Looking at the question on algorithm above, the correct answer is: [tex]O( {2}^{n} )[/tex]
Algorithm refers to a sequence of instructions that have been well-defined which helps to solve specific problems. Algorithm is used in computation.
The recurrence relation is:
T(n)=2.T(n-1)+c , n>0
T(n)=1, n=0.
Considering the back substitution method,
T(n) = 2kT(n-k)+ 2k-1c+....+20c
Substitute n-k=0
Therefore, we will have:
T(n) = 2nT(0)+ 2k-1c+....+20c
T(n) = [tex] {2}^{n - 1} + 1[/tex]
T(n) = [tex]O( {2}^{n} )[/tex]
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