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

The provided Julia code calculates and displays multifactorials for a range of n and k values. Here's a breakdown of the code:

1. Function multifact:

   • This function takes two integers n and k as input and computes the multifactorial of n with respect to k.
   • It checks if both n and k are positive (greater than 0) using the > 0 operator. If either is non-positive, it throws a DomainError exception.
   • If k is greater than 1, it returns the regular factorial of n (calculated using the factorial function) because the multifactorial of n with respect to k is equal to the factorial of n.
   • If both n and k are positive and k is not 1, it calculates the multifactorial as the product of n multiplied by n-k, n-2k, and so on, down to 2. This is done using the prod function.

2. Constants khi and nhi:

   • khi is set to 5, representing the maximum value of k up to which multifactorials will be displayed.
   • nhi is set to 10, representing the maximum value of n up to which multifactorials will be displayed.

3. Main Function:

   • The code starts by printing a header message indicating that it will display multifactorials for n values in the range [1, nhi] and k values in the range [1, khi].

   • It then enters a loop to iterate through k values from 1 to khi.

   • For each k, it calculates the multifactorials for n values in the range [1, nhi] using the multifact function and stores the results in a vector a.

   • It defines a string lab representing the label for the multifactorial, which is n with the ! character (representing factorial) repeated k times.

   • Finally, it uses the @printf macro to print the label and the multifactorial values for each n in a formatted manner.

using Printf

function multifact(n::Integer, k::Integer)
    n > 0 && k > 0 || throw(DomainError())
    k > 1 || factorial(n)
    return prod(n:-k:2)
end

const khi = 5
const nhi = 10
println("Showing multifactorial for n in [1, $nhi] and k in [1, $khi].")
for k = 1:khi
    a = multifact.(1:nhi, k)
    lab = "n" * "!" ^ k
    @printf("  %-6s →  %s\n", lab, a)
end