HOMEWORK 3 Program name hw3pr1.cpp


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NOTE: Homework will be graded on using g++ 5.3.0 with
-std=c++14. You are free to develop your programs on Visual C++ or any other
platform, but it is your responsibility to make sure your programs also compile
and execute correctly on using g++ -std=c++14.

The grade for this lab will be based on style (formatting, variable names,
comments, etc.), syntax (no compilation or link errors), and correctness
(passes all test cases). Follow the style guide at Your grade for this lab is:
Problem # 1 2 3 4
Style /2 /4 /4 /2
Syntax /3 /6 /6 /3
Correctness /5 /10 /10 /5
Total /10 /20 /20 /10
Grand total _____/50

1. (10 points) Write a program name hw3pr1.cpp which reads a list of doubles
terminated by end of file into a vector and prints the mean (or average) and the
standard deviation (look up the formula and tell where you got it in a
comment). Print an appropriate message if the list is empty.

2. (20 points) Use your my_cbrt_2 function from hw2pr4 to define a more
accurate cube root for all values of n using this pseudocode:
double my_cbrt_3(double n)
If n is zero return zero.
If n is negative return -my_cbrt_3(-n).
set x to my_cbrt_2(n)
do this 10 times: x = (2/3)x + n/(3*x*x)
return x

Write a main which repeatedly reads a number n and prints cbrt(n),
my_cbrt_3(n), and the relative error of my_cubrt_3(n). Name your program
hw3pr2.cpp. (The relative error should be quite small.)

3. (20 points) Write the fibonacci function described in Exercise 3 at the end
of Chapter 8, and a main which reads x, y, and n, calls fibonacci to fill the
vector, and then prints the ratio of the last element of v divided by the next
to last element. For example, an input of 1 2 7 prints a ratio of 1.61538.
Fun fact: No matter what x and y are, the larger n is, the closer the ratio is
to the golden mean. Name your program hw3pr3.cpp.

4. (10 points) In problem 2 the loop doesn’t need to be executed 10 times for
maximum accuracy. Write a program named hw3pr4.cpp to determine the smallest
number k such that looping k times is just as accurate as looping 10 times.
Hint: For k = 1 to 10, find the maximum relative error for n from 1/8 to 1
in steps of 1/1024. Use those 10 numbers to determine the smallest
number k such that looping k times is just as accurate as looping 10 times.
Name your program hw3pr4.cpp.

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