How to resolve the algorithm Averages/Pythagorean means step by step in the Euphoria programming language
Published on 12 May 2024 09:40 PM
How to resolve the algorithm Averages/Pythagorean means step by step in the Euphoria programming language
Table of Contents
Problem Statement
Compute all three of the Pythagorean means of the set of integers 1 through 10 (inclusive). Show that
A (
x
1
, … ,
x
n
) ≥ G (
x
1
, … ,
x
n
) ≥ H (
x
1
, … ,
x
n
)
{\displaystyle A(x_{1},\ldots ,x_{n})\geq G(x_{1},\ldots ,x_{n})\geq H(x_{1},\ldots ,x_{n})}
for this set of positive integers.
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Averages/Pythagorean means step by step in the Euphoria programming language
Source code in the euphoria programming language
function arithmetic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += s[i]
end for
return sum/length(s)
end if
end function
function geometric_mean(sequence s)
atom p
p = 1
for i = 1 to length(s) do
p *= s[i]
end for
return power(p,1/length(s))
end function
function harmonic_mean(sequence s)
atom sum
if length(s) = 0 then
return 0
else
sum = 0
for i = 1 to length(s) do
sum += 1/s[i]
end for
return length(s) / sum
end if
end function
function true_or_false(atom x)
if x then
return "true"
else
return "false"
end if
end function
constant s = {1,2,3,4,5,6,7,8,9,10}
constant arithmetic = arithmetic_mean(s),
geometric = geometric_mean(s),
harmonic = harmonic_mean(s)
printf(1,"Arithmetic: %g\n", arithmetic)
printf(1,"Geometric: %g\n", geometric)
printf(1,"Harmonic: %g\n", harmonic)
printf(1,"Arithmetic>=Geometric>=Harmonic: %s\n",
{true_or_false(arithmetic>=geometric and geometric>=harmonic)})
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