discrete mathematics/structures Transcribed Image Text: 3) Let consider the following algorithm: Polynomial evaluation

discrete mathematics/structures Transcribed Image Text: 3) Let consider the following algorithm: Polynomial evaluation
This algorithm evaluates the polynomial
p(x) -Σ-0Ck xT
Lk=0
n-k
At the point t.
Input: The sequence of coefficients co, C1, …, Cn, the value t and n
Output: p(t)
Procedure poly(c, n, t)
If n = 0 then
Return (co)
Return (t · poly(c, n-1, t) + Cn)
End poly
Let b, be the number of multiplications required to compute p(t).
a) Find the recurrence relation and initial condition for the sequence {bn}
b) Compute b1, b2 and b3.
c) Solve the recurrence relation.

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