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Thread: Analysis of Algorithms
 03292013, 09:45 AM #1Member
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Analysis of Algorithms
I haven't taken a programming class yet and this question really confuses me, any help is greatly appreciated.
The following pseudocode procedure can be used to evaluate the polynomial 8 – 10x + 〖7x〗^2  〖2x〗^3 + 〖3x〗^4 + 〖12x〗^5, when x is replaced by an arbitrary (but fixed) real number r. For this particular instance, n = 5 and a_0 = 8, a_1 = 10, a_2 = 7, a_3 = 2, a_4 = 3, and a_5 = 12.
Java Code:procedure PolynomialEvaluation1 (n: nonnegative integer; r, a_0, a_1, a_2,…, a_n: real) begin product := 1.0 value := a_0 for i := 1 to n do begin product := product * r value := value + a_i * product end end
 03292013, 10:28 AM #2
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Re: Analysis of Algorithms
That is Horner's rule: for a polynomial a(n)*x^(n) +a(n1)*x^(n1) + ... a(0), the polynomial can be rewritten as: x*(a(n)*x^(n1) ... a(1))+a(0). If you recursively apply this rule to the polynomial (of lower degree) you can see that it takes n1 multiplications and n1 additions to evaluate the entire polynomial.
kind regards,
JosI have the stamina of a seal; I lie on the beach instead of running on it.
 03292013, 07:17 PM #3Member
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Re: Analysis of Algorithms
Hmm, interesting and thank you. I am still having trouble finding how many additions and multiplications total.
 03292013, 07:37 PM #4
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Re: Analysis of Algorithms
Erm, I gave the answer already.
kind regards,
JosI have the stamina of a seal; I lie on the beach instead of running on it.
 03292013, 08:03 PM #5Member
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Re: Analysis of Algorithms
Oh sorry. I read that as soon as I woke up and things didn't click lol. My bad.
Thank you again!
 03292013, 08:47 PM #6
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Re: Analysis of Algorithms
I have the stamina of a seal; I lie on the beach instead of running on it.
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