In order to make an optimal algorithm implementation, it is extremely important to know how much resources are available for the algorithm. So, considering that you can find an optimal memory/time performance trade-offs. This will require thorough benchmarks and tests which will help to understand if the desired goals are met.

Thats depends on the business and product requirement. Are there minimum speed to ensure use satisfaction? Can the business benefit of the algorithm justify the computing cost (or the efficiency) ? Does this algorithm need scalability? Usually for prototypes or at early stage efficiency is not an issue due to small usage, and we should pick speed to iterate quickly or keep customers. As the system grow, efficiency starts to matter, especially the algorithm start running out of resources, or cloud bill is rising too fast. At this point it depends on the business. for example. High frequency or real time system might need more speed. While batch processing systems might focus on efficiency to control cost.

Define Requirements & Constraints: Clarify if the priority is speed, memory efficiency, or scalability, guiding algorithm choice based on project needs. Profile & Benchmark: Run initial benchmarks to gauge runtime and memory impact, focusing on realistic workloads to expose potential bottlenecks. Consider Scalability: Anticipate future data growth and select algorithms that maintain performance as inputs scale. Prioritize Simplicity: Favor maintainable solutions; opt for simpler algorithms if they support adaptability, even if slightly less efficient. Iterate & Optimize: Implement a working solution first, then use profiling to refine performance as needed.