We present a new algorithm that reduces the space complexity of heuristic search. It is most effective for problem spaces that grow polynomially with problem size, but contain large numbers of short cycles. For example, the problem of finding an optimal global alignment of several DNA or amino-acid sequences can be solved by finding a lowest-cost corner-to-corner path in a d-dimensional grid. A previous algorithm, called divide-and-conquer bidirectional search, saves memory by storing only the Open lists and not the Closed lists. We show that this idea can be applied in a unidirectional search as well. This extends the technique to problems where bidirectional search is not applicable, and is more efficient in both time and space than the bidirectional version. If n is the length of the strings, and d is the number of strings, this algorithm can reduce the memory requirement from O(n^d) to O(n^(d-1)). While our current implementation of DCFS is somewhat slower than existing dynamic programming approaches for optimal alignment of multiple gene sequences, DCFS is a more general algorithm.