In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n) < 2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases c) Proof: Inductive step setup. This is the beginning of the inductive step where you are stating the assumptions in the inductive step an what you will be proving in that step. As you do so, identify the inductive hypothesis.

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d) Proof: Inductive step
Transcribed Image Text:d) Proof: Inductive step
Q3 – Proof of Cost,
In this question you will use strong induction to prove that your new algorithm is very efficient.
Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the
total number of multiplications in the total execution of FP(x,n)
You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n
a) Predicate function (-
Your conjecture has already been stated in symbolic form:
It is a statement of the form VneN+, P(n)
What is the predicate function P(n)?
b) Proof: Base cases.
c) Proof: Inductive step setup .
This is the beginning of the inductive step where you are stating the assumptions in the inductive step and
what you will be proving in that step. As you do so, identify the inductive hypothesis.
Transcribed Image Text:Q3 – Proof of Cost, In this question you will use strong induction to prove that your new algorithm is very efficient. Given a non-zero real number x, and a natural number n, define CFP(x,n) to be the cost of FP(x,n) = the total number of multiplications in the total execution of FP(x,n) You will prove that VneN+VXER-{0} CFP(x,n)<2 log2 n a) Predicate function (- Your conjecture has already been stated in symbolic form: It is a statement of the form VneN+, P(n) What is the predicate function P(n)? b) Proof: Base cases. c) Proof: Inductive step setup . This is the beginning of the inductive step where you are stating the assumptions in the inductive step and what you will be proving in that step. As you do so, identify the inductive hypothesis.
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