Coalition structure generation, i.e., the problem of optimally partitioning a set of agents into disjoint exhaustive coalitions to maximize social welfare, is a fundamental computational problem in multi-agent systems. In this paper, we provide a new algorithm for optimal coalition structure generation. We analyze how parts of the solution space can be searched individually with guarantees of fully searching them. We introduce a new algorithm that searches the entire solution space using dynamic programming with a branch-and-bound technique both focused on solution subspaces. With experiments over several common value distributions, we show that dividing the search process enables our algorithm to rapidly search the solution subspaces and outperform current state-of-the-art for several value distributions.