What type of algorithm guarantees a solution after a finite number of steps?

The correct response is a deterministic algorithm. Deterministic algorithms are defined by their ability to produce the same output from the same input on each execution, following a specific set of rules or procedures. This nature ensures that they will arrive at a solution after a finite number of clearly defined steps.

This is in contrast to heuristic algorithms, which provide approximate solutions based on experience or rules of thumb and may not guarantee a solution within a finite timeframe. Randomized algorithms introduce an element of randomness, leading to variability in outcomes across different executions. While they might provide solutions quickly on average, they don't guarantee a solution every time or within a finite number of steps. Lastly, "aggressive algorithm" is not a standard term used in algorithm analysis, so it does not fit the context of guaranteeing a solution through a defined process.

Therefore, deterministic algorithms are the most reliable type for ensuring a solution is reached definitively after a finite number of steps.