The time complexities of the functions is (a) f1 = f3 < f2
The code of the functions f1, f2 and f3 are added as an attachment
To compare the time complexities of the functions, we check the loop and conditional statement in each function.
From the attached code, we can see that:
In function f2, we have:
The conditional statement in the second loop implies that the conditional statement would be executed several times as long as the loop is valid.
This implies that:
f2 > f1 and f2 > f3
The number of loops and conditional statement in functions f1 and f3 are equal
This means that
f1 = f3
So, we have:
f2 > f1 = f3
Rewrite f2 > f1 = f3 as:
f1 = f3 < f2
Hence, the time complexities of the functions is (a) f1 = f3 < f2
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