Range consolidation
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:
![Task](http://static.miraheze.org/rosettacodewiki/thumb/b/ba/Rcode-button-task-crushed.png/64px-Rcode-button-task-crushed.png)
You are encouraged to solve this task according to the task description, using any language you may know.
[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
<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)
AutoHotkey
<lang AutoHotkey>RangeConsolidation(arr){ arr1 := [], arr2 := [], result := []
for i, obj in arr arr1[i,1] := min(arr[i]*), arr1[i,2] := max(arr[i]*) ; sort each range individually
for i, obj in arr1 if (obj.2 > arr2[obj.1]) arr2[obj.1] := obj.2 ; creates helper array sorted by range
i := 1 for start, stop in arr2 if (i = 1) || (start > result[i-1, 2]) ; first or non overlapping range result[i, 1] := start, result[i, 2] := stop, i++ else ; overlapping range result[i-1, 2] := stop > result[i-1, 2] ? stop : result[i-1, 2] return result }</lang> Examples:<lang AutoHotkey>test1 := 1.1, 2.2 test2 := [[6.1, 7.2], [7.2, 8.3]] test3 := [[4, 3], [2, 1]] test4 := [[4, 3], [2, 1], [-1, -2], [3.9, 10]] test5 := [[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]]
result := "" loop, 5 { output := "" for i, obj in RangeConsolidation(test%A_Index%) output .= "[" format("{:g}", obj.1) ", " format("{:g}", obj.2) "], " result .= Trim(output, ", ") "`n" } MsgBox % result return</lang>
- Output:
[1.1, 2.2] [6.1, 8.3] [1, 2], [3, 4] [-2, -1], [1, 2], [3, 10] [-6, -1], [1, 8]
C
<lang c>#include <stdio.h>
- 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");
}
- 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#
<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>
- include <iostream>
- include <utility>
- 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
<lang dyalect>type Pt(s, e)
func Pt.min() => min(this::s, this::e) func Pt.max() => max(this::s, this::e) func Pt.toString() => "(\(this::s), \(this::e))"
let rng = [
[ Pt(1.1, 2.2) ], [ Pt(6.1, 7.2), Pt(7.2, 8.3) ], [ Pt(4.0, 3.0), Pt(2, 1) ], [ Pt(4.0, 3.0), Pt(2, 1), Pt(-1, 2), Pt(3.9, 10) ], [ Pt(1.0, 3.0), Pt(-6, -1), Pt(-4, -5), Pt(8, 2), Pt(-6, -6) ]
]
func overlap(left, right) =>
right.max() >= left.min() when left.max() > right.max() else left.max() >= right.min()
func consolidate(left, right) => Pt(min(left.min(), right.min()), max(left.max(), right.max()))
func normalize(range) => Pt(range.min(), range.max())
for list in rng {
var z = list.len() - 1 while z >= 1 { for y in (z - 1)^-1..0 when overlap(list[z], list[y]) { list[y] = consolidate(list[z], list[y]) break list.removeAt(z) } z -= 1 } for i in list.indices() { list[i] = normalize(list[i]) } list.sort((x,y) => x::s - y::s) print(list)
}</lang>
- Output:
[(1.1, 2.2)] [(6.1, 8.3)] [(1, 2), (3, 4)] [(-1, 2), (3, 10)] [(-6, -1), (1, 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
<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.
<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} => ${it.value}") })
}</lang>
- Output:
[[1.1, 2.2]] => [[1.1, 2.2]] [[6.1, 7.2], [7.2, 8.3]] => [[6.1, 8.3]] [[4, 3], [2, 1]] => [[1.0, 2.0], [3.0, 4.0]] [[4, 3], [2, 1], [-1, -2], [3.9, 10]] => [[-2.0, -1.0], [1.0, 2.0], [3.0, 10.0]] [[1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6]] => [[-6.0, -1.0], [1.0, 8.0]]
Nim
<lang Nim>import algorithm, strutils
- Definition of a range of values of type T.
type Range[T] = array[2, T]
proc `<`(a, b: Range): bool {.inline.} =
## Check if range "a" is less than range "b". Needed for sorting. if a[0] == b[0]: a[1] < b[1] else: a[0] < b[0]
proc consolidate[T](rangeList: varargs[Range[T]]): seq[Range[T]] =
## Consolidate a list of ranges of type T.
# Build a sorted list of normalized ranges. var list: seq[Range[T]] for item in rangeList: list.add if item[0] <= item[1]: item else: [item[1], item[0]] list.sort()
# Build the consolidated list starting from "smallest" range. result.add list[0] for i in 1..list.high: let rangeMin = result[^1] let rangeMax = list[i] if rangeMax[0] <= rangeMin[1]: result[^1] = [rangeMin[0], max(rangeMin[1], rangeMax[1])] else: result.add rangeMax
proc `$`[T](r: Range[T]): string {.inline.} =
# Return the string representation of a range. when T is SomeFloat: "[$1, $2]".format(r[0].formatFloat(ffDecimal, 1), r[1].formatFloat(ffDecimal, 1)) else: "[$1, $2]".format(r[0], r[1])
proc `$`[T](s: seq[Range[T]]): string {.inline.} =
## Return the string representation of a sequence of ranges. s.join(", ")
when isMainModule:
proc test[T](rangeList: varargs[Range[T]]) = echo ($(@rangeList)).alignLeft(52), "→ ", consolidate(rangeList)
test([1.1, 2.2]) test([6.1, 7.2], [7.2, 8.3]) test([4, 3], [2, 1]) test([4.0, 3.0], [2.0, 1.0], [-1.0, -2.0], [3.9, 10.0]) test([1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6])</lang>
- Output:
[1.1, 2.2] → [1.1, 2.2] [6.1, 7.2], [7.2, 8.3] → [6.1, 8.3] [4, 3], [2, 1] → [1, 2], [3, 4] [4.0, 3.0], [2.0, 1.0], [-1.0, -2.0], [3.9, 10.0] → [-2.0, -1.0], [1.0, 2.0], [3.0, 10.0] [1, 3], [-6, -1], [-4, -5], [8, 2], [-6, -6] → [-6, -1], [1, 8]
Perl
Note: the output is shown in the standard Perl notation for Ranges.
<lang perl>use strict; use warnings;
use List::Util qw(min max);
sub consolidate {
our @arr; local *arr = shift; my @sorted = sort { @$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
<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:
<lang python>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 -> c
def compose(g):
Right to left function composition. return lambda f: lambda x: g(f(x))
- tabulated :: String -> (a -> String) ->
- (b -> String) ->
- (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 ) )
- 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)
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)) }
- 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). */
- .= /*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.
- [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
}
- [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
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]