searches reasonable schemes by backtracking. All of these schemes meet any of the three or more non-adjacent panchromatic ball or fancy ball, they provide an effective way for the further design and development of automatic billiards machine.

Key words: billiards, placed scheme, mathematical model, algorithm