Order two numerical lists
You are encouraged to solve this task according to the task description, using any language you may know.
Write a function that orders two lists or arrays filled with numbers.
The function should accept two lists as arguments and return true if the first list should be ordered before the second, and false otherwise.
The order is determined by lexicographic order: Comparing the first element of each list.
If the first elements are equal, then the second elements should be compared, and so on, until one of the list has no more elements.
If the first list runs out of elements the result is true.
If the second list or both run out of elements the result is false.
Note: further clarification of lexicographical ordering is expounded on the talk page here and here.
ACL2
The built-in lexorder does this.
ACL2 !>(lexorder '(1 2 3) '(1 2 3 4)) T ACL2 !>(lexorder '(1 2 4) '(1 2 3)) NIL
Ada
This is already implemented in the built-in comparison operators for arrays of types that have a direct ordering. This also includes arrays of user defined types, using the type definition order from smallest to largest. Demonstrated in the program below: <lang Ada> with Ada.Text_IO; use Ada.Text_IO; procedure Order is
type IntArray is array (Positive range <>) of Integer; List1 : IntArray := (1, 2, 3, 4, 5); List2 : IntArray := (1, 2, 1, 5, 2, 2); List3 : IntArray := (1, 2, 1, 5, 2); List4 : IntArray := (1, 2, 1, 5, 2);
type Animal is (Rat, Cat, Elephant); type AnimalArray is array (Positive range <>) of Animal; List5 : AnimalArray := (Cat, Elephant, Rat, Cat); List6 : AnimalArray := (Cat, Elephant, Rat); List7 : AnimalArray := (Cat, Cat, Elephant);
begin
Put_Line (Boolean'Image (List1 > List2)); -- True Put_Line (Boolean'Image (List2 > List3)); -- True Put_Line (Boolean'Image (List3 > List4)); -- False, equal Put_Line (Boolean'Image (List5 > List6)); -- True Put_Line (Boolean'Image (List6 > List7)); -- True
end Order; </lang>
- Output:
TRUE TRUE FALSE TRUE TRUE
AppleScript
<= is not defined over lists in AppleScript
<lang AppleScript>-- <= for lists
-- compare :: [a] -> [a] -> Bool
on compare(xs, ys)
if length of xs = 0 then
true
else
if length of ys = 0 then
false
else
set {hx, txs} to uncons(xs)
set {hy, tys} to uncons(ys)
if hx < hy then
true
else if hx > hy then
false
else
compare(txs, tys)
end if
end if
end if
end compare
-- TEST on run
{compare([1, 2, 1, 3, 2], [1, 2, 0, 4, 4, 0, 0, 0]), ¬
compare([1, 2, 0, 4, 4, 0, 0, 0], [1, 2, 1, 3, 2])}
end run
-- GENERIC FUNCTION
-- uncons :: [a] -> Maybe (a, [a]) on uncons(xs)
if length of xs > 0 then
{item 1 of xs, rest of xs}
else
missing value
end if
end uncons</lang>
- Output:
<lang AppleScript>{false, true}</lang>
AutoHotkey
The function is overkill as we can just compare the list's ObjMaxIndex() <lang AHK>List1 := [1,2,1,3,2] List2 := [1,2,0,4,4,0,0,0] MsgBox % order(List1, List2)
order(L1, L2){ return L1.MaxIndex() < L2.MaxIndex() }</lang>
AWK
<lang AWK>
- syntax: GAWK -f ORDER_TWO_NUMERICAL_LISTS.AWK
BEGIN {
split("1,2,1,5,2",list1,",")
split("1,2,1,5,2,2",list2,",")
split("1,2,3,4,5",list3,",")
split("1,2,3,4,5",list4,",")
x = compare_array(list1,list2) ? "<" : ">=" ; printf("list1%slist2\n",x)
x = compare_array(list2,list3) ? "<" : ">=" ; printf("list2%slist3\n",x)
x = compare_array(list3,list4) ? "<" : ">=" ; printf("list3%slist4\n",x)
exit(0)
} function compare_array(arr1,arr2, ans,i) {
ans = 0
for (i=1; i<=length(arr1); i++) {
if (arr1[i] != arr2[i]) {
ans = 1
break
}
}
if (length(arr1) != length(arr2)) {
ans = 1
}
return(ans)
} </lang>
- Output:
list1<list2 list2<list3 list3>=list4
BBC BASIC
'Ordered before' means 'less than' (see talk page). <lang bbcbasic> DIM list1(4) : list1() = 1, 2, 1, 5, 2
DIM list2(5) : list2() = 1, 2, 1, 5, 2, 2
DIM list3(4) : list3() = 1, 2, 3, 4, 5
DIM list4(4) : list4() = 1, 2, 3, 4, 5
IF FNorder(list1(), list2()) PRINT "list1<list2" ELSE PRINT "list1>=list2"
IF FNorder(list2(), list3()) PRINT "list2<list3" ELSE PRINT "list2>=list3"
IF FNorder(list3(), list4()) PRINT "list3<list4" ELSE PRINT "list3>=list4"
END
DEF FNorder(list1(), list2())
LOCAL i%, l1%, l2%
l1% = DIM(list1(),1) : l2% = DIM(list2(),1)
WHILE list1(i%) = list2(i%) AND i% < l1% AND i% < l2%
i% += 1
ENDWHILE
IF list1(i%) < list2(i%) THEN = TRUE
IF list1(i%) > list2(i%) THEN = FALSE
= l1% < l2%</lang>
- Output:
list1<list2 list2<list3 list3>=list4
Bracmat
When evaluating a sum or a product, Bracmat creates an expression with a canonical order, which happens to be compatible with the order defined in this task.
In a pattern, only a sum or product on the left hand side (lhs) of the match (:) operator is evaluated.
In the solution below we match a composition of the two function arguments into a sum of two terms with itself.
If the match expression succeeds, the lhs must already have been in canonical order before evaluation, which means that the first argument is smaller than the second argument.
In that case the function outputs FALSE.
Notice that if the arguments are the same, evaluation of the sum produces the product of one of the terms and a factor two. This complicates the pattern a bit.
<lang bracmat>( 1 2 3 4 5:?List1
& 1 2 1 5 2 2:?List2
& 1 2 1 5 2:?List3
& 1 2 1 5 2:?List4
& Cat Elephant Rat Cat:?List5
& Cat Elephant Rat:?List6
& Cat Cat Elephant:?List7
& ( gt
= first second
. !arg:(?first,?second)
& out
$ ( (.!first)+(.!second)
: ((.!first)+(.!second)|2*(.!first))
& FALSE
| TRUE
)
)
& gt$(!List1,!List2) & gt$(!List2,!List3) & gt$(!List3,!List4) & gt$(!List4,!List5) & gt$(!List5,!List6) & gt$(!List6,!List7) );</lang>
- Output:
TRUE TRUE FALSE FALSE TRUE TRUE
C
<lang c>int list_cmp(int *a, int la, int *b, int lb)
{
int i, l = la;
if (l > lb) l = lb;
for (i = 0; i < l; i++) {
if (a[i] == b[i]) continue;
return (a[i] > b[i]) ? 1 : -1;
}
if (la == lb) return 0;
return la > lb ? 1 : -1;
}</lang>
This funciton returns one of three states, not a boolean. One can define boolean comparisons, such as list_less_or_eq, based on it:<lang c>#define list_less_or_eq(a,b,c,d) (list_cmp(a,b,c,d) != 1)</lang>
C#
<lang csharp>namespace RosettaCode.OrderTwoNumericalLists {
using System; using System.Collections.Generic;
internal static class Program
{
private static bool IsLessThan(this IEnumerable<int> enumerable,
IEnumerable<int> otherEnumerable)
{
using (
IEnumerator<int> enumerator = enumerable.GetEnumerator(),
otherEnumerator = otherEnumerable.GetEnumerator())
{
while (true)
{
if (!otherEnumerator.MoveNext())
{
return false;
}
if (!enumerator.MoveNext())
{
return true;
}
if (enumerator.Current == otherEnumerator.Current)
{
continue;
}
return enumerator.Current < otherEnumerator.Current;
}
}
}
private static void Main()
{
Console.WriteLine(
new[] {1, 2, 1, 3, 2}.IsLessThan(new[] {1, 2, 0, 4, 4, 0, 0, 0}));
}
}
}</lang>
- Output:
False
C++
The built-in comparison operators already do this: <lang cpp>#include <iostream>
- include <vector>
int main() {
std::vector<int> a; a.push_back(1); a.push_back(2); a.push_back(1); a.push_back(3); a.push_back(2); std::vector<int> b; b.push_back(1); b.push_back(2); b.push_back(0); b.push_back(4); b.push_back(4); b.push_back(0); b.push_back(0); b.push_back(0);
std::cout << std::boolalpha << (a < b) << std::endl; // prints "false" return 0;
}</lang>
clojure
<lang clojure> (defn lex? [a b]
(compare a b))
</lang>
Common Lisp
<lang Lisp>(defun list< (a b)
(cond ((not b) nil)
((not a) t)
((= (first a) (first b))
(list< (rest a) (rest b)))
(t (< (first a) (first b)))))</lang>
Alternate version
<lang Lisp>(defun list< (a b)
(let ((x (find-if-not #'zerop (mapcar #'- a b)))) (if x (minusp x) (< (length a) (length b)))))</lang>
D
The built-in comparison operators already do this: <lang d>void main() {
assert([1,2,1,3,2] >= [1,2,0,4,4,0,0,0]);
}</lang>
Ela
<lang ela>[] <. _ = true _ <. [] = false (x::xs) <. (y::ys) | x == y = xs <. ys
| else = x < y
[1,2,1,3,2] <. [1,2,0,4,4,0,0,0]</lang>
Elixir
The built-in comparison functions already do this (not only for lists of numbers, but for any arbitrary data type). <lang elixir>iex(1)> [1,2,3] < [1,2,3,4] true iex(2)> [1,2,3] < [1,2,4] true</lang>
Erlang
Builtin. Example use from Erlang shell: <lang Erlang> 5> [1,2,3] < [1,2,3,4]. true 6> [1,2,3] < [1,2,4]. true </lang>
F#
By using the Collection.Seq Module the static method Seq.compareWith fits our needs. <lang fsharp>let inline cmp x y = if x < y then -1 else if x = y then 0 else 1 let before (s1 : seq<'a>) (s2 : seq<'a>) = (Seq.compareWith cmp s1 s2) < 0
[
([0], []); ([], []); ([], [0]); ([-1], [0]); ([0], [0]); ([0], [-1]); ([0], [0; -1]); ([0], [0; 0]); ([0], [0; 1]); ([0; -1], [0]); ([0; 0], [0]); ([0; 0], [1]);
] |> List.iter (fun (x, y) -> printf "%A %s %A\n" x (if before x y then "< " else ">=") y)</lang>
- Output:
[0] >= [] [] >= [] [] < [0] [-1] < [0] [0] >= [0] [0] >= [-1] [0] < [0; -1] [0] < [0; 0] [0] < [0; 1] [0; -1] >= [0] [0; 0] >= [0] [0; 0] < [1]
Factor
All sequences respond to words in the math.order vocabulary.
IN: scratchpad { 2 3 } { 2 5 } before? .
t
Go
<lang go>package main
import "fmt"
// If your numbers happen to be in the range of Unicode code points (0 to 0x10ffff), this function // satisfies the task: func lessRune(a, b []rune) bool {
return string(a) < string(b) // see also bytes.Compare
}
// Otherwise, the following function satisfies the task for all integer // and floating point types, by changing the type definition appropriately. type numericType int
func lessNT(a, b []numericType) bool {
l := len(a)
if len(b) < l {
l = len(b)
}
for i := 0; i < l; i++ {
if a[i] != b[i] {
return a[i] < b[i]
}
}
return l < len(b)
}
var testCases = [][][]numericType{
{{0}, {}},
{{}, {}},
{{}, {0}},
{{-1}, {0}},
{{0}, {0}},
{{0}, {-1}},
{{0}, {0, -1}},
{{0}, {0, 0}},
{{0}, {0, 1}},
{{0, -1}, {0}},
{{0, 0}, {0}},
{{0, 0}, {1}},
}
func main() {
// demonstrate the general function
for _, tc := range testCases {
fmt.Printf("order %6s before %6s : %t\n",
fmt.Sprintf("%v", tc[0]),
fmt.Sprintf("%v", tc[1]),
lessNT(tc[0], tc[1]))
}
fmt.Println()
// demonstrate that the byte specific function gives identical results
// by offsetting test data to a printable range of characters.
for _, tc := range testCases {
a := toByte(tc[0])
b := toByte(tc[1])
fmt.Printf("order %6q before %6q : %t\n",
string(a),
string(b),
lessByte(a, b))
}
}
func toByte(a []numericType) []byte {
b := make([]byte, len(a))
for i, n := range a {
b[i] = 'b' + byte(n)
}
return b
}</lang>
- Output:
order [0] before [] : false order [] before [] : false order [] before [0] : true order [-1] before [0] : true order [0] before [0] : false order [0] before [-1] : false order [0] before [0 -1] : true order [0] before [0 0] : true order [0] before [0 1] : true order [0 -1] before [0] : false order [0 0] before [0] : false order [0 0] before [1] : true order "b" before "" : false order "" before "" : false order "" before "b" : true order "a" before "b" : true order "b" before "b" : false order "b" before "a" : false order "b" before "ba" : true order "b" before "bb" : true order "b" before "bc" : true order "ba" before "b" : false order "bb" before "b" : false order "bb" before "c" : true
Groovy
Solution: <lang groovy>class CList extends ArrayList implements Comparable {
CList() { }
CList(Collection c) { super(c) }
int compareTo(Object that) {
assert that instanceof List
def n = [this.size(), that.size()].min()
def comp = [this[0..<n], that[0..<n]].transpose().find { it[0] != it[1] }
comp ? comp[0] <=> comp[1] : this.size() <=> that.size()
}
}</lang>
Test: <lang groovy>CList a, b; (a, b) = [[], []]; assert ! (a < b) b = [1] as CList; assert (a < b) a = [1] as CList; assert ! (a < b) b = [2] as CList; assert (a < b) a = [2, -1, 0] as CList; assert ! (a < b) b = [2, -1] as CList; assert ! (a < b) b = [2, -1, 0] as CList; assert ! (a < b) b = [2, -1, 0, -17] as CList; assert (a < b) a = [2, 8, 0] as CList; assert ! (a < b)</lang>
Haskell
The built-in comparison operators already do this: <lang haskell>Prelude> [1,2,1,3,2] < [1,2,0,4,4,0,0,0] False</lang>
Icon and Unicon
List_llt is written in the style of all Icon/Unicon relational operators returning its right argument if successful and signaling failure otherwise.
<lang Icon>procedure main()
write( if list_llt([1,2,1,3,2],[1,2,0,4,4,0,0,0]) then "true" else "false" )
end
procedure list_llt(L1,L2) #: returns L2 if L1 lexically lt L2 or fails
every i := 1 to min(*L1,*L2) do
if L1[i] << L2[i] then return L2 else if L1[i] >> L2[i] then fail
if *L1 < *L2 then return L2 end</lang>
J
This is not a built-in in J.
<lang j>before=: -.@(-: /:~)@,&<~</lang>
Example use:
<lang j> (,0) before 0
before
0
before ,0
1
(,_1) before ,0
1
(,0) before ,0
0
(,0) before ,_1
0
(,0) before 0 _1
1
(,0) before 0 0
1
(,0) before 0 1
1
0 _1 before ,0
0
0 0 before ,0
0
0 0 before ,1
1
(,'b') before
0
before
0
before ,'b'
1
(,'a') before ,'b'
1
(,'b') before ,'b'
0
(,'b') before ,'a'
0
(,'b') before 'ba'
1
(,'b') before 'bb'
1
(,'b') before 'bc'
1
'ba' before ,'b'
0
'bb' before ,'b'
0
'bb' before ,'c'
1</lang>
Java
There are a few methods here. The method named "ordered" which works on arrays is a translation of Common Lisp. The other two are loose translations of Tcl (some tweaks were needed to get the length checks to work out) and are probably better options. <lang java5>import java.util.Arrays; import java.util.List;
public class ListOrder{ public static boolean ordered(double[] first, double[] second){ if(first.length == 0) return true; if(second.length == 0) return false; if(first[0] == second[0]) return ordered(Arrays.copyOfRange(first, 1, first.length), Arrays.copyOfRange(second, 1, second.length)); return first[0] < second[0]; }
public static <T extends Comparable<? super T>> boolean ordered(List<T> first, List<T> second){ int i = 0; for(; i < first.size() && i < second.size();i++){ int cmp = first.get(i).compareTo(second.get(i)); if(cmp == 0) continue; if(cmp < 0) return true; return false; } return i == first.size(); }
public static boolean ordered2(double[] first, double[] second){ int i = 0; for(; i < first.length && i < second.length;i++){ if(first[i] == second[i]) continue; if(first[i] < second[i]) return true; return false; } return i == first.length; } }</lang>
JavaScript
ES6
<= is already defined for numeric lists in JavaScript
<lang JavaScript>(() => {
'use strict';
// <= is already defined for lists in JS
// compare :: [a] -> [a] -> Bool const compare = (xs, ys) => xs <= ys;
// TEST
return [
compare([1, 2, 1, 3, 2], [1, 2, 0, 4, 4, 0, 0, 0]),
compare([1, 2, 0, 4, 4, 0, 0, 0], [1, 2, 1, 3, 2])
];
// --> [false, true]
})() </lang>
- Output:
<lang JavaScript>[false, true]</lang>
Joy
<lang Joy> DEFINE order == [equal] [false] [[[[size] dip size <=] [[<=] mapr2 true [and] fold]] [i] map i and] ifte. </lang>
Using it:
[1 2] [1 2 3] order. # true [1 2] [1 3] order. # true [1 2] [1 2] order. # false [1 3] [1 2] order. # false [1 2 3] [1 2] order. # false
jq
jq's builtin comparison operators use lexicographic ordering for arrays in general, not just arrays of integers.<lang jq> [1,2,3] < [1,2,3,4] # => true [1,2,3] < [1,2,4] # => true [1,2,3] < [1,2,3] # => false</lang>
Julia
islexfirst is a somewhat permissive function in that it will accept many sorts of lists for comparison. It does check that all of the elements of both input lists are of some real number type, and if not will throw a DomainError.
Functions <lang Julia> function isallreal{T<:AbstractArray}(a::T)
all(map(x->isa(x, Real), a))
end
function islexfirst{T<:AbstractArray,U<:AbstractArray}(a::T, b::U)
isallreal(a) && isallreal(b) || throw(DomainError())
for i in 1:min(length(a), length(b))
x = a[i]
y = b[i]
x != y || continue
return x < y
end
return length(a) < length(b)
end </lang>
Main <lang Julia> tests = {[1, 2, 3],
primes(10),
0:2:6,
[-Inf, 0.0, Inf],
[π, e, φ, catalan],
[2015, 5],
[-sqrt(50.0), 50.0^2],
}
println("Testing islexfirst:") for (a, b) in combinations(tests, 2)
tres = islexfirst(a, b) ? " is " : " is not "
tres *= "lexically prior to\n "
println("\n ", a, tres, b)
end </lang>
- Output:
Testing islexfirst:
[1,2,3] is lexically prior to
[2,3,5,7]
[1,2,3] is not lexically prior to
0:2:6
[1,2,3] is not lexically prior to
[-Inf,0.0,Inf]
[1,2,3] is lexically prior to
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219]
[1,2,3] is lexically prior to
[2015,5]
[1,2,3] is not lexically prior to
[-7.0710678118654755,2500.0]
[2,3,5,7] is not lexically prior to
0:2:6
[2,3,5,7] is not lexically prior to
[-Inf,0.0,Inf]
[2,3,5,7] is lexically prior to
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219]
[2,3,5,7] is lexically prior to
[2015,5]
[2,3,5,7] is not lexically prior to
[-7.0710678118654755,2500.0]
0:2:6 is not lexically prior to
[-Inf,0.0,Inf]
0:2:6 is lexically prior to
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219]
0:2:6 is lexically prior to
[2015,5]
0:2:6 is not lexically prior to
[-7.0710678118654755,2500.0]
[-Inf,0.0,Inf] is lexically prior to
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219]
[-Inf,0.0,Inf] is lexically prior to
[2015,5]
[-Inf,0.0,Inf] is lexically prior to
[-7.0710678118654755,2500.0]
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219] is lexically prior to
[2015,5]
[3.141592653589793,2.718281828459045,1.618033988749895,0.915965594177219] is not lexically prior to
[-7.0710678118654755,2500.0]
[2015,5] is not lexically prior to
[-7.0710678118654755,2500.0]
LabVIEW
This image is a VI Snippet, an executable image of LabVIEW code. The LabVIEW version is shown on the top-right hand corner. You can download it, then drag-and-drop it onto the LabVIEW block diagram from a file browser, and it will appear as runnable, editable code.
Lasso
This is built into the Lasso comparison operators <lang Lasso>local( first = array(1,2,1,3,2), second = array(1,2,0,4,4,0,0,0), )
- first < #second
local( first = array(1,1,1,3,2), second = array(1,2,0,4,4,0,0,0), )
- first < #second</lang>
- Output:
false true
Lhogho
Uses standard '=' notation
<lang logo>print [1 2] = [1 2] print [1 2] = [1 2 3] print [1 3] = [1 2] print [1 2 3] = [1 2]
make "list1 [1 2 3 4 5 6] make "list2 [1 2 3 4 5 7] print :list1 = :list2</lang>
- Output:
<lang logo>true false false false false</lang>
Lua
In Lua tables with numerical indices are used as lists or arrays and they do not support comparison out-of-the-box, so a function is needed to implement the comparison:
<lang lua>function arraycompare(a, b)
for i = 1, #a do
if b[i] == nil then
return true
end
if a[i] ~= b[i] then
return a[i] < b[1]
end
end
return true
end</lang>
Here is some demonstration code:
<lang lua>function randomarray()
local t = {}
for i = 1, math.random(1, 10) do
t[i] = math.random(1, 10)
end
return t
end
math.randomseed(os.time())
for i = 1, 10 do
local a = randomarray() local b = randomarray()
print(
string.format("{%s} %s {%s}",
table.concat(a, ', '),
arraycompare(a, b) and "<=" or ">",
table.concat(b, ', ')))
end</lang>
- Output:
(time used as random seed
{10, 7, 4, 9, 10, 3, 5, 5, 5, 5} > {7, 4, 6, 4, 3, 5, 10}
{5, 7} <= {6, 3, 7, 7, 7, 1}
{4} <= {10, 10, 3, 8, 10, 5, 2, 5, 10, 6}
{6} <= {6, 10, 2, 1, 9, 4, 5, 6, 9}
{9, 5, 7, 5, 5, 7, 9, 5, 6, 8} > {4, 7, 3, 5, 1, 2, 1, 2}
{10, 8, 6, 1, 8, 5, 4} > {1, 2}
{9, 7} > {4, 1, 5, 2, 6, 1, 9, 3, 5}
{5, 9, 7, 6, 10, 8} <= {9, 6, 9}
{4, 3, 4, 6, 3, 6, 7, 2, 2, 5} > {3, 10, 6, 8, 1}
{1, 5, 1, 5, 4} > {1, 3, 5, 3, 2, 10, 1}
Mathematica
<lang Mathematica> order[List1_, List2_] := With[{
L1 = List1[[1 ;; Min @@ Length /@ {List1, List2}]],
L2 = List2[[1 ;; Min @@ Length /@ {List1, List2}]]
},
If [Thread[Order[L1, L2]] == 0, Length[List1] < Length[List2], Thread[Order[L1, L2]] == 1 ]]</lang>
Example use:
order[ {1, 2, 1, 3, 2}, {1, 2, 0, 4, 4, 0, 0, 0} ]
->False
order[ {1, 2}, {1, 2, 4, 4, 0, 0} ]
->True
Maxima
<lang maxima>"<<"(a,b):=block([n:min(length(a),length(b))], catch(for i thru n do (if a[i]#b[i] then throw(is(a[i]<b[i]))), throw(is(length(a)<length(b)))))$ infix("<<")$
[1,2,3] << [1,2,4]; true
[1,2,3] << [1,2]; false
[1,2] << [1,2]; false</lang>
Mercury
For a particular numerical type, you can get away with
<lang Mercury>:- pred lt(list(int)::in, list(int)::in) is semidet. lt([], [_|_]). lt([H1|T1], [H2|T2]) :- H1 =< H2, T1 `lt` T2.</lang>
For a list of any numerical type, one way would be to use a typeclass:
<lang Mercury>:- pred lt(list(T)::in, list(T)::in) is semidet <= comparable(T). lt([], [_|_]). lt([H1|T1], [H2|T2]) :- H1 =< H2, T1 `lt` T2.</lang>
... which you would have to create:
<lang Mercury>:- module comparable.
- - interface.
- - import_module int, float, integer, list.
- - typeclass comparable(T) where [
pred '<'(T::in, T::in) is semidet,
pred '=<'(T::in, T::in) is semidet
].
- - instance comparable(int).
- - instance comparable(float).
- - instance comparable(integer).
- - instance comparable(list(T)) <= comparable(T).
- - implementation.
- - instance comparable(int) where [
pred('<'/2) is int.(<),
pred('=<'/2) is int.(=<)
]. % likewise for float and integer...
- - instance comparable(list(T)) <= comparable(T) where [
pred('<'/2) is lt, % the 'lt' above.
pred('=<'/2) is lte % 'lt' with: lte([], []).
].
% pred lt % pred lte</lang>
Which would be used in this way - note the typeclass and the comparison operator.
<lang Mercury>:- pred test(list(T), list(T), io, io) <= comparable(T).
- - mode test(in, in, di, uo) is det.
test(A, B) -->
io.write(A), io.write_string(" < "), io.write(B),
io.write_string(" : "), io.write_string(S), io.nl,
{ A < B -> S = "yes" ; S = "no" }.</lang>
Nim
<lang nim>proc `<`[T](a, b: openarray[T]): bool =
for i in 0 .. min(a.len, b.len): if a[i] < b[i]: return true if a[i] > b[i]: return false return a.len < b.len
echo([1,2,1,3,2] < [1,2,0,4,4,0,0,0])</lang>
- Output:
false
OCaml
The built-in comparison operators already do this for lists (although this is not documented): <lang ocaml># [1;2;1;3;2] < [1;2;0;4;4;0;0;0];; - : bool = false</lang>
(Warning: However, the built-in comparison operators do not do this for arrays: <lang ocaml># [|1;2;1;3;2|] < [|1;2;0;4;4;0;0;0|];; - : bool = true</lang> )
But we could write it explicitly this way:
<lang ocaml>let rec ordered_lists = function
| x1::tl1, x2::tl2 ->
(match compare x1 x2 with
| 0 -> ordered_lists (tl1, tl2)
| 1 -> false
| _ -> true)
| [], _ -> true
| _ -> false</lang>
Here is a small script to test this function:
<lang ocaml>(* copy-paste the code of ordered_lists here *)
let make_num_list p n =
let rec aux acc = if Random.int p = 0 then acc else aux (Random.int n :: acc) in aux []
let print_num_list lst =
List.iter (Printf.printf " %d") lst; print_newline()
let () =
Random.self_init(); let lst1 = make_num_list 8 5 in let lst2 = make_num_list 8 5 in print_num_list lst1; print_num_list lst2; Printf.printf "ordered: %B\n" (ordered_lists (lst1, lst2))</lang>
Sample execution:
$ ocaml ordered_lists.ml 1 2 1 3 2 1 2 0 4 4 0 0 0 ordered: false
Also notice that the function ordered_lists will work with anything the function Pervasives.compare is able to compare (most OCaml types and structures made from the base types). In the prototype of this function below 'a list means a list of anything:
<lang ocaml>val ordered_lists : 'a list * 'a list -> bool</lang>
Oforth
In Oforth, list comparison is already defined.
- Output:
[1,2,0,4,4,0,0,0] [1,2,1,3,2] <= . 1 ok
PARI/GP
<lang parigp>lex(u,v)<1</lang>
Perl
<lang Perl>use strict; use warnings;
sub orderlists {
my ($firstlist, $secondlist) = @_;
my ($first, $second);
while (@{$firstlist}) {
$first = shift @{$firstlist};
if (@{$secondlist}) {
$second = shift @{$secondlist};
if ($first < $second) {
return 1;
}
if ($first > $second) {
return 0;
}
}
else {
return 0;
}
}
@{$secondlist} ? 1 : 0;
}
foreach my $pair (
[[1, 2, 4], [1, 2, 4]], [[1, 2, 4], [1, 2, ]], [[1, 2, ], [1, 2, 4]], [[55,53,1], [55,62,83]], [[20,40,51],[20,17,78,34]],
) {
my $first = $pair->[0]; my $second = $pair->[1]; my $before = orderlists([@$first], [@$second]) ? 'true' : 'false'; print "(@$first) comes before (@$second) : $before\n";
}</lang>
- Output:
(1 2 4) comes before (1 2 4) : false (1 2 4) comes before (1 2) : false (1 2) comes before (1 2 4) : true (55 53 1) comes before (55 62 83) : true (20 40 51) comes before (20 17 78 34) : false
Perl 6
There is already a built-in comparison operator. <lang perl6>my @a = <1 2 4>; my @b = <1 2 4>; say @a," before ",@b," = ", @a before @b;
@a = <1 2 4>; @b = <1 2>; say @a," before ",@b," = ", @a before @b;
@a = <1 2>; @b = <1 2 4>; say @a," before ",@b," = ", @a before @b;
for 1..10 {
my @a = flat (^100).roll((2..3).pick);
my @b = flat @a.map: { Bool.pick ?? $_ !! (^100).roll((0..2).pick) }
say @a," before ",@b," = ", @a before @b;
}</lang>
- Output:
1 2 4 before 1 2 4 = False 1 2 4 before 1 2 = False 1 2 before 1 2 4 = True 63 52 before 0 52 = False 17 75 24 before 31 75 24 = True 43 32 before 43 32 = False 73 84 before 2 84 = False 73 92 before 40 24 46 = False 16 24 before 41 24 = True 9 12 22 before 9 12 32 67 = True 81 23 before 81 23 = False 55 53 1 before 55 62 83 = True 20 40 51 before 20 17 78 34 = False
PicoLisp
The built-in comparison functions already do this (not only for lists of numbers, but for any arbitrary data type). <lang PicoLisp>: (> (1 2 0 4 4 0 0 0) (1 2 1 3 2)) -> NIL</lang>
Pike
<lang Pike>int(0..1) order_array(array a, array b) {
if (!sizeof(a)) return true; if (!sizeof(b)) return false; if (a[0] == b[0]) return order_array(a[1..], b[1..]); return a[0] < b[0];
}</lang>
Pikes Array.sort_array() function can sort an array of arrays using the < operator, but it will sort longer arrays before shorter ones. Therefore the above function is still needed if the intent is to use the comparison for a sort operation.
If the numbers are in 32bit signed integer range, the following works too: <lang Pike>(string)a < (string)b;</lang>
PL/I
<lang PL/I>lists: procedure options (main); /* 8 June 2014 */
declare a(10) fixed initial (1, 2, 3, 4, 5, 8, 9, 10, 16, 17),
b(15) fixed initial (5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 20, 22, 23);
put skip list (compare(a, b)); put skip list (compare(b, a)); put skip list (compare(a, a));
compare: procedure (a, b) returns (bit (1));
declare (a, b)(*) fixed; declare (i, m, n) fixed binary;
m = hbound(a,1); n = hbound(b,1);
do i = 1 to min(m, n);
return (a(i) < b(i));
end;
return (m < n);
end compare;
end lists;</lang> Results:
'1'B (true) '0'B (false) '0'B
PowerShell
<lang PowerShell> function order($as,$bs) {
if($as -and $bs) {
$a, $as = $as
$b, $bs = $bs
if($a -eq $b) {order $as $bs}
else{$a -lt $b}
} elseif ($bs) {$true} else {$false}
} "$(order @(1,2,1,3,2) @(1,2,0,4,4,0,0,0))" </lang> Output:
False
Non-Recursive Version
<lang PowerShell> function Test-Order ([int[]]$ReferenceArray, [int[]]$DifferenceArray) {
for ($i = 0; $i -lt $ReferenceArray.Count; $i++)
{
if ($ReferenceArray[$i] -lt $DifferenceArray[$i])
{
return $true
}
elseif ($ReferenceArray[$i] -gt $DifferenceArray[$i])
{
return $false
}
}
return ($ReferenceArray.Count -lt $DifferenceArray.Count) -or (Compare-Object $ReferenceArray $DifferenceArray) -eq $null
} </lang> <lang PowerShell> Test-Order -ReferenceArray 1, 2, 1, 3, 2 -DifferenceArray 1, 2, 0, 4, 4, 0, 0, 0 Test-Order -ReferenceArray 1, 2, 1, 3, 2 -DifferenceArray 1, 2, 2, 4, 4, 0, 0, 0 Test-Order -ReferenceArray 1, 2, 3 -DifferenceArray 1, 2 Test-Order -ReferenceArray 1, 2 -DifferenceArray 1, 2, 3 Test-Order -ReferenceArray 1, 2 -DifferenceArray 1, 2 </lang>
- Output:
False True False True True
PureBasic
<lang purebasic>DataSection
Array_1: Data.i 5 ;element count Data.i 1, 2, 3, 4, 5 ;element data Array_2: Data.i 6 Data.i 1, 2, 1, 5, 2, 2 Array_3: Data.i 5 Data.i 1, 2, 1, 5, 2 Array_4: Data.i 5 Data.i 1, 2, 1, 5, 2 Array_5: Data.i 4 Data.i 1, 2, 1, 6 Array_6: Data.i 5 Data.i 1, 2, 1, 6, 2
EndDataSection
- False = 0
- True = 1
- helper subrountine to initialize a dataset, *dataPtr points to the elementcount followed by the element data
Procedure initArrayData(Array a(1), *dataPtr)
Protected elementCount = PeekI(*dataPtr) Dim a(elementCount - 1) For i = 0 To elementCount - 1 *dataPtr + SizeOf(Integer) a(i) = PeekI(*dataPtr) Next
EndProcedure
- helper subroutine that returns 'True' or 'False' for a boolean input
Procedure.s booleanText(b)
If b: ProcedureReturn "True": EndIf ProcedureReturn "False"
EndProcedure
Procedure order(Array a(1), Array b(1))
Protected len_a = ArraySize(a()), len_b = ArraySize(b()), elementIndex
While elementIndex <= len_a And elementIndex <= len_b And a(elementIndex) = b(elementIndex) elementIndex + 1 Wend If (elementIndex > len_a And elementIndex <= len_b) Or (elementIndex <= len_b And a(elementIndex) <= b(elementIndex)) ProcedureReturn #True EndIf
EndProcedure
Dim A_1(0): initArrayData(A_1(), ?Array_1) Dim A_2(0): initArrayData(A_2(), ?Array_2) Dim A_3(0): initArrayData(A_3(), ?Array_3) Dim A_4(0): initArrayData(A_4(), ?Array_4) Dim A_5(0): initArrayData(A_5(), ?Array_5) Dim A_6(0): initArrayData(A_6(), ?Array_6)
If OpenConsole()
PrintN(booleanText(order(A_1(), A_2()))) ;False PrintN(booleanText(order(A_2(), A_3()))) ;False PrintN(booleanText(order(A_3(), A_4()))) ;False PrintN(booleanText(order(A_4(), A_5()))) ;True PrintN(booleanText(order(A_5(), A_6()))) ;True Print(#crlf$ + #crlf$ + "Press ENTER to exit"): Input() CloseConsole()
EndIf
</lang>
- Output:
False False False True True
Python
The built-in comparison operators already do this: <lang python>>>> [1,2,1,3,2] < [1,2,0,4,4,0,0,0] False</lang>
Racket
<lang Racket>#lang racket
(define (lex<? a b)
(cond ((null? b) #f)
((null? a) #t)
((= (car a) (car b)) (lex<? (cdr a) (cdr b)))
(else (< (car a) (car b)))))
(lex<? '(1 2 3 4 5) '(1 2 3 4 4)) ; -> #f </lang>
Rascal
The built-in comparison operator already does this: <lang rascal>rascal>[2,1,3] < [5,2,1,3] bool: true</lang>
REXX
This REXX example uses the same lists as BBC BASIC.
This example will also work with non-numeric strings.
<lang rexx>/*REXX pgm determines if a list < previous list, & returns true | false*/
@. =
@.1 = 1 2 1 5 2
@.2 = 1 2 1 5 2 2
@.3 = 1 2 3 4 5
@.4 = 1 2 3 4 5 /* [↓] compare list to previous.*/
do j=2 while @.j\==; p=j-1 /*P is the previous.*/
answer=FNorder(@.p, @.j) /*obtain the answer.*/
if answer=='true' then is= ' < ' /*convert from true */
else is= ' ≥ ' /*convert from false*/
say right('['@.p"]", 40) is '['@.j"]"; say
end /*i*/ /* [↑] display (+ a blank line)*/
exit /*stick a fork in it, we're done.*/ /*──────────────────────────────────FNORDER subroutine──────────────────*/ FNorder: procedure; parse arg x,y; wx=words(x); wy=words(y)
do k=1 for min(wx,wy)
a=word(x,k); b=word(y,k)
if ab then return 'false'
end /*k*/
if wx<wy then return 'true'
return 'false'</lang>
- Output:
[1 2 1 5 2] < [1 2 1 5 2 2]
[1 2 1 5 2 2] < [1 2 3 4 5]
[1 2 3 4 5] ≥ [1 2 3 4 5]
Ring
<lang ring> list1 = "1, 2, 1, 5, 2" list2 = "5, 2, 1, 5, 2, 2" list3 = "1, 2, 3, 4, 5" list4 = "1, 2, 3, 4, 5"
if order(list1, list2) = 0 see "list1=list2" + nl but order(list1, list2) < 0 see "list1<list2" + nl else see "list1>list2" + nl ok
if order(list2, list3) = 0 see "list2=list3" + nl but order(list2, list3) < 0 see "list2<list3" + nl else see "list2>list3" + nl ok
if order(list3, list4) = 0 see "list3=list4" + nl but order(list3, list4) < 0 see "list3<list4" + nl else see "list3>list4" + nl ok
func order alist, blist
return strcmp(alist, blist)
</lang> Output:
list1<list2 list2>list3 list3=list4
Ruby
The built-in <=> operator already does this:
<lang ruby>>> ([1,2,1,3,2] <=> [1,2,0,4,4,0,0,0]) < 0
=> false</lang>
Scala
<lang Scala>def lessThan1(a: List[Int], b: List[Int]): Boolean =
if (b.isEmpty) false
else if (a.isEmpty) true
else if (a.head != b.head) a.head < b.head
else lessThan1(a.tail, b.tail)</lang><lang Scala>def lessThan2(a: List[Int], b: List[Int]): Boolean = (a, b) match {
case (_, Nil) => false
case (Nil, _) => true
case (a :: _, b :: _) if a != b => a < b
case _ => lessThan2(a.tail, b.tail)
}</lang><lang Scala>def lessThan3(a: List[Int], b: List[Int]): Boolean =
a.zipAll(b, Integer.MIN_VALUE, Integer.MIN_VALUE)
.find{case (a, b) => a != b}
.map{case (a, b) => a < b}
.getOrElse(false)</lang><lang Scala>val tests = List(
(List(1, 2, 3), List(1, 2, 3)) -> false,
(List(3, 2, 1), List(3, 2, 1)) -> false,
(List(1, 2, 3), List(3, 2, 1)) -> true,
(List(3, 2, 1), List(1, 2, 3)) -> false,
(List(1, 2), List(1, 2, 3)) -> true,
(List(1, 2, 3), List(1, 2)) -> false
)
tests.foreach{case test @ ((a, b), c) =>
assert(lessThan1(a, b) == c, test) assert(lessThan2(a, b) == c, test) assert(lessThan3(a, b) == c, test)
}</lang>
Scheme
<lang scheme>(define (lex<? a b)
(cond ((null? b) #f)
((null? a) #t)
((= (car a) (car b)) (lex<? (cdr a) (cdr b)))
(else (< (car a) (car b)))))</lang>
Seed7
The operator corresponding to the ordering described in this example is less than.
<lang seed7>$ include "seed7_05.s7i";
const proc: main is func
begin writeln([] (1) < [] (1, 2)); # If the first list runs out of elements the result is TRUE. writeln([] (1, 2) < [] (1)); # If the second list runs out of elements the result is FALSE. writeln([] (1, 2) < [] (1, 2)); # If both lists run out of elements the result is FALSE. writeln([] (1, 2, 3) < [] (1, 1, 3)); # The second element is greater than --> FALSE writeln([] (1, 2, 3) < [] (1, 3, 3)); # The second element is less than --> TRUE writeln(0 times 0 < [] (1)); # The empty list is less than any nonempty list --> TRUE writeln([] (1) < 0 times 0); # Any nonempty list is not less than the empty list --> FALSE writeln(0 times 0 < 0 times 0); # The empty list is not less than the empty list --> FALSE end func;</lang>
- Output:
TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE
Sidef
Built-in, via the comparison operator (`<=>`): <lang ruby>func ordered(a, b) {
(a <=> b) < 0
}
for p in [
Pair([1,2,4], [1,2,4]), Pair([1,2,4], [1,2] ), Pair([1,2], [1,2,4]),
] {
var a = p.first
var b = p.second
var before = ordered(a, b)
say "#{a} comes before #{b} : #{before}"
}</lang>
- Output:
[1, 2, 4] comes before [1, 2, 4] : false [1, 2, 4] comes before [1, 2] : false [1, 2] comes before [1, 2, 4] : true
Standard ML
<lang sml>- List.collate Int.compare ([1,2,1,3,2], [1,2,0,4,4,0,0,0]) = LESS; val it = false : bool</lang>
Swift
<lang swift>let a = [1,2,1,3,2] let b = [1,2,0,4,4,0,0,0] println(lexicographicalCompare(a, b)) // this is "less than"</lang>
- Output:
false
Tcl
<lang tcl>proc numlist< {A B} {
foreach a $A b $B {
if {$a<$b} {
return 1
} elseif {$a>$b} {
return 0
}
}
return 0
}</lang>
TUSCRIPT
<lang tuscript> $$ MODE TUSCRIPT MODE DATA $$ numlists=* 1'2'1'3'2 1'2'0'4'4'0'0'0 1'2'3'4'5 1'2'1'5'2'2 1'2'1'6 1'2'1'6'2 1'2'4 1'2'4 1'2 1'2'4 $$ MODE TUSCRIPT list1="1'2'5'6'7" LOOP n,list2=numlists text=CONCAT (" ",list1," < ",list2) IF (list1<list2) THEN PRINT " true: ",text ELSE PRINT "false: ",text ENDIF list1=VALUE(list2) ENDLOOP </lang>
- Output:
false: 1'2'5'6'7 < 1'2'1'3'2 false: 1'2'1'3'2 < 1'2'0'4'4'0'0'0 true: 1'2'0'4'4'0'0'0 < 1'2'3'4'5 false: 1'2'3'4'5 < 1'2'1'5'2'2 true: 1'2'1'5'2'2 < 1'2'1'6 true: 1'2'1'6 < 1'2'1'6'2 true: 1'2'1'6'2 < 1'2'4 false: 1'2'4 < 1'2'4 false: 1'2'4 < 1'2 true: 1'2 < 1'2'4
VBScript
<lang vb> Function order_list(arr1,arr2) order_list = "FAIL" n1 = UBound(arr1): n2 = UBound(arr2) n = 0 : p = 0 If n1 > n2 Then max = n2 Else max = n1 End If For i = 0 To max If arr1(i) > arr2(i) Then n = n + 1 ElseIf arr1(i) = arr2(i) Then p = p + 1 End If Next If (n1 < n2 And n = 0) Or _ (n1 = n2 And n = 0 And p - 1 <> n1) Or _ (n1 > n2 And n = 0 And p = n2) Then order_list = "PASS" End If End Function
WScript.StdOut.WriteLine order_list(Array(-1),Array(0)) WScript.StdOut.WriteLine order_list(Array(0),Array(0)) WScript.StdOut.WriteLine order_list(Array(0),Array(-1)) WScript.StdOut.WriteLine order_list(Array(0),Array(0,-1)) WScript.StdOut.WriteLine order_list(Array(0),Array(0,0)) WScript.StdOut.WriteLine order_list(Array(0),Array(0,1)) WScript.StdOut.WriteLine order_list(Array(0,-1),Array(0)) WScript.StdOut.WriteLine order_list(Array(0,0),Array(0)) WScript.StdOut.WriteLine order_list(Array(0,0),Array(1)) WScript.StdOut.WriteLine order_list(Array(1,2,1,3,2),Array(1,2,0,4,4,0,0,0)) </lang>
- Output:
PASS FAIL FAIL PASS PASS PASS FAIL FAIL PASS FAIL
Wart
We'll simply overload < for lists.
<lang python>def (a < b) :case (or list?.a list?.b)
if not.b
nil
not.a
b
(car.a = car.b)
(cdr.a < cdr.b)
:else
(car.a < car.b)</lang>
- Output:
(< '(1 2 3) '(1 2 4)) => 4 (< '(1 2 4) '(1 2 3)) => nil (< '(1 2 3) '(1 2 3 4)) => (4) (< '(1 2 4) '(1 2 3 4)) => nil
zkl
<lang zkl>fcn listLT(a,b){
a.walker().zip(b).filter1(fcn([(a,b)]){ a<b }) : // lazy
if(_) return(True);;
a.len()<b.len()
}</lang>
- Output:
listLT(T(1,2,3),T(2,3,4)).println(); //-->True listLT(T(2,3,4),T(1,2,3)).println(); //-->False listLT(T(1,2),T(1,2,3,4)).println(); //-->True listLT(T(1,2,3,4),T(1,2,3)).println(); //-->False listLT(T(1,2,3),T(1,2,3)).println(); //-->False
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