Your colleague is working on two algorithms, $$X$$ and $$Y$$, that determine whether two people are a certain distance apart. They use a number of different inputs, $$n$$. They are seeking your advice.
1. If they tell you that algorithm $$X$$ has a worst-case runtime complexity of $$O(n^2)$$ and algorithm $$Y$$ has a worst-case runtime complexity of $$O(n^3)$$, which algorithm would you recommend and why?
2. Your colleague then adds that the average-case time complexity for $$X$$ is $$Î˜(n^2)$$ and for $$Y$$ is $$Î˜(n)$$. Does this change your advice at all, and why? Your answers should be no longer than a sentence or two.