Consider the polynomial $p(x) = a_0 + a_1x + a_2x^2 + a_3x^3$ , where $a_i \neq 0$, $\forall i$. The minimum number of multiplications needed to evaluate $p$ on an input $x$ is:
apply the Horner's Rules
P(x)= a0 + a1x + a2x^2 + a3x^3
P(x)= a0 +(( a1+a2x + a3x^2) x ) // 1 multipication taking the x common
P(x)= a0 +(( a1+(a2 + a3x ) x ) x // 2 multipication in x in inner bracket
P(x)= a0 +( ( a1+(a2 + a3x ) x ) x ) // 3 multipication entire bracket
Sir, if the question would be-:
Total number of arithmetic operation required,then answer would be $6(3+3)$.right?
https://gateoverflow.in/2045/gate2014-3-11
Answer will be 3
mul= pair of brackets
p(x)=a0+x(a1+x(a2+a3(x)))
64.3k questions
77.9k answers
243k comments
79.7k users