To address the challenges of time-consuming minimum cycle basis acquisition in large-scale distribution networks and the inability of existing optimization algorithms to generate high-quality fault reconfiguration solutions within a short timeframe, a coding improvement and application algorithm for rapid distribution network fault reconfiguration method is proposed. First, the Tarjan algorithm is employed to detect and eliminate islanded regions caused by faults. Based on the correlation between minimum cycles and back edges, the minimum cycle basis on the maximum biconnected component subgraph is identified via breadth first search (BFS). Then, an encoding based on the identified minimum cycles is established, and encoding optimization is performed to eliminate the causes of infeasible solutions during the cycle elimination process. Subsequently, for the fault reconfiguration problem, three key search processes of the Hippopotamus optimization algorithm are enhanced using sampling, graph theory, and crossover methods. Finally, simulation analysis is conducted on a real-world large-scale distribution network with 751 buses. Experimental results demonstrate that the proposed method requires only 3.45% of the time compared to existing methods for acquiring the minimum cycle basis. Moreover, the fault reconfiguration strategy generated within 5 seconds outperforms other algorithms in terms of network loss, number of switching operations, and voltage deviation.