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

This code defines a module Hailstone that contains a function hailstone and a function countstones and a script that uses these functions. Here is a breakdown of the code:

• Hailstone module:

  • The hailstone function takes an integer n as input and returns a list of integers representing the hailstone sequence for n.
  • The hailstone sequence for n is defined as follows:
    • If n is even, then n is replaced by n/2.
    • If n is odd, then n is replaced by 3n + 1.
    • The sequence continues until n reaches 1.
  • The hailstone function generates the sequence by repeatedly applying the above rules to n and appending the resulting values to a list.
  • The hailstone function is exported from the module, making it available for use in other modules or scripts.

• countstones function:

  • The countstones function takes two integers, mi and mx, as input and returns a tuple containing two values:
    • The most common hailstone sequence length for n in the range mi to mx.
    • The number of times the most common sequence length occurs.
  • The function generates a dictionary where the keys are hailstone sequence lengths and the values are the number of times that length occurs.
  • The function then iterates through the dictionary to find the key (sequence length) with the highest value (number of occurrences).
  • The function returns the key and the value as a tuple.

• Script:

  • The script includes the Hailstone module and uses the hailstone and countstones functions to calculate the most common hailstone sequence length for n in the range 1 to 99999.
  • The script prints the most common sequence length and the number of times it occurs.

In summary, this code defines a module with functions for generating hailstone sequences and counting the occurrences of different sequence lengths. The script uses these functions to find the most common hailstone sequence length for a given range of integers.

############### in file hailstone.jl ###############
module Hailstone

function hailstone(n)
    ret = [n]
    while n > 1
        if n & 1 > 0
            n = 3n + 1
        else 
            n = Int(n//2)
        end
        append!(ret, n)
    end
    return ret
end

export hailstone

end

if PROGRAM_FILE == "hailstone.jl"
    using Hailstone
    h = hailstone(27)
    n = length(h)
    println("The sequence of hailstone(27) is:\n $h.\nThis sequence is of length $n. It starts with $(h[1:4]) and ends with $(h[n-3:end]).")
end
############ in file moduletest.jl ####################
include("hailstone.jl")
using Hailstone
function countstones(mi, mx)
    lengths2occurences = Dict()
    mostfreq = mi
    maxcount = 1
    for i in mi:mx
        h = hailstone(i)
        n = length(h)
        if haskey(lengths2occurences, n)
            newoccurences = lengths2occurences[n] + 1
            if newoccurences > maxcount
                maxcount = newoccurences
                mostfreq = n
            end
            lengths2occurences[n] = newoccurences
        else
            lengths2occurences[n] = 1
        end
    end
    mostfreq, maxcount
end

nlen, cnt = countstones(1,99999)

print("The most common hailstone sequence length for hailstone(n) for 1 <= n < 100000 is $nlen, which occurs $cnt times.")