Quantifying how hard it is to build a molecular graph matters for biosignature detection, chemical complexity, and cheminformatics. We present an exact, scalable algorithm to compute the molecular assembly index (MA) which prioritizes the largest duplicate subgraphs, represents fragmentation with an 'assembly state' array of edge-lists, reuses states via hashing/DAGs, and prunes the search using a dynamic-programming branch-and-bound guided by a conditional-addition-chain lower bound. For organic molecules in the greater than 500 Da range our approach is up to six orders of magnitude faster than prior methods and yields exact MAs where previous algorithms would have timed out. We compute MAs to convergence for ~300k COCONUT natural products with <50 bonds, profiling time and memory scaling. Finally, we exploit the speed of our algorithm to calculate joint assembly spaces and introduce the Joint Assembly Overlap (JAO), a Jaccard-like metric that emphasizes global scaffold reuse and show that the JAO yields substantially different rankings from Tanimoto similarity with ECFP fingerprints and MCS (e.g. in steroids 270-380/Da and short peptides), accounting for substructural similarity beyond local environments. Together, these advances turn the molecular assembly index into a practical tool for large-scale exploration of chemical space.