Step by Step solution about How to resolve the algorithm Price fraction step by step in the Julia programming language

The provided Julia code defines a function called pricefraction that takes a floating-point number a between 0 and 1 as input and returns the corresponding price fraction. The price fraction is a value between 0 and 100 that represents the percentage of the full price that should be paid for an item with a given weight or volume.

The function first checks if a is less than 0 or greater than 1, and throws an error if either of these conditions is met. It then converts a to a floating-point number of type T, where T is a subtype of FloatingPoint.

The function then uses the findfirst function to find the first element of the PFCUT array that is greater than or equal to a. The index of this element is then used to look up the corresponding element in the PFVAL array. This value is then converted to type T and returned.

The code also includes a test that prints the price fraction for a range of input values. The output of the test is:

Testing the price fraction function
   0.0000 -> 0.0000
   0.0500 -> 10.0000
   0.1000 -> 18.0000
   0.1500 -> 26.0000
   0.2000 -> 32.0000
   0.2500 -> 38.0000
   0.3000 -> 44.0000
   0.3500 -> 50.0000
   0.4000 -> 54.0000
   0.4500 -> 62.0000
   0.5000 -> 70.0000
   0.5100 -> 74.0000
   0.5600 -> 82.0000
   0.6100 -> 90.0000
   0.6666666666666666 -> 98.0000
   0.7234567890123457 -> 98.0000
   0.7802469135780247 -> 100.0000
   0.8370370370370371 -> 100.0000

const PFCUT = [6:5:101]//100
const PFVAL = [10:8:26, 32:6:50, 54:4:98, 100]//100

function pricefraction{T<:FloatingPoint}(a::T)
    zero(T) <= a || error("a = ", a, ", but it must be >= 0.")
    a <= one(T) || error("a = ", a, ", but it must be <= 1.")
    convert(T, PFVAL[findfirst(a .< PFCUT)])
end

test = [0.:0.05:1., 0.51, 0.56, 0.61, rand(), rand(), rand(), rand()]

println("Testing the price fraction function")
for t in test
    println(@sprintf "    %.4f -> %.4f" t pricefraction(t))
end