Range consolidation

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Revision as of 05:45, 19 February 2021 by Alextretyak (talk | contribs) (Added 11l)
Task
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 region 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]
Task:

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.

See also



11l

Translation of: Python

<lang 11l>F consolidate(ranges)

  F normalize(s)
     R sorted(s.filter(bounds -> !bounds.empty).map(bounds -> sorted(bounds)))
  V norm = normalize(ranges)
  L(&r1) norm
     V i = L.index
     I !r1.empty
        L(j) i + 1 .< norm.len
           V& r2 = norm[j]
           I !r2.empty & r1.last >= r2[0]
              r1 = [r1[0], max(r1.last, r2.last)]
              r2.clear()
  R norm.filter(rnge -> !rnge.empty)

L(s) [[[1.1, 2.2]],

     [[6.1, 7.2], [7.2, 8.3]],
     [[4.0, 3.0], [2.0, 1.0]],
     [[4.0, 3.0], [2.0, 1.0], [-1.0, -2.0], [3.9, 10.0]],
     [[1.0, 3.0], [-6.0, -1.0], [-4.0, -5.0], [8.0, 2.0], [-6.0, -6.0]]]
  print(String(s)[1 .< (len)-1]‘ => ’String(consolidate(s))[1 .< (len)-1])/lang>
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]

Ada

<lang Ada>with Ada.Text_IO; with Ada.Containers.Vectors;

procedure Range_Consolidation is

  type Set_Type is record
     Left, Right : Float;
  end record;
  package Set_Vectors is
     new Ada.Containers.Vectors (Positive, Set_Type);
  procedure Normalize (Set : in out Set_Vectors.Vector) is
     function Less_Than (Left, Right : Set_Type) return Boolean is
        begin Return Left.Left < Right.Left; end;
     package Set_Sorting is
        new Set_Vectors.Generic_Sorting (Less_Than);
  begin
     for Elem of Set loop
        Elem := (Left  => Float'Min (Elem.Left,  Elem.Right),
                 Right => Float'Max (Elem.Left,  Elem.Right));
     end loop;
     Set_Sorting.Sort (Set);
  end Normalize;
  procedure Consolidate (Set : in out Set_Vectors.Vector) is
     use Set_Vectors;
     First : Cursor := Set.First;
     Last  : Cursor := Next (First);
  begin
     while Last /= No_Element loop
        if Element (First).Right < Element (Last).Left then      -- non-overlap
           First := Last;
           Last  := Next (Last);
        elsif Element (First).Right >= Element (Last).Left then  -- overlap
           Replace_Element (Set, First, (Left  => Element (First).Left,
                                         Right => Float'Max (Element (First).Right,
                                                             Element (Last) .Right)));
           Delete (Set, Last);
           Last := Next (First);
        end if;
     end loop;
  end Consolidate;
  procedure Put (Set : in Set_Vectors.Vector) is
     package Float_IO is
        new Ada.Text_IO.Float_IO (Float);
  begin
     Float_IO.Default_Exp  := 0;
     Float_IO.Default_Aft  := 1;
     Float_IO.Default_Fore := 3;
     for Elem of Set loop
        Ada.Text_IO.Put ("(");
        Float_IO.Put (Elem.Left);
        Float_IO.Put (Elem.Right);
        Ada.Text_IO.Put (") ");
     end loop;
  end Put;
  procedure Show (Set : in out Set_Vectors.Vector) is
     use Ada.Text_IO;
  begin
     Put (Set);
     Normalize (Set);
     Consolidate (Set);
     Set_Col (70);
     Put (Set);
     New_Line;
  end Show;
  use Set_Vectors;
  Set_0 : Set_Vectors.Vector := Empty_Vector;
  Set_1 : Set_Vectors.Vector := Empty_Vector & (1.1, 2.2);
  Set_2 : Set_Vectors.Vector := (6.1, 7.2) & (7.2, 8.3);
  Set_3 : Set_Vectors.Vector := (4.0, 3.0) & (2.0, 1.0);
  Set_4 : Set_Vectors.Vector := (4.0, 3.0) & (2.0, 1.0) & (-1.0, -2.0) & (3.9, 10.0);
  Set_5 : Set_Vectors.Vector := (1.0, 3.0) & (-6.0, -1.0) & (-4.0, -5.0) & (8.0, 2.0) & (-6.0, -6.0);

begin

  Show (Set_0);
  Show (Set_1);
  Show (Set_2);
  Show (Set_3);
  Show (Set_4);
  Show (Set_5);

end Range_Consolidation;</lang>

Output:
(  1.1  2.2)                                                         (  1.1  2.2)
(  6.1  7.2) (  7.2  8.3)                                            (  6.1  8.3)
(  4.0  3.0) (  2.0  1.0)                                            (  1.0  2.0) (  3.0  4.0)
(  4.0  3.0) (  2.0  1.0) ( -1.0 -2.0) (  3.9 10.0)                  ( -2.0 -1.0) (  1.0  2.0) (  3.0 10.0)
(  1.0  3.0) ( -6.0 -1.0) ( -4.0 -5.0) (  8.0  2.0) ( -6.0 -6.0)     ( -6.0 -1.0) (  1.0  8.0)

C

<lang c>#include <stdio.h>

  1. include <stdlib.h>

typedef struct range_tag {

   double low;
   double high;

} range_t;

void normalize_range(range_t* range) {

   if (range->high < range->low) {
       double tmp = range->low;
       range->low = range->high;
       range->high = tmp;
   }

}

int range_compare(const void* p1, const void* p2) {

   const range_t* r1 = p1;
   const range_t* r2 = p2;
   if (r1->low < r2->low)
       return -1;
   if (r1->low > r2->low)
       return 1;
   if (r1->high < r2->high)
       return -1;
   if (r1->high > r2->high)
       return 1;
   return 0;

}

void normalize_ranges(range_t* ranges, size_t count) {

   for (size_t i = 0; i < count; ++i)
       normalize_range(&ranges[i]);
   qsort(ranges, count, sizeof(range_t), range_compare);

}

// Consolidates an array of ranges in-place. Returns the // number of ranges after consolidation. size_t consolidate_ranges(range_t* ranges, size_t count) {

   normalize_ranges(ranges, count);
   size_t out_index = 0;
   for (size_t i = 0; i < count; ) {
       size_t j = i;
       while (++j < count && ranges[j].low <= ranges[i].high) {
           if (ranges[i].high < ranges[j].high)
               ranges[i].high = ranges[j].high;
       }
       ranges[out_index++] = ranges[i];
       i = j;
   }
   return out_index;

}

void print_range(const range_t* range) {

   printf("[%g, %g]", range->low, range->high);

}

void print_ranges(const range_t* ranges, size_t count) {

   if (count == 0)
       return;
   print_range(&ranges[0]);
   for (size_t i = 1; i < count; ++i) {
       printf(", ");
       print_range(&ranges[i]);
   }

}

void test_consolidate_ranges(range_t* ranges, size_t count) {

   print_ranges(ranges, count);
   printf(" -> ");
   count = consolidate_ranges(ranges, count);
   print_ranges(ranges, count);
   printf("\n");

}

  1. define LENGTHOF(a) sizeof(a)/sizeof(a[0])

int main() {

   range_t test1[] = { {1.1, 2.2} };
   range_t test2[] = { {6.1, 7.2}, {7.2, 8.3} };
   range_t test3[] = { {4, 3}, {2, 1} };
   range_t test4[] = { {4, 3}, {2, 1}, {-1, -2}, {3.9, 10} };
   range_t test5[] = { {1, 3}, {-6, -1}, {-4, -5}, {8, 2}, {-6, -6} };
   test_consolidate_ranges(test1, LENGTHOF(test1));
   test_consolidate_ranges(test2, LENGTHOF(test2));
   test_consolidate_ranges(test3, LENGTHOF(test3));
   test_consolidate_ranges(test4, LENGTHOF(test4));
   test_consolidate_ranges(test5, LENGTHOF(test5));
   return 0;

}</lang>

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]

C#

Works with: C sharp version 7

<lang csharp>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));

}</lang>

Output:
(1.1, 2.2)
(6.1, 8.3)
(1, 2), (3, 4)
(-1, 2), (3, 10)
(-6, -1), (1, 8)

C++

<lang cpp>#include <algorithm>

  1. include <iostream>
  2. include <utility>
  3. include <vector>

// A range is represented as std::pair<from, to>

template <typename iterator> void normalize_ranges(iterator begin, iterator end) {

   for (iterator i = begin; i != end; ++i) {
       if (i->second < i->first)
           std::swap(i->first, i->second);
   }
   std::sort(begin, end);

}

// Merges a range of ranges in-place. Returns an iterator to the // end of the resulting range, similarly to std::remove. template <typename iterator> iterator merge_ranges(iterator begin, iterator end) {

   iterator out = begin;
   for (iterator i = begin; i != end; ) {
       iterator j = i;
       while (++j != end && j->first <= i->second)
           i->second = std::max(i->second, j->second);
       *out++ = *i;
       i = j;
   }
   return out;

}

template <typename iterator> iterator consolidate_ranges(iterator begin, iterator end) {

   normalize_ranges(begin, end);
   return merge_ranges(begin, end);

}

template <typename pair> void print_range(std::ostream& out, const pair& range) {

   out << '[' << range.first << ", " << range.second << ']';

}

template <typename iterator> void print_ranges(std::ostream& out, iterator begin, iterator end) {

   if (begin != end) {
       print_range(out, *begin++);
       for (; begin != end; ++begin) {
           out << ", ";
           print_range(out, *begin);
       }
   }

}

int main() {

   std::vector<std::pair<double, double>> test_cases[] = {
       { {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 (auto&& ranges : test_cases) {
       print_ranges(std::cout, std::begin(ranges), std::end(ranges));
       std::cout << " -> ";
       auto i = consolidate_ranges(std::begin(ranges), std::end(ranges));
       print_ranges(std::cout, std::begin(ranges), i);
       std::cout << '\n';
   }
   return 0;

}</lang>

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]


Clojure

<lang Clojure>(defn normalize [r]

 (let [[n1 n2] r]
   [(min n1 n2) (max n1 n2)]))

(defn touch? [r1 r2]

 (let [[lo1 hi1] (normalize r1)
       [lo2 hi2] (normalize r2)]
   (or (<= lo2 lo1 hi2)
       (<= lo2 hi1 hi2))))

(defn consolidate-touching-ranges [rs]

 (let [lows  (map #(apply min %) rs)
       highs (map #(apply max %) rs)]
   [ (apply min lows) (apply max highs) ]))

(defn consolidate-ranges [rs]

 (loop [res []
        rs  rs]
   (if (empty? rs)
     res
     (let [r0 (first rs)
           touching (filter #(touch? r0 %) rs)
           remove-used (fn [rs used]
                         (remove #(contains? (set used) %) rs))]
       (recur (conj res (consolidate-touching-ranges touching))
              (remove-used (rest rs) touching))))))</lang>
Output:
  (def test-data [ [[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]] ])

  (map consolidate-ranges test-data)
  ;; ==>   ([[1.1 2.2]]
            [[6.1 8.3]]
            [[3 4] [1 2]]
            [[3 10] [1 2] [-2 -1]]
            [[1 8] [-6 -1] [-5 -4]]))

Dyalect

Translation of: C#

<lang dyalect>func max(x, y) {

   if x > y {
       x
   } else {
       y
   }

}

func min(x, y) {

   if x < y {
       x
   } else {
       y
   }

}

func overlap(left, right) {

   if max(left:s, left:e) > max(right:s, right:e) {
       max(right:s, right:e) >= min(left:s, left:e) 
   } else {
       max(left:s, left:e) >= min(right:s, right:e)
   }

}

func consolidate(left, right) {

   (s = min(min(left:s, left:e), min(right:s, right:e)), e = max(max(left:s, left:e), max(right:s, right:e)))

}

func normalize(range) {

   (s = min(range:s, range:e), e = max(range:s, range:e))

}

for list in [

   [ (s = 1.1, e = 2.2) ],
   [ (s = 6.1, e = 7.2), (s = 7.2, e = 8.3) ],
   [ (s = 4.0, e = 3.0), (s = 2, e = 1) ],
   [ (s = 4.0, e = 3.0), (s = 2, e = 1), (s = -1, e = 2), (s = 3.9, e = 10) ],
   [ (s = 1.0, e = 3.0), (s = -6, e = -1), (s = -4, e = -5), (s = 8, e = 2), (s = -6, e = -6) ]

] {

   var z = list.len()-1
   while z >= 1 {
       for y in (z - 1)..0 {
           if overlap(list[z], list[y]) {
               list[y] = consolidate(list[z], list[y])
               list.removeAt(z)
               break
           }
       }
       z -= 1
   }
   for i in list.indices() {
       list[i] = normalize(list[i])
   }
   list.sort((x,y) => x:s - y:s)
   print(list)

}</lang>

Output:
[(s: 1.1, e: 2.2)]
[(s: 6.1, e: 8.3)]
[(s: 1, e: 2), (s: 3, e: 4)]
[(s: -1, e: 2), (s: 3, e: 10)]
[(s: -6, e: -1), (s: 1, e: 8)]

Go

<lang 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{
       Template: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])
   }

}</lang>

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]

Haskell

<lang haskell>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] -> String tabulated 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)] -> String showPairs xs

 | null xs = "[]"
 | otherwise = '[' : intercalate ", " (showPair <$> xs) ++ "]"

showPair :: (Float, Float) -> String showPair (a, b) = '(' : showNum a ++ ", " ++ showNum b ++ ")"

showNum :: Float -> String showNum n

 | 0 == (n - fromIntegral (round n)) = show (round n)
 | otherwise = show n</lang>
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: <lang j>ensure2D=: ,:^:(1 = #@$) NB. if list make 1 row table normalise=: ([: /:~ /:~"1)@ensure2D NB. normalises list of ranges merge=: ,:`(<.&{. , >.&{:)@.(>:/&{: |.) NB. merge ranges x and y consolidate=: (}.@] ,~ (merge {.)) ensure2D</lang> Required Examples: <lang j> tests=: <@".;._2 noun define 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 )

  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| | +-------+-------+---+-----+-----+</lang>

Java

<lang java> import java.util.ArrayList; import java.util.Arrays; import java.util.Collections; import java.util.Comparator; import java.util.List;

public class RangeConsolidation {

   public static void main(String[] args) {
       displayRanges( Arrays.asList(new Range(1.1, 2.2)));
       displayRanges( Arrays.asList(new Range(6.1, 7.2), new Range(7.2, 8.3)));
       displayRanges( Arrays.asList(new Range(4, 3), new Range(2, 1)));
       displayRanges( Arrays.asList(new Range(4, 3), new Range(2, 1), new Range(-1, -2), new Range(3.9, 10)));
       displayRanges( Arrays.asList(new Range(1, 3), new Range(-6, -1), new Range(-4, -5), new Range(8, 2), new Range(-6, -6)));
       displayRanges( Arrays.asList(new Range(1, 1), new Range(1, 1)));
       displayRanges( Arrays.asList(new Range(1, 1), new Range(1, 2)));
       displayRanges( Arrays.asList(new Range(1, 2), new Range(3, 4), new Range(1.5, 3.5), new Range(1.2, 2.5)));
   }
   
   private static final void displayRanges(List<Range> ranges) {
       System.out.printf("ranges = %-70s, colsolidated = %s%n", ranges, Range.consolidate(ranges));
   }
   
   private static final class RangeSorter implements Comparator<Range> {
       @Override
       public int compare(Range o1, Range o2) {
           return (int) (o1.left - o2.left);
       }        
   }
   private static class Range {
       double left;
       double right;
       
       public Range(double left, double right) {
           if ( left <= right ) {
               this.left = left;
               this.right = right;
           }
           else {
               this.left = right;
               this.right = left;
           }
       }
       
       public Range consolidate(Range range) {
           //  no overlap
           if ( this.right < range.left ) {
               return null;
           }
           //  no overlap
           if ( range.right < this.left ) {
               return null;
           }
           //  contained
           if ( this.left <= range.left && this.right >= range.right ) {
               return this;
           }
           //  contained
           if ( range.left <= this.left && range.right >= this.right ) {
               return range;
           }
           //  overlap
           if ( this.left <= range.left && this.right <= range.right ) {
               return new Range(this.left, range.right);
           }
           //  overlap
           if ( this.left >= range.left && this.right >= range.right ) {
               return new Range(range.left, this.right);
           }
           throw new RuntimeException("ERROR:  Logic invalid.");
       }
       
       @Override
       public String toString() {
           return "[" + left + ", " + right + "]";
       }
       
       private static List<Range> consolidate(List<Range> ranges) {
           List<Range> consolidated = new ArrayList<>();
           
           Collections.sort(ranges, new RangeSorter());
           
           for ( Range inRange : ranges ) {
               Range r = null;
               Range conRange = null;
               for ( Range conRangeLoop : consolidated ) {
                   r = inRange.consolidate(conRangeLoop);
                   if (r != null ) {
                       conRange = conRangeLoop;
                       break;
                   }
               }
               if ( r == null ) {
                   consolidated.add(inRange);
               }
               else {
                   consolidated.remove(conRange);
                   consolidated.add(r);                    
               }
           }
           
           Collections.sort(consolidated, new RangeSorter());
           
           return consolidated;
       }
   }

} </lang>

Output:

Required and other examples.

ranges = [[1.1, 2.2]]                                                          , consolidated = [[1.1, 2.2]]
ranges = [[6.1, 7.2], [7.2, 8.3]]                                              , consolidated = [[6.1, 8.3]]
ranges = [[1.0, 2.0], [3.0, 4.0]]                                              , consolidated = [[1.0, 2.0], [3.0, 4.0]]
ranges = [[-2.0, -1.0], [1.0, 2.0], [3.0, 4.0], [3.9, 10.0]]                   , consolidated = [[-2.0, -1.0], [1.0, 2.0], [3.0, 10.0]]
ranges = [[-6.0, -1.0], [-6.0, -6.0], [-5.0, -4.0], [1.0, 3.0], [2.0, 8.0]]    , consolidated = [[-6.0, -1.0], [1.0, 8.0]]
ranges = [[1.0, 1.0], [1.0, 1.0]]                                              , consolidated = [[1.0, 1.0]]
ranges = [[1.0, 1.0], [1.0, 2.0]]                                              , consolidated = [[1.0, 2.0]]
ranges = [[1.0, 2.0], [1.5, 3.5], [1.2, 2.5], [3.0, 4.0]]                      , consolidated = [[1.0, 4.0]]

JavaScript

Translation of: Haskell
Translation of: Python

<lang javascript>(() => {

   '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();

})();</lang>

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

<lang julia>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()

</lang>
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]]

Kotlin

<lang Kotlin>fun <T> consolidate(ranges: Iterable<ClosedRange<T>>): List<ClosedRange<T>> where T : Comparable<T> {

   return ranges
       .sortedWith(compareBy({ it.start }, { it.endInclusive }))
       .asReversed()
       .fold(mutableListOf<ClosedRange<T>>()) {
           consolidatedRanges, range ->
           if (consolidatedRanges.isEmpty())
           {
               consolidatedRanges.add(range)
           }
           // Keep in mind the reverse-sorting applied above:
           // If the end of the current-range is higher, than it must start at a lower value,
           else if (range.endInclusive >= consolidatedRanges[0].endInclusive)
           {
               consolidatedRanges[0] = range
           }
           else if (range.endInclusive >= consolidatedRanges[0].start)
           {
               consolidatedRanges[0] = range.start .. consolidatedRanges[0].endInclusive
           }
           else
           {
               consolidatedRanges.add(0, range)
           }
           return@fold consolidatedRanges
       }
       .toList()

}

// What a bummer! Kotlin's range syntax (a..b) doesn't meet the task requirements when b < b, // and on the other hand, the syntax for constructing lists, arrays and pairs isn't close enough // to the range notation. Instead then, here's a *very* naive parser. Don't take it seriously. val rangeRegex = Regex("""\[(.+),(.+)\]""") fun parseDoubleRange(rangeStr: String): ClosedFloatingPointRange<Double> {

   val parts = rangeRegex
       .matchEntire(rangeStr)
       ?.groupValues
       ?.drop(1)
       ?.map { it.toDouble() }
       ?.sorted()
   if (parts == null) throw IllegalArgumentException("Unable to parse range $rangeStr")
   return parts[0] .. parts[1]

}

fun serializeRange(range: ClosedRange<*>) = "[${range.start}, ${range.endInclusive}]"

// See above. In practice you'd probably use consolidate directly fun consolidateDoubleRanges(rangeStrings: Iterable<String>): List<String> {

   return consolidate(rangeStrings.asSequence().map(::parseDoubleRange).toList()).map(::serializeRange)

}


fun main() {

   val inputRanges = listOf(
       listOf("[1.1, 2.2]"),
       listOf("[6.1, 7.2]", "[7.2, 8.3]"),
       listOf("[4, 3]", "[2, 1]"),
       listOf("[4, 3]", "[2, 1]", "[-1, -2]", "[3.9, 10]"),
       listOf("[1, 3]", "[-6, -1]", "[-4, -5]", "[8, 2]", "[-6, -6]")
   )
   inputRanges.associateBy(Any::toString, ::consolidateDoubleRanges).forEach({ println("${it.key} => ${it.value}") })

}</lang>

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]] => [[1.0, 2.0], [3.0, 4.0]]
[[4, 3], [2, 1], [-1, -2], [3.9, 10]] => [[-2.0, -1.0], [1.0, 2.0], [3.0, 10.0]]
[[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]] => [[-6.0, -1.0], [1.0, 8.0]]

Perl

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

<lang perl>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;

}</lang>

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

<lang 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(Template: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}})</lang>

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}}

Prolog

Works with: SWI Prolog

<lang prolog>consolidate_ranges(Ranges, Consolidated):-

   normalize(Ranges, Normalized),
   sort(Normalized, Sorted),
   merge(Sorted, Consolidated).

normalize([], []):-!. normalize([r(X, Y)|Ranges], [r(Min, Max)|Normalized]):-

   (X > Y -> Min = Y, Max = X; Min = X, Max = Y),
   normalize(Ranges, Normalized).

merge([], []):-!. merge([Range], [Range]):-!. merge([r(Min1, Max1), r(Min2, Max2)|Rest], Merged):-

   Min2 =< Max1,
   !,
   Max is max(Max1, Max2),
   merge([r(Min1, Max)|Rest], Merged).

merge([Range|Ranges], [Range|Merged]):-

   merge(Ranges, Merged).

write_range(r(Min, Max)):-

   writef('[%w, %w]', [Min, Max]).

write_ranges([]):-!. write_ranges([Range]):-

   !,
   write_range(Range).

write_ranges([Range|Ranges]):-

   write_range(Range),
   write(', '),
   write_ranges(Ranges).

test_case([r(1.1, 2.2)]). test_case([r(6.1, 7.2), r(7.2, 8.3)]). test_case([r(4, 3), r(2, 1)]). test_case([r(4, 3), r(2, 1), r(-1, -2), r(3.9, 10)]). test_case([r(1, 3), r(-6, -1), r(-4, -5), r(8, 2), r(-6, -6)]).

main:-

   forall(test_case(Ranges),
          (consolidate_ranges(Ranges, Consolidated),
           write_ranges(Ranges), write(' -> '),
           write_ranges(Consolidated), nl)).</lang>
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

<lang python>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]}")

</lang>

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:

Translation of: Haskell
Works with: Python version 3.7

<lang python>Range consolidation

from functools import reduce


  1. 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),
       []
   )


  1. TEST ----------------------------------------------------
  2. 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)]
       ])
   )


  1. GENERIC FUNCTIONS FOR DISPLAY ---------------------------


  1. compose (<<<) :: (b -> c) -> (a -> b) -> a -> c

def compose(g):

   Right to left function composition.
   return lambda f: lambda x: g(f(x))


  1. tabulated :: String -> (a -> String) ->
  2. (b -> String) ->
  3. (a -> b) -> [a] -> String

def 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
       )
   )


  1. MAIN ---

if __name__ == '__main__':

   main()</lang>
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)]

Racket

<lang racket>#lang racket

Racket's max and min allow inexact numbers to contaminate exact numbers
Use argmax and argmin instead, as they don't have this problem

(define (max . xs) (argmax identity xs)) (define (min . xs) (argmin identity xs))

a bag is a list of disjoint intervals

(define ((irrelevant? x y) item) (or (< (second item) x) (> (first item) y)))

(define (insert bag x y)

 (define-values (irrelevant relevant) (partition (irrelevant? x y) bag))
 (cons (list (apply min x (map first relevant))
             (apply max y (map second relevant))) irrelevant))

(define (solve xs)

 (sort (for/fold ([bag '()]) ([x (in-list xs)])
         (insert bag (apply min x) (apply max x))) < #:key first))

(define inputs '(([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 ([xs (in-list inputs)]) (printf "~a => ~a\n" xs (solve xs)))</lang>

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))

Raku

(formerly Perl 6)

Works with: Rakudo version 2020.08.1

In Raku, a Range is a first class object with its own specialized notation. Raku 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 Raku notation for Ranges.

<lang perl6># Union sub infix:<∪> (Range $a, Range $b) { Range.new($a.min,max($a.max,$b.max)) }

  1. Intersection

sub 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.raku;
   say reverse consolidate |@intervals.grep(*.elems)».sort.sort({ [.[0], .[*-1]] }).map: { Range.new(.[0], .[*-1]) }

}</lang>

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)

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:     /*■■■■►*/ <lang rexx>/*REXX program performs range consolidation (they can be [equal] ascending/descending). */

  1. .= /*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.*/
         y= strip(y, 'L', ",")                  /*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; @.j=@.k; @.k=_; _=@.j
           end   /*k*/
         end     /*j*/;        return</lang>
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: []

Rust

Most of the implementation below belongs to the test and formatting support. If the output might be more arbitrary, the source would be quite small. The algorithm relies on normalizing the ranges and folding a sorted sequence of them.

<lang Rust>use std::fmt::{Display, Formatter};

// We could use std::ops::RangeInclusive, but we would have to extend it to // normalize self (not much trouble) and it would not have to handle pretty // printing for it explicitly. So, let's make rather an own type.

  1. [derive(Clone, Debug, PartialEq, PartialOrd)]

pub struct ClosedRange<Idx> {

   start: Idx,
   end: Idx,

}

impl<Idx> ClosedRange<Idx> {

   pub fn start(&self) -> &Idx {
       &self.start
   }
   pub fn end(&self) -> &Idx {
       &self.end
   }

}

impl<Idx: PartialOrd> ClosedRange<Idx> {

   pub fn new(start: Idx, end: Idx) -> Self {
       if start <= end {
           Self { start, end }
       } else {
           Self {
               end: start,
               start: end,
           }
       }
   }

}

// To make test input more compact impl<Idx: PartialOrd> From<(Idx, Idx)> for ClosedRange<Idx> {

   fn from((start, end): (Idx, Idx)) -> Self {
       Self::new(start, end)
   }

}

// For the required print format impl<Idx: Display> Display for ClosedRange<Idx> {

   fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
       write!(f, "[{}, {}]", self.start, self.end)
   }

}

fn consolidate<Idx>(a: &ClosedRange<Idx>, b: &ClosedRange<Idx>) -> Option<ClosedRange<Idx>> where

   Idx: PartialOrd + Clone,

{

   if a.start() <= b.start() {
       if b.end() <= a.end() {
           Some(a.clone())
       } else if a.end() < b.start() {
           None
       } else {
           Some(ClosedRange::new(a.start().clone(), b.end().clone()))
       }
   } else {
       consolidate(b, a)
   }

}

fn consolidate_all<Idx>(mut ranges: Vec<ClosedRange<Idx>>) -> Vec<ClosedRange<Idx>> where

   Idx: PartialOrd + Clone,

{

   // Panics for incomparable elements! So no NaN for floats, for instance.
   ranges.sort_by(|a, b| a.partial_cmp(b).unwrap());
   let mut ranges = ranges.into_iter();
   let mut result = Vec::new();
   if let Some(current) = ranges.next() {
       let leftover = ranges.fold(current, |mut acc, next| {
           match consolidate(&acc, &next) {
               Some(merger) => {
                   acc = merger;
               }
               None => {
                   result.push(acc);
                   acc = next;
               }
           }
           acc
       });
       result.push(leftover);
   }
   result

}

  1. [cfg(test)]

mod tests {

   use super::{consolidate_all, ClosedRange};
   use std::fmt::{Display, Formatter};
   struct IteratorToDisplay<F>(F);
   impl<F, I> Display for IteratorToDisplay<F>
   where
       F: Fn() -> I,
       I: Iterator,
       I::Item: Display,
   {
       fn fmt(&self, f: &mut Formatter<'_>) -> std::fmt::Result {
           let mut items = self.0();
           if let Some(item) = items.next() {
               write!(f, "{}", item)?;
               for item in items {
                   write!(f, ", {}", item)?;
               }
           }
           Ok(())
       }
   }
   macro_rules! parameterized {
       ($($name:ident: $value:expr,)*) => {
           $(
               #[test]
               fn $name() {
                   let (input, expected) = $value;
                   let expected: Vec<_> = expected.into_iter().map(ClosedRange::from).collect();
                   let output = consolidate_all(input.into_iter().map(ClosedRange::from).collect());
                   println!("{}: {}", stringify!($name), IteratorToDisplay(|| output.iter()));
                   assert_eq!(expected, output);
               }
           )*
       }
   }
   parameterized! {
       single: (vec![(1.1, 2.2)], vec![(1.1, 2.2)]),
       touching: (vec![(6.1, 7.2), (7.2, 8.3)], vec![(6.1, 8.3)]),
       disjoint: (vec![(4, 3), (2, 1)], vec![(1, 2), (3, 4)]),
       overlap: (vec![(4.0, 3.0), (2.0, 1.0), (-1.0, -2.0), (3.9, 10.0)], vec![(-2.0, -1.0), (1.0, 2.0), (3.0, 10.0)]),
       integer: (vec![(1, 3), (-6, -1), (-4, -5), (8, 2), (-6, -6)], vec![(-6, -1), (1, 8)]),
   }

}

fn main() {

   // To prevent dead code and to check empty input
   consolidate_all(Vec::<ClosedRange<usize>>::new());
   println!("Run: cargo test -- --nocapture");

}</lang>

Output:
running 5 tests
integer: [-6, -1], [1, 8]
disjoint: [1, 2], [3, 4]
single: [1.1, 2.2]
touching: [6.1, 8.3]
overlap: [-2, -1], [1, 2], [3, 10]
test tests::integer ... ok
test tests::disjoint ... ok
test tests::single ... ok
test tests::touching ... ok
test tests::overlap ... ok

test result: ok. 5 passed; 0 failed; 0 ignored; 0 measured; 0 filtered out

Wren

Library: Wren-math

As Wren already has a built-in Range class (which is not quite the same as what's required here), we create a Span class instead. <lang ecmascript>import "/math" for Math

class Span {

   construct new(r) {
       if (r.type != Range || !r.isInclusive) Fiber.abort("Argument must be an inclusive range.")
       _low = r.from
       _high = r.to
       if (_low > _high) {
           _low = r.to
           _high = r.from
       }
   }
   low  { _low }
   high { _high }
   consolidate(r) {
        if (r.type != Span) Fiber.abort("Argument must be a Span.")
        if (_high < r.low) return [this, r]
        if (r.high < _low) return [r, this]
        return [Span.new(Math.min(_low, r.low)..Math.max(_high, r.high))]
   }
   toString { "[%(_low), %(_high)]" }

}

var spanLists = [

   [Span.new(1.1..2.2)],
   [Span.new(6.1..7.2), Span.new(7.2..8.3)],
   [Span.new(4..3), Span.new(2..1)],
   [Span.new(4..3), Span.new(2..1), Span.new(-1..-2), Span.new(3.9..10)],
   [Span.new(1..3), Span.new(-6..-1), Span.new(-4..-5), Span.new(8..2), Span.new(-6..-6)]

]

for (spanList in spanLists) {

   if (spanList.count == 1) {
       System.print(spanList.toString[1..-2])
   } else if (spanList.count == 2) {
       System.print(spanList[0].consolidate(spanList[1]).toString[1..-2])
   } else {
       var first = 0
       while (first < spanList.count-1) {
           var next = first + 1
           while (next < spanList.count) {
               var res = spanList[first].consolidate(spanList[next])
               spanList[first] = res[0]
               if (res.count == 2) {
                   spanList[next] = res[1]
                   next = next + 1
               } else {
                   spanList.removeAt(next)
               }
           }
           first = first + 1
       }
       System.print(spanList.toString[1..-2])
   } 

}</lang>

Output:
[1.1, 2.2]
[6.1, 8.3]
[1, 2], [3, 4]
[-2, -1], [1, 2], [3, 10]
[-6, -1], [1, 8]

Yabasic

<lang 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
   next

end 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 = 10^30 read 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</lang>

zkl

<lang 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] }) }</lang> <lang zkl>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(", ", "[", "] ") }) }</lang>

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]