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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,
JosBuild a wall around Donald Trump; I'll pay for 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,
JosBuild a wall around Donald Trump; I'll pay for 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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