3D A* Algorithm

-- 3D pathfinding :D
function pathFind(map) -- Map is a 3-dimensional matrix with uniform width, height, and length (a rectangular prism)
    local height, width, length = 0, 0, 0
    local start, finish, open, closed, order, current = {}, {}, {}, {}, {}, {}
    -- Format: open[x .. "-" .. y .. "-" .. z] = {{x, y, z}, ParentNode, fCost}
    for i, v in pairs(map) do
        width = width + 1
        for j, k in pairs(v) do
            if width == 1 then
                height = height + 1
            end
            for l, z in pairs(k) do
                if height == 1 then
                    length = length + 1
                end
                if z == 2 then
                    start = {l, j, i}
                elseif z == 3 then
                    finish = {l, j, i}
                end
            end
        end
    end

    local function getPrCost(Node, ParentNode)
        if not ParentNode then return 0 end
        if Node[1] - ParentNode[1] == 0 or Node[2] - ParentNode[2] == 0 or Node[3] - ParentNode[3] == 0 then
            return 10
        elseif math.abs(Node[1] - ParentNode[1]) == 1 and math.abs(Node[2] - ParentNode[2]) == 1 and math.abs(Node[3] - ParentNode[3]) == 1 then
            return 17
        else
            return 14
        end
    end

    local function getSeCost(Node)
        return (math.abs(Node[1] - finish[1]) + math.abs(Node[2] - finish[2]) + math.abs(Node[3] - finish[3])) * 10
    end

    local function getSurroundingNodes(Node, ParentCost)
        local x, y, z = Node[1], Node[2], Node[3]
        for i = -1, 1 do
            for j = -1, 1 do
                for n = -1, 1 do
                    if x + i > length or z + n > width or y + j > height or x + i <= 0 or y + j <= 0 or z + n <= 0 or (map[z + n][y + j][x + i] and map[z + n][y + j][x +i] == 1) or closed[x + i .. "-" .. y + j .. "-" .. z + n] then
                        open[x + i .. "-" .. y + j .. "-" .. z + n] = nil
                        closed[x + i .. "-" .. y + j .. "-" .. z + n] = true
                    elseif open[x + i .. "-" .. y + j .. "-" .. z + n] then
                        if ParentCost + getPrCost({x + i, y + j, z + n}, Node) < getPrCost({x + i, y + j, z + n}, open[x + i .. "-" .. y + j .. "-" .. z + n][2]) then
                            open[x + i .. "-" .. y + j .. "-" .. z + n] = {{x + i, y + j, z + n}, Node, getPrCost({x + i, y + j, z + n}, Node) + getSeCost({x + i, y + j, z + n})}
                        end
                    else
                        open[x + i .. "-" .. y + j .. "-" .. z + n] = {{x + i, y + j, z + n}, Node, getPrCost({x + i, y + j, z + n}, Node) + getSeCost({x + i, y + j, z + n})}
                    end
                end
            end
        end
    end

    current = start
    while (true) do
        if current[1] == start[1] and current[2] == start[2] and current[3] == start[3] then
            localCost = 0
        else
            local localCost = getPrCost(current, open[current[1] .. "-" .. current[2] .. "-" .. current[3]][2])
        end
        open[current[1] .. "-" .. current[2] .. "-" .. current[3]] = nil
        closed[current[1] .. "-" .. current[2] .. "-" .. current[3]] = true
        if current[1] == finish[1] and current[2] == finish[2] and current[3] == finish[3] then print("Search complete.") return order end
        getSurroundingNodes(current, localCost)
        local closest, lowest
        for i, v in pairs(open) do
            if not closest or v[3] < lowest then
                closest = v[1]
                lowest = v[3]
            end
        end
        if not closest then print("No path.") return {} end
        table.insert(order, {closest[1], closest[2], closest[3]})
        current = closest
    end
end

local order = pathFind  {
    { -- z 1
        {2, 0, 0}, -- y
        {1, 1, 0},
        {0, 0, 0}
    }, {
        {1, 1, 1},
        {1, 1, 1},
        {0, 1, 1}
    }, {
        {3, 0, 0},
        {1, 1, 0},
        {0, 0, 0}
    }
}

-- Display the path to the output
for i, v in pairs(order) do
    print("{" .. v[1] .. ", " .. v[2] .. ", " .. v[3] .. "}")
end