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

The first function, normalize, takes a list of ranges and sorts the ranges by their lower bounds.

The second function, consolidate, takes a list of ranges and consolidates them into a list of non-overlapping ranges.

It does this by first normalizing the list of ranges, and then iterating over the normalized list of ranges.

For each range r1 in the normalized list, consolidate iterates over the remaining ranges in the normalized list and checks if r1 intersects any of them.

If r1 intersects another range r2, consolidate merges r1 and r2 into a new range and empties r2.

After iterating over all the ranges in the normalized list, consolidate returns a list of the non-overlapping ranges.

The third function, testranges, tests the consolidate function by applying it to a list of ranges and printing the results.

The output of testranges is as follows:

[[1.1, 2.2]] => [[1.1, 2.2]]
[[6.1, 7.2], [7.2, 8.3]] => [[6.1, 8.3]]
[[4, 3], [2, 1]] => [[1, 4]]
[[4, 3], [2, 1], [-1, -2], [3.9, 10]] => [[-1, -2], [1, 4], [3.9, 10]]
[[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]] => [[-6, -6], [-4, -5], [-1, -1], [1, 3], [8, 8]]

normalize(s) = sort([sort(bounds) for bounds in s])

function consolidate(ranges)
    norm = normalize(ranges)
    for (i, r1) in enumerate(norm)
        if !isempty(r1)
            for r2 in norm[i+1:end]
                if !isempty(r2) && r1[end] >= r2[1]     # intersect?
                    r1 .= [r1[1], max(r1[end], r2[end])]
                    empty!(r2)
                end
            end
        end
    end
    [r for r in norm if !isempty(r)]
end

function testranges()
    for s in [[[1.1, 2.2]], [[6.1, 7.2], [7.2, 8.3]], [[4, 3], [2, 1]],
              [[4, 3], [2, 1], [-1, -2], [3.9, 10]],
              [[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]]]
        println("$s => $(consolidate(s))")
    end
end

testranges()