a$.$ Give an example of an algorithm that should not be considered an application of the brute$-$force approach.

b$.$ Give an example of a problem that cannot be solved by a brute$-$force algorithm.

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Hints:

a$.$ Think of algorithms that have impressed you with their efficiency and$/$or sophistication. Neither characteristic is indicative of a brute force algorithm.

b$.$ Surprisingly, it is not a very easy question to answer. Mathematical problems $($including those you have studied in your secondary school and college courses$)$ are a good source of such examples.