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Consider the following recurrence relation and the first few steps of iterative substitution that have been applied to it: Recurrence Relation: T(0) = c0 T(1)

Consider the following recurrence relation and the first few steps of iterative substitution that have been applied to it:

Recurrence Relation:

T(0) = c0

T(1) = c1

T(2) = c2

T(n) = nc + 3T(n-2) for n > 2

Iterative Substitution:

T(n) = nc + 3T(n-2)

= nc + 3[(n-2)c + 3T(n-4)] = nc + 3(n-2)c + 9T(n-4)

= nc + 3(n-2)c + 9[ __________________ ]

Which of the following should be used to fill in the blank above?

a) nc + 3T(n-2)
b) 3nc + 3T(n-3)
c) nc + 3T(n-4)
d) 4nc + 3T(n-4)
e) (n-2)c + 3T(n-2)
f) 9(n-2)c + 3T(n-4)
g) (n-2)c + 9T(n-4)
h) (n-4)c + T(n-4)
i) (n-4)c + T(n-4)
j) (n-4)c + 3T(n-6)
k) (n-6)c + 3T(n-4)
l) (n-6)c + 9T(n-4)
m) (n-4)c + 6T(n-4)
n) (n-4)c + 6T(n-6)
o) (n-6)c + 3T(n-6)

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