# Range consolidation

Range consolidation
You are encouraged to solve this task according to the task description, using any language you may know.

Define a range of numbers `R`, with bounds `b0` and `b1` covering all numbers between and including both bounds. That range can be shown as:

`[b0, b1]`

or equally as:

`[b1, b0]`.

Given two ranges, the act of consolidation between them compares the two ranges:

• If one range covers all of the other then the result is that encompassing range.
• If the ranges touch or intersect then the result is one new single range covering the overlapping ranges.
• Otherwise the act of consolidation is to return the two non-touching ranges.

Given N ranges where N>2 then the result is the same as repeatedly replacing all combinations of two ranges by their consolidation until no further consolidation between range pairs is possible. If N<2 then range consolidation has no strict meaning and the input can be returned.

Example 1:
Given the two ranges [1, 2.5] and [3, 4.2] then there is no
common area between the ranges and the result is the same as the input.
Example 2:
Given the two ranges [1, 2.5] and [1.8, 4.7] then there is
an overlap [2.5, 1.8] between the ranges and the result is the single
range [1, 4.7]. Note that order of bounds in a range is not, (yet), stated.
Example 3:
Given the two ranges [6.1, 7.2] and [7.2, 8.3] then they
touch at 7.2 and the result is the single range [6.1, 8.3].
Example 4:
Given the three ranges [1, 2] and [4, 8] and [2, 5]
then there is no intersection of the ranges [1, 2] and [4, 8]
but the ranges [1, 2] and [2, 5] overlap and consolidate to
produce the range [1, 5]. This range, in turn, overlaps the other range
[4, 8], and so consolidates to the final output of the single range
[1, 8]

Let a normalized range display show the smaller bound to the left; and show the range with the smaller lower bound to the left of other ranges when showing multiple ranges.

Output the normalised result of applying consolidation to these five sets of ranges:

```        [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]
```

Show output here.

## C#

Works with: C sharp version 7
`using static System.Math;using System.Linq;using System; public static class RangeConsolidation{    public static void Main() {        foreach (var list in new [] {            new[] { (1.1, 2.2) }.ToList(),            new[] { (6.1, 7.2), (7.2, 8.3) }.ToList(),            new[] { (4d, 3d), (2, 1) }.ToList(),            new[] { (4d, 3d), (2, 1), (-1, 2), (3.9, 10) }.ToList(),            new[] { (1d, 3d), (-6, -1), (-4, -5), (8, 2), (-6, -6) }.ToList()        })        {            for (int z = list.Count-1; z >= 1; z--) {                for (int y = z - 1; y >= 0; y--) {                    if (Overlap(list[z], list[y])) {                        list[y] = Consolidate(list[z], list[y]);                        list.RemoveAt(z);                        break;                    }                }            }            Console.WriteLine(string.Join(", ", list.Select(Normalize).OrderBy(range => range.s)));        }    }     private static bool Overlap((double s, double e) left, (double s, double e) right) =>        Max(left.s, left.e) > Max(right.s, right.e)        ? Max(right.s, right.e) >= Min(left.s, left.e)        : Max(left.s, left.e) >= Min(right.s, right.e);     private static (double s, double e) Consolidate((double s, double e) left, (double s, double e) right) =>        (Min(Min(left.s, left.e), Min(right.s, right.e)), Max(Max(left.s, left.e), Max(right.s, right.e)));     private static (double s, double e) Normalize((double s, double e) range) =>        (Min(range.s, range.e), Max(range.s, range.e));}`
Output:
```(1.1, 2.2)
(6.1, 8.3)
(1, 2), (3, 4)
(-1, 2), (3, 10)
(-6, -1), (1, 8)```

## Go

`package main import (    "fmt"    "math"    "sort") type Range struct{ Lower, Upper float64 } func (r Range) Norm() Range {    if r.Lower > r.Upper {        return Range{r.Upper, r.Lower}    }    return r} func (r Range) String() string {    return fmt.Sprintf("[%g, %g]", r.Lower, r.Upper)} func (r1 Range) Union(r2 Range) []Range {    if r1.Upper < r2.Lower {        return []Range{r1, r2}    }    r := Range{r1.Lower, math.Max(r1.Upper, r2.Upper)}    return []Range{r}} func consolidate(rs []Range) []Range {    for i := range rs {        rs[i] = rs[i].Norm()    }    le := len(rs)    if le < 2 {        return rs    }    sort.Slice(rs, func(i, j int) bool {        return rs[i].Lower < rs[j].Lower    })    if le == 2 {        return rs[0].Union(rs[1])    }    for i := 0; i < le-1; i++ {        for j := i + 1; j < le; j++ {            ru := rs[i].Union(rs[j])            if len(ru) == 1 {                rs[i] = ru[0]                copy(rs[j:], rs[j+1:])                rs = rs[:le-1]                le--                i--                break            }        }    }    return rs} func main() {    rss := [][]Range{        {{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}},    }    for _, rs := range rss {        s := fmt.Sprintf("%v", rs)        fmt.Printf("%40s => ", s[1:len(s)-1])        rs2 := consolidate(rs)        s = fmt.Sprintf("%v", rs2)        fmt.Println(s[1 : len(s)-1])    }}`
Output:
```                              [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, 2] [3, 4]
[4, 3] [2, 1] [-1, -2] [3.9, 10] => [-2, -1] [1, 2] [3, 10]
[1, 3] [-6, -1] [-4, -5] [8, 2] [-6, -6] => [-6, -1] [1, 8]
```

`import Data.List (intercalate, maximumBy, sort)import Data.Ord (comparing) consolidated :: [(Float, Float)] -> [(Float, Float)]consolidated xs =  let go xy [] = [xy]      go xy@(x, y) abetc@((a, b):etc)        | y >= b = xy : etc        | y >= a = (x, b) : etc        | otherwise = xy : abetc      ab (a, b)        | a <= b = (a, b)        | otherwise = (b, a)  in foldr go [] (sort . fmap ab \$ xs)  -- TEST ---------------------------------------------------tests :: [[(Float, Float)]]tests =  [ []  , [(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)]  ] main :: IO ()main =  putStrLn \$  tabulated "Range consolidations:" showPairs showPairs consolidated tests  -- DISPLAY FORMATTING ------------------------------------- tabulated :: String -> (a -> String) -> (b -> String) -> (a -> b) -> [a] -> Stringtabulated s xShow fxShow f xs =  let w = length \$ maximumBy (comparing length) (xShow <\$> xs)      rjust n c s = drop (length s) (replicate n c ++ s)  in unlines \$     s : fmap (((++) . rjust w ' ' . xShow) <*> ((" -> " ++) . fxShow . f)) xs showPairs :: [(Float, Float)] -> StringshowPairs xs  | null xs = "[]"  | otherwise = '[' : intercalate ", " (showPair <\$> xs) ++ "]" showPair :: (Float, Float) -> StringshowPair (a, b) = '(' : showNum a ++ ", " ++ showNum b ++ ")" showNum :: Float -> StringshowNum n  | 0 == (n - fromIntegral (round n)) = show (round n)  | otherwise = show n`
Output:
```Range consolidations:
[] -> []
[(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, 2), (3, 4)]
[(4, 3), (2, 1), (-1, -2), (3.9, 10)] -> [(-2, -1), (1, 2), (3, 10)]
[(1, 3), (-6, -1), (-4, -5), (8, 2), (-6, -6)] -> [(-6, -1), (1, 8)]```

## J

Solution:

`ensure2D=: ,:^:(1 = #@\$)                 NB. if list make 1 row tablenormalise=: ([: /:~ /:~"1)@ensure2D      NB. normalises list of rangesmerge=: ,:`(<.&{. , >.&{:)@.(>:/&{: |.)  NB. merge ranges x and yconsolidate=: (}[email protected]] ,~ (merge {.)) ensure2D`

Required Examples:

`   tests=:  <@".;._2 noun define1.1 2.26.1 7.2 ,: 7.2 8.34 3 ,: 2 14 3 , 2 1 , _1 _2 ,: 3.9 101 3 , _6 _1 , _4 _5 , 8 2 ,: _6 _6)    consolidate/@normalise&.> tests+-------+-------+---+-----+-----+|1.1 2.2|6.1 8.3|1 2|_2 _1|_6 _1||       |       |3 4| 1  2| 1  8||       |       |   | 3 10|     |+-------+-------+---+-----+-----+`

## JavaScript

Translation of: Python
`(() => {    'use strict';     const main = () => {         // consolidated :: [(Float, Float)] -> [(Float, Float)]        const consolidated = xs =>            foldl((abetc, xy) =>                0 < abetc.length ? (() => {                    const                        etc = abetc.slice(1),                        [a, b] = abetc[0],                        [x, y] = xy;                     return y >= b ? (                        cons(xy, etc)                    ) : y >= a ? (                        cons([x, b], etc)                    ) : cons(xy, abetc);                })() : [xy],                [],                sortBy(flip(comparing(fst)),                    map(([a, b]) => a < b ? (                            [a, b]                        ) : [b, a],                        xs                    )                )            );         // TEST -------------------------------------------        console.log(            tabulated(                'Range consolidations:',                JSON.stringify,                JSON.stringify,                consolidated,                [                    [                        [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]                    ]                ]            )        );    };     // GENERIC FUNCTIONS ----------------------------     // comparing :: (a -> b) -> (a -> a -> Ordering)    const comparing = f =>        (x, y) => {            const                a = f(x),                b = f(y);            return a < b ? -1 : (a > b ? 1 : 0);        };     // compose (<<<) :: (b -> c) -> (a -> b) -> a -> c    const compose = (f, g) => x => f(g(x));     // cons :: a -> [a] -> [a]    const cons = (x, xs) => [x].concat(xs);     // flip :: (a -> b -> c) -> b -> a -> c    const flip = f =>        1 < f.length ? (            (a, b) => f(b, a)        ) : (x => y => f(y)(x));     // foldl :: (a -> b -> a) -> a -> [b] -> a    const foldl = (f, a, xs) => xs.reduce(f, a);     // fst :: (a, b) -> a    const fst = tpl => tpl[0];     // justifyRight :: Int -> Char -> String -> String    const justifyRight = (n, cFiller, s) =>        n > s.length ? (            s.padStart(n, cFiller)        ) : s;     // Returns Infinity over objects without finite length.    // This enables zip and zipWith to choose the shorter    // argument when one is non-finite, like cycle, repeat etc     // length :: [a] -> Int    const length = xs =>        (Array.isArray(xs) || 'string' === typeof xs) ? (            xs.length        ) : Infinity;     // map :: (a -> b) -> [a] -> [b]    const map = (f, xs) =>        (Array.isArray(xs) ? (            xs        ) : xs.split('')).map(f);     // maximumBy :: (a -> a -> Ordering) -> [a] -> a    const maximumBy = (f, xs) =>        0 < xs.length ? (            xs.slice(1)            .reduce((a, x) => 0 < f(x, a) ? x : a, xs[0])        ) : undefined;     // sortBy :: (a -> a -> Ordering) -> [a] -> [a]    const sortBy = (f, xs) =>        xs.slice()        .sort(f);     // tabulated :: String -> (a -> String) ->    //                        (b -> String) ->    //           (a -> b) -> [a] -> String    const tabulated = (s, xShow, fxShow, f, xs) => {        // Heading -> x display function ->        //           fx display function ->        //    f -> values -> tabular string        const            ys = map(xShow, xs),            w = maximumBy(comparing(x => x.length), ys).length,            rows = zipWith(                (a, b) => justifyRight(w, ' ', a) + ' -> ' + b,                ys,                map(compose(fxShow, f), xs)            );        return s + '\n' + unlines(rows);    };     // take :: Int -> [a] -> [a]    // take :: Int -> String -> String    const take = (n, xs) =>        'GeneratorFunction' !== xs.constructor.constructor.name ? (            xs.slice(0, n)        ) : [].concat.apply([], Array.from({            length: n        }, () => {            const x = xs.next();            return x.done ? [] : [x.value];        }));     // unlines :: [String] -> String    const unlines = xs => xs.join('\n');     // zipWith :: (a -> b -> c) -> [a] -> [b] -> [c]    const zipWith = (f, xs, ys) => {        const            lng = Math.min(length(xs), length(ys)),            as = take(lng, xs),            bs = take(lng, ys);        return Array.from({            length: lng        }, (_, i) => f(as[i], bs[i], i));    };     // MAIN ---    return main();})();`
Output:
```Range consolidations:
[[1.1,2.2]] -> [[1.1,2.2]]
[[6.1,7.2],[7.2,8.3]] -> [[6.1,8.3]]
[[4,3],[2,1]] -> [[1,2],[3,4]]
[[4,3],[2,1],[-1,-2],[3.9,10]] -> [[-2,-1],[1,2],[3,10]]
[[1,3],[-6,-1],[-4,-5],[8,2],[-6,-6]] -> [[-6,-1],[1,8]]```

## Julia

In Julia, a Range is a type of iterator, generally one over a specified interval. The task as specified is orthogonal to the iteration purpose of a Julia Range, since the task is about merging sets of numbers, not iterations. Therefore, a translation of the Python code is done, rather than using a native Julia Range.

Translation of: Python
`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))")    endend testranges() `
Output:
```Array{Float64,1}[[1.1, 2.2]] => Array{Float64,1}[[1.1, 2.2]]
Array{Float64,1}[[6.1, 7.2], [7.2, 8.3]] => Array{Float64,1}[[6.1, 8.3]]
Array{Float64,1}[[4.0, 3.0], [2.0, 1.0]] => Array{Float64,1}[[1.0, 2.0], [3.0, 4.0]]
Array{Float64,1}[[4.0, 3.0], [2.0, 1.0], [-1.0, -2.0], [3.9, 10.0]] => Array{Float64,1}[[-2.0, -1.0], [1.0, 2.0], [3.0, 10.0]]
Array{Float64,1}[[1.0, 3.0], [-6.0, -1.0], [-4.0, -5.0], [8.0, 2.0], [-6.0, -6.0]] => Array{Float64,1}[[-6.0, -1.0], [1.0, 8.0]]
```

## Perl

Note: the output is shown in the standard Perl notation for Ranges.

`use strict;use warnings; use List::Util qw(min max); sub consolidate {    our @arr; local *arr = shift;    my @sorted = sort { @\$a[0] <=> @\$b[0] } map { [sort { \$a <=> \$b } @\$_] } @arr;    my @merge = shift @sorted;    for my \$i (@sorted) {        if (\$merge[-1][1] >= @\$i[0]) {            \$merge[-1][0] = min(\$merge[-1][0], @\$i[0]);            \$merge[-1][1] = max(\$merge[-1][1], @\$i[1]);        } else {            push @merge, \$i;        }    }    return @merge;} for my \$intervals (    [[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]]) {        my(\$in,\$out);        \$in   = join ', ', map { '[' . join(', ', @\$_) . ']' } @\$intervals;        \$out .= join('..', @\$_). ' ' for consolidate(\$intervals);        printf "%44s => %s\n", \$in, \$out;}`
Output:
```                                  [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..2 3..4
[4, 3], [2, 1], [-1, -2], [3.9, 10] => -2..-1 1..2 3..10
[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6] => -6..-1 1..8```

## Perl 6

Works with: Rakudo version 2018.12

In Perl 6, a Range is a first class object with its own specialized notation. Perl 6 Ranges allow for exclusion of the boundary numbers. This example doesn't since it isn't a requirement in this task. Much of the logic is lifted from the Set_of_real_numbers task with simplified logic for the much simpler requirements.

Note: the output is in standard Perl 6 notation for Ranges.

`# Unionsub infix:<∪> (Range \$a, Range \$b) { Range.new(\$a.min,max(\$a.max,\$b.max)) } # Intersectionsub infix:<∩> (Range \$a, Range \$b) { so \$a.max >= \$b.min } multi consolidate() { () } multi consolidate(\$this is copy, **@those) {    gather {        for consolidate |@those -> \$that {            if \$this ∩ \$that { \$this ∪= \$that }            else             { take \$that }        }        take \$this;    }} for [[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]]-> @intervals {    printf "%46s => ", @intervals.perl;    say reverse consolidate |@intervals.grep(*.elems)».sort.sort({ [.[0], .[*-1]] }).map: { Range.new(.[0], .[*-1]) }}`
Output:
```                                 [[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..2 3..4)
[[4, 3], [2, 1], [-1, -2], [3.9, 10]] => (-2..-1 1..2 3..10)
[[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]] => (-6..-1 1..8)
```

## Phix

`function consolidate(sequence sets)    for i=length(sets) to 1 by -1 do        sets[i] = sort(sets[i])        atom {is,ie} = sets[i]        for j=length(sets) to i+1 by -1 do            atom {js,je} = sets[j]            bool overlap = iff(is<=js?js<=ie:is<=je)            if overlap then                sets[i] = {min(is,js),max(ie,je)}                sets[j..j] = {}            end if        end for    end for    return sort(sets)end function procedure test(sequence set)    printf(1,"%40v => %v\n",{set,consolidate(set)})end procedure test({{1.1,2.2}})test({{6.1,7.2},{7.2,8.3}})test({{4,3},{2,1}})test({{4,3},{2,1},{-1,-2},{3.9,10}})test({{1,3},{-6,-1},{-4,-5},{8,2},{-6,-6}})`
Output:
```                             {{1.1,2.2}} => {{1.1,2.2}}
{{6.1,7.2},{7.2,8.3}} => {{6.1,8.3}}
{{4,3},{2,1}} => {{1,2},{3,4}}
{{4,3},{2,1},{-1,-2},{3.9,10}} => {{-2,-1},{1,2},{3,10}}
{{1,3},{-6,-1},{-4,-5},{8,2},{-6,-6}} => {{-6,-1},{1,8}}
```

## Python

### Procedural

`def normalize(s):    return sorted(sorted(bounds) for bounds in s if bounds) def consolidate(ranges):    norm = normalize(ranges)    for i, r1 in enumerate(norm):        if r1:            for r2 in norm[i+1:]:                if r2 and r1[-1] >= r2[0]:     # intersect?                    r1[:] = [r1[0], max(r1[-1], r2[-1])]                    r2.clear()    return [rnge for rnge in norm if rnge] if __name__ == '__main__':    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]],            ]:        print(f"{str(s)[1:-1]} => {str(consolidate(s))[1:-1]}") `
Output:
```[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, 2], [3, 4]
[4, 3], [2, 1], [-1, -2], [3.9, 10] => [-2, -1], [1, 2], [3, 10]
[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6] => [-6, -1], [1, 8]```

### Functional

Defining consolidation as a fold over a list of tuples:

Works with: Python version 3.7
`'''Range consolidation''' from functools import reduce  # consolidated :: [(Float, Float)] -> [(Float, Float)]def consolidated(xs):    '''A consolidated list of       [(Float, Float)] ranges.'''     def go(abetc, xy):        '''A copy of the accumulator abetc,           with its head range ab either:           1. replaced by or           2. merged with           the next range xy, or           with xy simply prepended.'''        if abetc:            a, b = abetc[0]            etc = abetc[1:]            x, y = xy            return [xy] + etc if y >= b else (   # ab replaced.                [(x, b)] + etc if y >= a else (  # xy + ab merged.                    [xy] + abetc                 # xy simply prepended.                )            )        else:            return [xy]     def tupleSort(ab):        a, b = ab        return ab if a <= b else (b, a)     return reduce(        go,        sorted(map(tupleSort, xs), reverse=True),        []    )  # TEST ----------------------------------------------------# main :: IO ()def main():    '''Tests'''     print(        tabulated('Consolidation of numeric ranges:')(str)(str)(            consolidated        )([            [(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)]        ])    )  # GENERIC FUNCTIONS FOR DISPLAY ---------------------------  # compose (<<<) :: (b -> c) -> (a -> b) -> a -> cdef compose(g):    '''Right to left function composition.'''    return lambda f: lambda x: g(f(x))  # tabulated :: String -> (a -> String) ->#                        (b -> String) ->#                        (a -> b) -> [a] -> Stringdef tabulated(s):    '''Heading -> x display function -> fx display function ->          f -> value list -> tabular string.'''    def go(xShow, fxShow, f, xs):        w = max(map(compose(len)(xShow), xs))        return s + '\n' + '\n'.join([            xShow(x).rjust(w, ' ') + ' -> ' + fxShow(f(x)) for x in xs        ])    return lambda xShow: lambda fxShow: (        lambda f: lambda xs: go(            xShow, fxShow, f, xs        )    )  # MAIN ---if __name__ == '__main__':    main()`
Output:
```Consolidation of numeric ranges:
[(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, 2), (3, 4)]
[(4, 3), (2, 1), (-1, -2), (3.9, 10)] -> [(-2, -1), (1, 2), (3, 10)]
[(1, 3), (-6, -1), (-4, -5), (8, 2), (-6, -6)] -> [(-6, -1), (1, 8)]```

## REXX

Most of the REXX code was testing (and rebuilding) the syntax (insuring blanks after commas), and handling of a null set.

The actual logic for the range consolidation is marked with the comments:     /*■■■■►*/

`/*REXX program performs range consolidation (they can be [equal] ascending/descending). */#.=                                              /*define the default for range sets.   */parse arg #.1                                    /*obtain optional arguments from the CL*/if #.1=''  then do                               /*Not specified?  Then use the defaults*/                #.1= '[1.1, 2.2]'                #.2= '[6.1, 7.2], [7.2, 8.3]'                #.3= '[4, 3], [2, 1]'                #.4= '[4, 3], [2, 1], [-1, -2], [3.9, 10]'                #.5= '[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]'                #.6= '[]'                end        do j=1  while #.j\=='';   \$= #.j          /*process each of the range sets.      */       say copies('═', 75)                       /*display a fence between range sets.  */       say '         original ranges:'     \$     /*display the original range set.      */       \$= order(\$)                               /*order low and high ranges; normalize.*/       call xSort  words(\$)                      /*sort the ranges using a simple sort. */       \$= merge(\$)                               /*consolidate the ranges.              */       say '     consolidated ranges:'     \$     /*display the consolidated range set.  */       end   /*j*/exit                                             /*stick a fork in it,  we're all done. *//*──────────────────────────────────────────────────────────────────────────────────────*/merge: procedure expose @.; parse arg y       if words(y)<2  then signal build          /*Null or only 1 range?  Skip merging. */           do j=1  to @.0-1;         if @.j==''  then iterate      /*skip deleted ranges.*/            do k=j+1  to  @.0;      if @.k==''  then iterate      /*  "     "       "   */            parse var  @.j  a   b;  parse var  @.k  aa  bb        /*extract low and high*//*■■■■►*/   if a<=aa & b>=bb  then  do; @.k=;  iterate;            end  /*within a range*//*■■■■►*/   if a<=aa & b>=aa  then  do; @.j= a bb; @.k=; iterate;  end  /*abutted ranges*/            end   /*k*/          end     /*j*/build: z=             do r=1  for @.0;  z= z translate(@.r, ',', " ");  end   /*r*/   /*add comma*/       f=;   do s=1  for words(z);   f= f '['word(z, s)"], ";  end   /*s*/   /*add [ ], */       if f==''  then return '[]'                                            /*null set.*/       return space( changestr(',',  strip( space(f), 'T', ","), ", ") )     /*add blank*//*──────────────────────────────────────────────────────────────────────────────────────*/order: procedure expose @.; parse arg y,,z;  @.= /*obtain arguments from the invocation.*/       y= space(y, 0)                            /*elide superfluous blanks in the sets.*/          do k=1  while y\==''  &  y\=='[]'      /*process ranges while range not blank.*/          if left(y,1)==','  then y= substr(y,2) /*elide commas between sets of ranges. */          parse var  y   '['  L  ","  H  ']'   y /*extract  the "low" and "high" values.*/          if H<L  then parse value  L H with H L /*order     "    "    "     "      "   */          L= L / 1;     H= H / 1                 /*normalize the  L  and the  H  values.*/          @.k= L H;     z= z L','H               /*re─build the set w/o and with commas.*/          end   /*k*/                            /* [↓]  at this point, K is one to big.*/       @.0= k - 1                                /*keep track of the number of ranges.  */       return strip(z)                           /*elide the extra leading blank in set.*//*──────────────────────────────────────────────────────────────────────────────────────*/xSort: procedure expose @.; parse arg n          /*a simple sort for small set of ranges*/          do j=1  to n-1;                        _= @.j            do k=j+1  to n; if word(@.k,1)>=word(_,1)  then iterate; @.[email protected].k; @.k=_; [email protected].j            end   /*k*/`
output   when using the default inputs:
```═══════════════════════════════════════════════════════════════════════════
original ranges: [1.1, 2.2]
consolidated ranges: [1.1, 2.2]
═══════════════════════════════════════════════════════════════════════════
original ranges: [6.1, 7.2], [7.2, 8.3]
consolidated ranges: [6.1, 8.3]
═══════════════════════════════════════════════════════════════════════════
original ranges: [4, 3], [2, 1]
consolidated ranges: [1, 2], [3, 4]
═══════════════════════════════════════════════════════════════════════════
original ranges: [4, 3], [2, 1], [-1, -2], [3.9, 10]
consolidated ranges: [-2, -1], [1, 2], [3, 10]
═══════════════════════════════════════════════════════════════════════════
original ranges: [1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]
consolidated ranges: [-6, -1], [1, 8]
═══════════════════════════════════════════════════════════════════════════
original ranges: []
consolidated ranges: []
```

## Yabasic

`sub sort(tabla())    local items, i, t1, t2, s     items = arraysize(tabla(), 1)     repeat        s = true        for i = 1 to items-1            if tabla(i, 1) > tabla(i+1, 1) then                t1 = tabla(i, 1) : t2 = tabla(i, 2)                tabla(i, 1) = tabla(i + 1, 1) : tabla(i, 2) = tabla(i + 1, 2)                tabla(i + 1, 1) = t1 : tabla(i + 1, 2) = t2                s = false            end if        next    until(s)end sub sub normalize(tabla())    local items, i, t     items = arraysize(tabla(), 1)     for i = 1 to items        if tabla(i, 1) > tabla(i, 2) then            t = tabla(i, 1)            tabla(i, 1) = tabla(i, 2)            tabla(i, 2) = t        end if    next     sort(tabla())end sub sub consolidate(tabla())    local items, i     normalize(tabla())    items = arraysize(tabla(), 1)     for i = 1 to items - 1        if tabla(i + 1, 1) <= tabla(i, 2) then            tabla(i + 1, 1) = tabla(i, 1)            if tabla(i + 1, 2) <= tabla(i, 2) then                tabla(i + 1, 2) = tabla(i, 2)            end if            tabla(i, 1) = void : tabla(i, 2) = void        end if    nextend sub // data 1, 1.1, 2.2// data 2, 6.1, 7.2, 7.2, 8.3// data 2, 4, 3, 2, 1// data 4, 4, 3, 2, 1, -1, -2, 3.9, 10 data 5, 1,3, -6,-1, -4,-5, 8,2, -6,-6 void = 10^30read items dim tabla(items,  2) for i = 1 to items    read tabla(i, 1), tabla(i, 2)next consolidate(tabla()) for i = 1 to items    if tabla(i, 1) <> void print tabla(i, 1), "..", tabla(i, 2);next`

## zkl

`fcn consolidate(rs){   (s:=List()).append(      normalize(rs).reduce('wrap(ab,cd){	 if(ab[1]>=cd[0]) L(ab[0],ab[1].max(cd[1])); // consolidate	 else{ s.append(ab); cd }		     // no overlap      }) )}fcn normalize(s){ s.apply("sort").sort(fcn(a,b){ a[0]<b[0] }) }`
`foreach rs in (L(   L(L(1.1, 2.2)),    L(L(6.1, 7.2), L(7.2, 8.3)),    L(L(4, 3), L(2, 1)),   L(L(4.0, 3.0), L(2.0, 1.0), L(-1.0, -2.0), L(3.9, 10.0)),   L(L(1, 3), L(-6, -1), L(-4, -5), L(8, 2), L(-6, -6)), )){ println(ppp(rs),"--> ",ppp(consolidate(rs))) }fcn ppp(ll){ ll.pump(String,fcn(list){ list.concat(", ",  "[",  "] ") }) }`
Output:
```[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, 2] [3, 4]
[4, 3] [2, 1] [-1, -2] [3.9, 10] --> [-2, -1] [1, 2] [3, 10]
[1, 3] [-6, -1] [-4, -5] [8, 2] [-6, -6] --> [-6, -1] [1, 8]
```