You are tasked with optimizing a complex algorithm that processes large datasets. The algorithm currently has a time complexity of O(n³) and needs to be reduced to at least O(n² log n). Additionally, you must reduce the space complexity from O(n²) to O(n). Identify the specific bottlenecks in the following algorithm, propose alternative approaches, and implement your solution. Discuss the trade-offs of your optimization and analyze the worst-case scenario.