GATE 2014 CS (CS3) – Question 21
Find the minimum arithmetic operations needed to evaluate $P(X)=X^5+4X^3+6X+5$ for given X, using only one temporary variable.
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Correct answer: 7 to 7
Explanation
Use the form((X²+4)X²+6)X+5. Compute the first X², add4, recompute X²for its multiplication, add6, multiply byXand add5. This uses four multiplications and three additions, **7operations**, with one stored temporary. It improves on ordinary Horner treatment of the zero coefficients.