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

The code implements a nonogram solver, that is, it takes a list of block lengths and a total length and outputs all possible solutions to the nonogram puzzle. A nonogram is a logic puzzle with a grid of squares. Each row and column is assigned a set of numbers that indicate the lengths of unbroken lines of filled-in squares. The code uses a recursive function sequences to generate all possible sequences of filled-in squares that satisfy the given block lengths. The function takes two arguments: blockseq, a vector of block lengths, and numblanks, the total number of cells in the row or column. The function returns a vector of strings, each of which represents a possible sequence of filled-in squares. The function first checks if the blockseq is empty. If it is, the function returns a vector of strings containing a single string of the form "." ^ numblanks, which represents a row or column with no filled-in squares. If the blockseq is not empty, the function checks if the minlen of the blockseq is equal to the numblanks. The minlen of a blockseq is the sum of the block lengths plus the number of blocks minus 1. If the minlen is equal to the numblanks, the function returns a vector of strings containing a single string of the form join(map(x->"#"^x, blockseq), "."), which represents a row or column with the given block lengths. If the minlen is not equal to the numblanks, the function calls itself recursively with the allbuthead of the blockseq and the rightspace, which is the numblanks minus the minlen of the blockseq. The function returns a vector of strings containing all possible sequences of filled-in squares that satisfy the given block lengths and total length. The function nonoblocks takes two arguments: bvec, a vector of block lengths, and len, the total length. The function first prints a message to the console indicating the block lengths and the total length. If the len is less than the minlen of the bvec, the function prints a message to the console indicating that there is no solution. Otherwise, the function calls the sequences function with the bvec and len as arguments and prints each of the resulting sequences to the console.

Here is an example of how to use the nonoblocks function:

julia> nonoblocks([2, 1], 5)
With blocks [2, 1] and 5 cells:
.##...
##...

This example shows that there are two possible solutions to the nonogram puzzle with block lengths [2, 1] and total length 5.

minsized(arr) = join(map(x->"#"^x, arr), ".")
minlen(arr) = sum(arr) + length(arr) - 1
 
function sequences(blockseq, numblanks)
    if isempty(blockseq)
        return ["." ^ numblanks]
    elseif minlen(blockseq) == numblanks
        return minsized(blockseq)
    else    
        result = Vector{String}()
        allbuthead = blockseq[2:end]
        for leftspace in 0:(numblanks - minlen(blockseq))
            header = "." ^ leftspace * "#" ^ blockseq[1] * "."
            rightspace = numblanks - length(header)
            if isempty(allbuthead)
                push!(result, rightspace <= 0 ? header[1:numblanks] : header * "." ^ rightspace)            
            elseif minlen(allbuthead) == rightspace
                push!(result, header * minsized(allbuthead))
            else
                map(x -> push!(result, header * x), sequences(allbuthead, rightspace))
            end
        end
    end
    result
end

function nonoblocks(bvec, len)
    println("With blocks $bvec and $len cells:")
    len < minlen(bvec) ? println("No solution") : for seq in sequences(bvec, len) println(seq) end
end

nonoblocks([2, 1], 5)
nonoblocks(Vector{Int}([]), 5)
nonoblocks([8], 10)
nonoblocks([2, 3, 2, 3], 15)
nonoblocks([2, 3], 5)