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Index finite lists of positive integers: Difference between revisions

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Index finite lists of positive integers (view source)

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→‎{{header|jq}}: simplify
m (→‎base 11: bigint->mpfr)
(→‎{{header|jq}}: simplify)
 
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Make the &nbsp; ''rank'' &nbsp; function as a &nbsp; [[wp:bijection| <u>bijection</u>]] &nbsp; and show &nbsp; ''unrank(n)'' &nbsp; for &nbsp; <big>'''n'''</big> &nbsp; varying from &nbsp; '''0''' &nbsp; to &nbsp; '''10'''.
<br><br>
 
=={{header|11l}}==
{{trans|Python}}
 
<syntaxhighlight lang="11l">F rank(x)
R BigInt(([1] [+] x).map(String).join(‘A’), radix' 11)
 
F unrank(n)
V s = String(n, radix' 11)
R s.split(‘A’).map(Int)[1..]
 
V l = [1, 2, 3, 10, 100, 987654321]
print(l)
V n = rank(l)
print(n)
l = unrank(n)
print(l)</syntaxhighlight>
 
{{out}}
<pre>
[1, 2, 3, 10, 100, 987654321]
1723765384735274025865314
[1, 2, 3, 10, 100, 987654321]
</pre>
 
=={{header|Arturo}}==
 
<syntaxhighlight lang="rebol">rank: function [arr][
if empty? arr -> return 0
from.binary "1" ++ join.with:"0" map arr 'a -> repeat "1" a
]
 
unrank: function [rnk][
if rnk=1 -> return [0]
bn: as.binary rnk
map split.by:"0" slice bn 1 dec size bn => size
]
 
l: [1, 2, 3, 5, 8]
 
print ["The initial list:" l]
 
r: rank l
print ["Ranked:" r]
 
u: unrank r
print ["Unranked:" u]</syntaxhighlight>
 
{{out}}
 
<pre>The initial list: [1 2 3 5 8]
Ranked: 14401279
Unranked: [1 2 3 5 8]</pre>
 
=={{header|D}}==
This solution isn't efficient.
{{trans|Python}}
<langsyntaxhighlight lang="d">import std.stdio, std.algorithm, std.array, std.conv, std.bigint;
 
BigInt rank(T)(in T[] x) pure /*nothrow*/ @safe {
Line 48 ⟶ 101:
s.rank.writeln;
s.rank.unrank.writeln;
}</langsyntaxhighlight>
{{out}}
<pre>[1, 2, 3, 10, 100, 987654321]
Line 54 ⟶ 107:
[1, 2, 3, 10, 100, 987654321]
</pre>
 
=={{header|FreeBASIC}}==
Restricted to shortish lists with smallish integers, because the rank integers get really big really fast, and bloating the code with arbitrary precision arithmetic isn't illustrative.
<syntaxhighlight lang="freebasic">type duple
A as ulongint
B as ulongint
end type
 
function two_to_one( A as ulongint, B as ulongint ) as ulongint 'converts two numbers into one
dim as uinteger ret = A*A + B*B + 2*A*B - 3*A - B 'according to the table
return 1 + ret/2 ' 1 2 3 4 5
end function ' -------------
' 1| 1 3 6 10 15
function one_to_two( R as ulongint ) as duple ' 2| 2 5 9 14 20
dim as uinteger t = int((-1+sqr(8*R-7))/2) ' 3| 4 8 13 19 26
dim as duple ret ' 4| 7 12 18 25 33
ret.A = (t*t+3*t+4)/2-R
t = int((-1+sqr(8*R-7))/2) 'and the inverse of this
ret.B = R-t*(t+1)/2
return ret
end function
 
function rank( N() as ulongint) as ulongint
dim as uinteger ret, num = ubound(N)+1
if num = 0 then return 0 'define a value of 0 for the empty list
if num = 1 then return two_to_one( N(0), 1 )
ret = two_to_one( N(0), N(1) )
for i as uinteger = 2 to num-1 'progressively encode the list by
ret = two_to_one( ret, N(i) ) 'applying 2to1 on the result of the
next i 'previous calculation with the next list element
return two_to_one(ret, num) 'store the length of the list as
end function 'the final component
 
sub unrank( R as ulongint, N() as ulongint )
dim as duple temp
if R = 0 then 'zero yields the empty list
redim N(-1)
return
end if
dim as ulongint num, Q(0 to 1)
temp = one_to_two( R )
num = temp.B 'first get the length of the encoded list
redim N(0 to num-1) as ulongint
if num = 1 then '(singleton handled as a special case)
N(0)=temp.A
return
end if
for i as integer = num-1 to 2 step -1 'get back the list elements one by one
temp = one_to_two( temp.A ) 'in the reverse order they were added
N(i) = temp.B
next i
temp = one_to_two( temp.A ) 'finally get the initial two list elements
N(0) = temp.A
N(1) = temp.B
end sub
 
sub show_list( L() as ulongint )
dim as integer num = ubound(L)
if num=-1 then
print "[]"
return
end if
print "[";
for i as integer = 0 to num-1
print str(L(i))+", ";
next i
print str(L(num))+"]"
end sub
'A few tests
dim as duple temp
redim as uinteger ex0(-1) 'empty list
dim as ulongint R = rank(ex0())
R = rank(ex0())
print R,
redim as ulongint X(0 to 1)
unrank R, X()
show_list(X())
 
dim as uinteger ex1(0 to 0) = {13} 'list with 1 element
R = rank(ex1())
print R,
unrank R, X()
show_list(X())
 
dim as uinteger ex2(0 to 1) = {19, 361} 'list with 2 elements
R = rank(ex2())
print R,
redim as ulongint X(0 to 1)
unrank R, X()
show_list(X())
 
dim as uinteger ex6(0 to 5) = {1,2,1,2,3,1} 'list with 6 elements
R = rank(ex6())
print R,
unrank R, X()
show_list(X())</syntaxhighlight>
{{out}}
<pre>0 []
79 [13]
2591460030 [19, 361]
9576882 [1, 2, 1, 2, 3, 1]</pre>
 
=={{header|Go}}==
Line 59 ⟶ 213:
 
A list element n is encoded as a 1 followed by n 0's. Element encodings are concatenated to form a single integer rank. An advantage of this encoding is that no special case is required to handle the empty list.
<langsyntaxhighlight lang="go">package main
 
import (
Line 97 ⟶ 251:
r := rank(u)
fmt.Printf("\n%v\n%d\n%d\n", &b, u, &r)
}</langsyntaxhighlight>
{{out}}
<pre>
Line 119 ⟶ 273:
 
A bit of a hack to make a base 11 number then interpret it as base 16, just because that's easiest. Not bijective. Practical though for small lists of large numbers.
<langsyntaxhighlight lang="go">package main
 
import (
Line 211 ⟶ 365:
}
return l
}</langsyntaxhighlight>
{{out}}
<pre>
Line 228 ⟶ 382:
Rank: 1 unrank not bijective
</pre>
 
=={{header|Haskell}}==
 
<syntaxhighlight lang="haskell">import Data.List
 
toBase :: Int -> Integer -> [Int]
toBase b = unfoldr f
where
f 0 = Nothing
f n = let (q, r) = n `divMod` fromIntegral b in Just (fromIntegral r, q)
 
fromBase :: Int -> [Int] -> Integer
fromBase n lst = foldr (\x r -> fromIntegral n*r + fromIntegral x) 0 lst
 
------------------------------------------------------------
listToInt :: Int -> [Int] -> Integer
listToInt b lst = fromBase (b+1) $ concat seq
where
seq = [ let (q, r) = divMod n b
in replicate q 0 ++ [r+1]
| n <- lst ]
 
intToList :: Int -> Integer -> [Int]
intToList b lst = go 0 $ toBase (b+1) lst
where
go 0 [] = []
go i (0:xs) = go (i+1) xs
go i (x:xs) = (i*b + x - 1) : go 0 xs</syntaxhighlight>
 
Using different bases we may enumerate lists.
 
<pre>*Main> intToList 2 <$> [1..20]
[[0],[1],[2],[0,0],[1,0],[3],[0,1],[1,1],[4],[0,2],[1,2],[2,0],[0,0,0],[1,0,0],[3,0],[0,1,0],[1,1,0],[5],[0,3],[1,3]]
 
*Main> intToList 3 <$> [1..20]
[[0],[1],[2],[3],[0,0],[1,0],[2,0],[4],[0,1],[1,1],[2,1],[5],[0,2],[1,2],[2,2],[6],[0,3],[1,3],[2,3],[3,0]]
 
*Main> intToList 10 <$> [1..20]
[[0],[1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[0,0],[1,0],[2,0],[3,0],[4,0],[5,0],[6,0],[7,0],[8,0]]
 
*Main> listToInt 2 <$> permutations [1,2,3,4]
[2360,2370,2382,2406,2292,2288,5274,5190,5136,5922,5916,5160,4680,4646,4628,4950,4944,4638,2736,2702,2450,2844,2760,2454]</pre>
 
This mapping is a bijection:
 
<pre>*Main> (listToInt 3 . intToList 3 <$> [0..100]) == [0..100]
True</pre>
 
 
 
 
=={{header|J}}==
Line 235 ⟶ 440:
Implementation:
 
<langsyntaxhighlight lang="j">scrunch=:3 :0
n=.1x+>./y
#.(1#~##:n),0,n,&#:n#.y
Line 245 ⟶ 450:
n=.#.m{.(m+1)}.b
n #.inv#.(1+2*m)}.b
)</langsyntaxhighlight>
 
Example use:
 
<langsyntaxhighlight Jlang="j"> scrunch 4 5 7 9 0 8 8 7 4 8 8 4 1
4314664669630761
hcnurcs 4314664669630761
4 5 7 9 0 8 8 7 4 8 8 4 1</langsyntaxhighlight>
 
Explanation. We treat the sequence as an n digit number in base m where n is the length of the list and m is 1+the largest value in the list. (This is equivalent to treating it as a polynomial in m with coefficients which are the values of the list, with powers of m increasing from right to left.) In other words 4 5 7 9 0 8 8 7 4 8 8 4 1 becomes 4579088748841. Now we just need to encode the base (10, in this case). To do that we treat this number as a sequence of bits and prepend it with 1 1 1 1 0 1 0 1 0. This is a sequence of '1's whose length matches the number of bits needed to represent the base of our polynomial, followed by a 0 followed by the base of our polynomial.
 
To extract the original list we reverse this process: Find the position of the first zero, that's the size of our base, extract the base and then use that to find the coefficients of our polynomial, which is or original list.
 
Whether this is an efficient representation or not depends, of course, on the nature of the list being represented.
 
 
=== Tacit versions ===
Line 265 ⟶ 469:
Base 11 encoding:
 
<langsyntaxhighlight lang="j"> rank =. 11&#.@:}.@:>@:(,&:>/)@:(<@:(10&,)@:(10&#.^:_1)"0)@:x:
unrank=. 10&#.;._1@:(10&,)@:(11&#.^:_1)</langsyntaxhighlight>
 
Example use:
 
<langsyntaxhighlight Jlang="j"> rank 1 2 3 10 100 987654321 135792468107264516704251 7x
187573177082615698496949025806128189691804770100426
unrank 187573177082615698496949025806128189691804770100426x
1 2 3 10 100 987654321 135792468107264516704251 7</langsyntaxhighlight>
 
Prime factorization (Gödelian) encoding:
 
<langsyntaxhighlight lang="j"> rank=. */@:(^~ p:@:i.@:#)@:>:@:x:
unrank=. <:@:(#;.1@:~:@:q:)</langsyntaxhighlight>
 
Example use:
 
<langsyntaxhighlight Jlang="j"> rank 1 11 16 1 3 9 0 2 15 7 19 10
6857998574998940803374702726455974765530187550029640884386375715876970128518999225074067307280381624132537960815429687500
unrank 6857998574998940803374702726455974765530187550029640884386375715876970128518999225074067307280381624132537960815429687500x
1 11 16 1 3 9 0 2 15 7 19 10</langsyntaxhighlight>
 
=== Bijective ===
Line 293 ⟶ 497:
Using the method of the Python version (shifted):
 
<langsyntaxhighlight lang="j"> rank=. 1 -~ #.@:(1 , >@:(([ , 0 , ])&.>/)@:(<@:($&1)"0))@:x:
unrank=. #;._2@:((0 ,~ }.)@:(#.^:_1)@:(1&+))</langsyntaxhighlight>
 
Example use:
 
<langsyntaxhighlight Jlang="j"> >@:((] ; unrank ; rank@:unrank)&.>)@:i. 11
┌──┬───────┬──┐
│0 │0 │0 │
Line 326 ⟶ 530:
┌─────────┬────────┬─────────┐
│1 2 3 5 8│14401278│1 2 3 5 8│
└─────────┴────────┴─────────┘</langsyntaxhighlight>
 
=={{header|Java}}==
Translation of [[Index_finite_lists_of_positive_integers#Python|Python]] via [[Index_finite_lists_of_positive_integers#D|D]]
{{works with|Java|8}}
<langsyntaxhighlight lang="java">import java.math.BigInteger;
import static java.util.Arrays.stream;
import java.util.*;
Line 358 ⟶ 562:
System.out.println(unrank(rank(s)));
}
}</langsyntaxhighlight>
<pre>[1, 2, 3, 10, 100, 987654321]
37699814998383067155219233
[1, 2, 3, 10, 100, 987654321]</pre>
 
=={{header|jq}}==
'''Works with gojq'''
 
'''Works with jq''' within the limits of jq's support for large integer arithmetic
 
'''Works with jaq within the limits of jaq's support for large integers'''
 
The main point of interest of this entry is probably the use of the
Fibonacci encoding of positive integers (see
e.g. https://en.wikipedia.org/wiki/Fibonacci_coding and
[[:Category:jq/fibonacci.jq]]). This is the focus of the first
subsection. The second subsection focuses on the "n 0s" encoding.
 
The Go implementation of jq supports indefinitely large integers and
so, apart from machine limitations, the programs shown here should
work using gojq without further qualification.
 
The C implementation of jq, as of version 1.6, supports arbitrarily
large literal integers, and the `tonumber` filter retains precision
allowing seamless translation between strings and numbers.
 
The following is slightly more verbose than it need be but for the
sake of compatibility with jaq. Also note that trivial changes would
be required if using jaq as jaq does not (as of this writing in 2024)
support the `include` or `module` directives.
 
===Map based on Fibonacci encoding===
 
Since each Fibonacci-encoded integer ends with "11" and
contains no other instances of "11" before the end,
the original sequence of integers can trivially be recovered after
simple concatenation of the encodings. However, the Fibonacci
encoding of an integer can begin with 0s, so here we simply prefix
the binary string with a "1".
 
For example: 1 2 3 => 11 011 0011 => 1110110011
 
In the following, we will simply interpret
this as an integer in base 2 to avoid unnecessary complications
arising from implementation-specific limits.
<syntaxhighlight lang="jq">
include "fibonacci" {search: "./"}; # see https://rosettacode.org/wiki/Category:Jq/fibonacci.jq
 
# Input: an array of integers
# Output: an integer-valued binary string, being the reverse of the concatenated Fibonacci-encoded values
def rank:
map(fibencode | map(tostring) | join(""))
| "1" + join("");
 
# Input a bitstring or 0-1 integer interpreted as a bitstring
# Output: an array of integers
def unrank:
tostring
| .[1:]
| split("11")
| .[:-1]
| map(. + "11" | fibdecode) ;
 
# Output: a PRN in range(0;$n) where $n is .
def prn:
if . == 1 then 0
else . as $n
| (($n-1)|tostring|length) as $w
| [limit($w; inputs) | tostring] | join("") | sub("^0+";"") | tonumber
| if . < $n then . else $n | prn end
end;
 
### The task
# Encode and decode a random number of distinct positive numbers chosen at random.
# Produce a JSON object showing the set of numbers, their encoding, and
# the result of comparing the original set with the reconstructed set.
def task:
(11 | prn) + 1
| . as $numbers
| [range(0;$numbers) | 100000 | prn + 1]
| . as $numbers
| rank
| . as $encoded
# now decode:
| unrank
| {$numbers, encoded: ($encoded|tonumber), check: ($numbers == .)}
;
 
task
</syntaxhighlight>
'''Invocation''':
<pre>
< /dev/random tr -cd '0-9' | fold -w 1 | jq -nrf index-finite-lists-of-positive-integers.jq
</pre>
{{output}}
<pre>
{
"numbers": [
92408,
42641,
35563,
17028,
49093
],
"encoded": 101000101000001010101000111000001010001000100101100010101010000000010011001001001001000101011000101010100000010000011,
"check": true
}
</pre>
 
 
===Bijective map based on "n 0s" encoding===
<syntaxhighlight lang="jq">
### Infrastructure
 
# Input: a string in base $b (2 to 35 inclusive)
# Output: the decimal value
def frombase($b):
def decimalValue:
if 48 <= . and . <= 57 then . - 48
elif 65 <= . and . <= 90 then . - 55 # (10+.-65)
elif 97 <= . and . <= 122 then . - 87 # (10+.-97)
else "decimalValue" | error
end;
reduce (explode|reverse[]|decimalValue) as $x ({p:1};
.value += (.p * $x)
| .p *= $b)
| .value ;
 
def binary_digits:
if . == 0 then 0
else [recurse( if . == 0 then empty else ./2 | floor end ) % 2 | tostring]
| reverse
| .[1:] # remove the leading 0
| join("")
end ;
 
 
### rank and unrank
# Each integer n in the list is mapped to '1' plus n '0's.
# The empty list is mapped to '0'
def rank:
if length == 0 then 0
else reduce .[] as $i ("";
. += "1" + ("0" * $i))
| frombase(2)
end ;
 
def unrank:
if . == 0 then []
else binary_digits
| split("1")
| .[1:]
| map(length)
end ;
 
### Illustration
range(1;11)
| . as $i
| unrank
| . as $unrank
| [$i, $unrank, rank]
</syntaxhighlight>
{{output}}
<pre>
[1,[0],1]
[2,[1],2]
[3,[0,0],3]
[4,[2],4]
[5,[1,0],5]
[6,[0,1],6]
[7,[0,0,0],7]
[8,[3],8]
[9,[2,0],9]
[10,[1,1],10]
</pre>
 
=={{header|Julia}}==
{{works with|Julia|0.6}}
{{trans|Python}}
 
<syntaxhighlight lang="julia">using LinearAlgebra
<lang julia>Base.rank(x::Vector{<:Integer}) = parse(BigInt, "1a" * join(x, 'a'), 11)
LinearAlgebra.rank(x::Vector{<:Integer}) = parse(BigInt, "1a" * join(x, 'a'), base=11)
function unrank(n::Integer)
s = ""
Line 381 ⟶ 756:
n = rank(v)
v = unrank(n)
println("# v = $v\n -> n = $n\n -> v = $v")</langsyntaxhighlight>
 
{{out}}
Line 389 ⟶ 764:
 
=={{header|Kotlin}}==
<langsyntaxhighlight lang="scala">// version 1.1.2
 
import java.math.BigInteger
Line 442 ⟶ 817:
println("${"%2d".format(i)} -> ${li.toString().padEnd(9)} -> ${rank2(li)}")
}
}</langsyntaxhighlight>
 
{{out}}
Line 468 ⟶ 843:
10 -> [1, 1] -> 10
</pre>
 
=={{header|Mathematica}} / {{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[Rank,Unrank]
Rank[x_List]:=FromDigits[Catenate[Riffle[IntegerDigits/@x,{{15}},{1,-1,2}]],16]
Unrank[n_Integer]:=FromDigits/@SequenceSplit[IntegerDigits[n,16],{15}]
Rank[{0,1,2,3,10,100,987654321,0}]
Unrank[%]
First@*Unrank@*Rank@*List /@ Range[0, 20]</syntaxhighlight>
{{out}}
<pre>4886947482322057719812858634706703
{0, 1, 2, 3, 10, 100, 987654321, 0}
{0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}</pre>
 
=={{header|Nim}}==
{{trans|Go}}
{{libheader|bignum}}
<syntaxhighlight lang="nim">import strformat, strutils
import bignum
 
func rank(list: openArray[uint]): Int =
result = newInt(0)
for n in list:
result = result shl (n + 1)
result = result.setBit(n)
 
func unrank(n: Int): seq[uint] =
var m = n.clone
var a = if m.isZero: 0u else: m.bitLen.uint
while a > 0:
m = m.clearBit(a - 1)
let b = if m.isZero: 0u else: m.bitLen.uint
result.add(a - b - 1)
a = b
 
when isMainModule:
 
var b: Int
for i in 0..10:
b = newInt(i)
let u = b.unrank()
let r = u.rank()
echo &"{i:2d} {u:>9s} {r:>2s}"
 
b = newInt("12345678901234567890")
let u = b.unrank()
let r = u.rank()
echo &"\n{b}\n{u}\n{r}"</syntaxhighlight>
 
{{out}}
<pre> 0 @[] 0
1 @[0] 1
2 @[1] 2
3 @[0, 0] 3
4 @[2] 4
5 @[1, 0] 5
6 @[0, 1] 6
7 @[0, 0, 0] 7
8 @[3] 8
9 @[2, 0] 9
10 @[1, 1] 10
 
12345678901234567890
@[1, 1, 1, 0, 1, 1, 1, 2, 1, 1, 2, 0, 3, 0, 2, 0, 0, 1, 1, 0, 3, 0, 0, 0, 0, 4, 1, 1, 0, 1, 2, 1]
12345678901234567890</pre>
 
=={{header|Perl}}==
The base-11 approach requires <code>bigint</code> pragma for all but trivial lists. Using <code>ntheory</code> module for base conversions.
{{trans|Perl 6Raku}}
{{libheader|ntheory}}
<langsyntaxhighlight lang="perl">use bigint;
use ntheory qw(fromdigits todigitstring);
use feature 'say';
Line 482 ⟶ 921:
say join ' ', @n = qw<12 11 0 7 9 15 15 5 7 13 5 5>;
say $n = rank(@n);
say join ' ', unrank $n;</langsyntaxhighlight>
{{out}}
<pre>12 11 0 7 9 15 15 5 7 13 5 5
16588666500024842935939135419
12 11 0 7 9 15 15 5 7 13 5 5</pre>
 
=={{header|Perl 6}}==
Here is a cheap solution using a base-11 encoding and string operations:
<lang perl6>sub rank(*@n) { :11(@n.join('A')) }
sub unrank(Int $n) { $n.base(11).split('A') }
 
say my @n = (1..20).roll(12);
say my $n = rank(@n);
say unrank $n;</lang>
{{out}}
<pre>1 11 16 1 3 9 0 2 15 7 19 10
25155454474293912130094652799
1 11 16 1 3 9 0 2 15 7 19 10</pre>
 
Here is a bijective solution that does not use string operations.
 
<lang perl6>multi infix:<rad> () { 0 }
multi infix:<rad> ($a) { $a }
multi infix:<rad> ($a, $b) { $a * $*RADIX + $b }
multi expand(Int $n is copy, 1) { $n }
multi expand(Int $n is copy, Int $*RADIX) {
my \RAD = $*RADIX;
my @reversed-digits = gather while $n > 0 {
take $n % RAD;
$n div= RAD;
}
eager for ^RAD {
[rad] reverse @reversed-digits[$_, * + RAD ... *]
}
}
multi compress(@n where @n == 1) { @n[0] }
multi compress(@n is copy) {
my \RAD = my $*RADIX = @n.elems;
[rad] reverse gather while @n.any > 0 {
(state $i = 0) %= RAD;
take @n[$i] % RAD;
@n[$i] div= RAD;
$i++;
}
}
sub rank(@n) { compress (compress(@n), @n - 1)}
sub unrank(Int $n) { my ($a, $b) = expand $n, 2; expand $a, $b + 1 }
 
my @list = (^10).roll((2..20).pick);
my $rank = rank @list;
say "[$@list] -> $rank -> [{unrank $rank}]";
 
for ^10 {
my @unrank = unrank $_;
say "$_ -> [$@unrank] -> {rank @unrank}";
}</lang>
 
{{out}}
<pre>[7 1 4 7 7 0 2 7 7 0 7 7] -> 20570633300796394530947471 -> [7 1 4 7 7 0 2 7 7 0 7 7]
0 -> [0] -> 0
1 -> [1] -> 1
2 -> [0 0] -> 2
3 -> [1 0] -> 3
4 -> [2] -> 4
5 -> [3] -> 5
6 -> [0 1] -> 6
7 -> [1 1] -> 7
8 -> [0 0 0] -> 8
9 -> [1 0 0] -> 9</pre>
 
=={{header|Phix}}==
===base 11===
{{trans|Sidef}}
<lang {{libheader|Phix>include /mpfr.e}}
Note this is ''not'' supported under pwa/p2js because mpz_set_str() currently only handles bases 2, 8, 10, and 16.
<!--<syntaxhighlight lang="phix">-->
procedure rank(mpz r, sequence s)
<span style="color: #008080;">without</span> <span style="color: #008080;">javascript_semantics</span>
for i=1 to length(s) do
<span style="color: #008080;">include</span> <span style="color: #004080;">mpfr</span><span style="color: #0000FF;">.</span><span style="color: #000000;">e</span>
s[i] = sprintf("%d",s[i])
end for
<span style="color: #008080;">procedure</span> <span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">r</span><span style="color: #0000FF;">,</span> <span style="color: #004080;">sequence</span> <span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
mpz_set_str(r,join(s,'a'),11)
<span style="color: #000000;">s</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">deep_copy</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span>
end procedure
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">s</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
function unrank(mpz i)
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
sequence res = split(mpz_get_str(i,11),'a')
<span style="color: #7060A8;">mpz_set_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">s</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'a'</span><span style="color: #0000FF;">),</span><span style="color: #000000;">11</span><span style="color: #0000FF;">)</span>
for j=1 to length(res) do
<span style="color: #008080;">end</span> <span style="color: #008080;">procedure</span>
{{res[j]}} = scanf(res[j],"%d")
end for
<span style="color: #008080;">function</span> <span style="color: #000000;">unrank</span><span style="color: #0000FF;">(</span><span style="color: #004080;">mpz</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
return res
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span><span style="color: #000000;">11</span><span style="color: #0000FF;">),</span><span style="color: #008000;">'a'</span><span style="color: #0000FF;">)</span>
end function
<span style="color: #008080;">for</span> <span style="color: #000000;">j</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #0000FF;">{{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">]}}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">scanf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">j</span><span style="color: #0000FF;">],</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">)</span>
sequence l = {1, 2, 3, 10, 100, 987654321}
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
mpz n = mpz_init()
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
rank(n,l)
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
sequence u = unrank(n)
?{l,mpz_get_str(n),u}</lang>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">10</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">100</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">987654321</span><span style="color: #0000FF;">}</span>
<span style="color: #004080;">mpz</span> <span style="color: #000000;">n</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">mpz_init</span><span style="color: #0000FF;">()</span>
<span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">,</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">u</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unrank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%V\n"</span><span style="color: #0000FF;">,{{</span><span style="color: #000000;">l</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">mpz_get_str</span><span style="color: #0000FF;">(</span><span style="color: #000000;">n</span><span style="color: #0000FF;">),</span><span style="color: #000000;">u</span><span style="color: #0000FF;">}})</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
Line 590 ⟶ 965:
===bijective===
{{trans|Python}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<lang Phix>include bigint.e
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
 
<span style="color: #008080;">function</span> <span style="color: #000000;">unrank</span><span style="color: #0000FF;">(</span><span style="color: #004080;">atom</span> <span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
function unrank(object n)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">sprintf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"%0b"</span><span style="color: #0000FF;">,</span><span style="color: #000000;">n</span><span style="color: #0000FF;">)</span>
sequence res = bi_sprint(n,2)
<span style="color: #008080;">if</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">=</span><span style="color: #008000;">"1"</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">0</span><span style="color: #0000FF;">}</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
if res="1" then return {0} end if
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">split</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$],</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">,</span><span style="color: #004600;">false</span><span style="color: #0000FF;">)</span>
res = split(res[2..$],'0')
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span> <span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">res</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span> <span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
for i=1 to length(res) do res[i] = length(res[i]) end for
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
return res
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
end function
<span style="color: #008080;">function</span> <span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">x</span><span style="color: #0000FF;">={}</span> <span style="color: #008080;">then</span> <span style="color: #008080;">return</span> <span style="color: #000000;">0</span> <span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">y</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #000000;">0</span><span style="color: #0000FF;">,</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">))</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">1</span> <span style="color: #008080;">to</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #000000;">y</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">]</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">repeat</span><span style="color: #0000FF;">(</span><span style="color: #008000;">'1'</span><span style="color: #0000FF;">,</span><span style="color: #000000;">x</span><span style="color: #0000FF;">[</span><span style="color: #000000;">i</span><span style="color: #0000FF;">])</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
<span style="color: #004080;">atom</span> <span style="color: #0000FF;">{{</span><span style="color: #000000;">res</span><span style="color: #0000FF;">}}</span> <span style="color: #0000FF;">=</span> <span style="color: #7060A8;">scanf</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"0b1"</span><span style="color: #0000FF;">&</span><span style="color: #7060A8;">join</span><span style="color: #0000FF;">(</span><span style="color: #000000;">y</span><span style="color: #0000FF;">,</span><span style="color: #008000;">'0'</span><span style="color: #0000FF;">),</span><span style="color: #008000;">"%d"</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">res</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #008080;">for</span> <span style="color: #000000;">i</span><span style="color: #0000FF;">=</span><span style="color: #000000;">0</span> <span style="color: #008080;">to</span> <span style="color: #000000;">10</span> <span style="color: #008080;">do</span>
function rank(sequence x)
<span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">unrank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">i</span><span style="color: #0000FF;">)</span>
if x={} then return "0" end if
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%3d : %-18v: %d\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">i</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)})</span>
for i=1 to length(x) do
<span style="color: #008080;">end</span> <span style="color: #008080;">for</span>
x[i] = repeat('1',x[i])
end for
<span style="color: #004080;">sequence</span> <span style="color: #000000;">x</span> <span style="color: #0000FF;">=</span> <span style="color: #0000FF;">{</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">2</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">3</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">5</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">8</span><span style="color: #0000FF;">}</span>
bigint res = bi_new("0b1"&join(x,'0'))
<span style="color: #7060A8;">printf</span><span style="color: #0000FF;">(</span><span style="color: #000000;">1</span><span style="color: #0000FF;">,</span><span style="color: #008000;">"%v =&gt; %d =&gt; %v\n"</span><span style="color: #0000FF;">,{</span><span style="color: #000000;">x</span><span style="color: #0000FF;">,</span><span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">),</span><span style="color: #000000;">unrank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">rank</span><span style="color: #0000FF;">(</span><span style="color: #000000;">x</span><span style="color: #0000FF;">))})</span>
return res
<!--</syntaxhighlight>-->
end function
for i=0 to 10 do
sequence a = unrank(i)
printf(1,"%3d : %-18s: %s\n",{i, sprint(a), bi_sprint(rank(a))})
end for
 
sequence x = {1, 2, 3, 5, 8}
printf(1,"%s => %s => %s\n",{sprint(x),bi_sprint(rank(x)),sprint(unrank(rank(x)))})</lang>
{{out}}
<pre>
Line 633 ⟶ 1,010:
 
=={{header|Python}}==
<langsyntaxhighlight lang="python">def rank(x): return int('a'.join(map(str, [1] + x)), 11)
 
def unrank(n):
Line 645 ⟶ 1,022:
print n
l = unrank(n)
print l</langsyntaxhighlight>
{{out}}
<pre>
Line 655 ⟶ 1,032:
=== Bijection ===
Each number in the list is stored as a length of 1s, separated by 0s, and the resulting string is prefixed by '1', then taken as a binary number. Empty list is mapped to 0 as a special case. Don't use it on large numbers.
<langsyntaxhighlight lang="python">def unrank(n):
return map(len, bin(n)[3:].split("0")) if n else []
 
Line 667 ⟶ 1,044:
x = [1, 2, 3, 5, 8];
print x, rank(x), unrank(rank(x))
</syntaxhighlight>
</lang>
{{out}}
<pre>
Line 684 ⟶ 1,061:
[1, 2, 3, 5, 8] 14401279 [1, 2, 3, 5, 8]
</pre>
 
=={{header|Quackery}}==
 
<syntaxhighlight lang="quackery"> [ $ "" swap
witheach
[ number$
char A join join ]
11 base put
$->n drop
base release ] is rank ( [ --> n )
 
[ 11 base put
number$
base release
[] $ "" rot
witheach
[ dup char A = iff
[ drop
$->n drop join
$ "" ]
else join ]
drop ] is unrank ( n --> [ )
</syntaxhighlight>
 
{{out}}
Testing in the Quackery shell.
<pre>/O> []
... 5 random 5 + times
... [ 10 random 1+ join ]
... say " Random list: "
... dup echo cr
... rank
... say " That list, ranked: "
... dup echo cr
... unrank
... say "That number, unranked: "
... echo cr
...
Random list: [ 9 9 10 6 1 7 5 2 ]
That list, ranked: 459086440222376570
That number, unranked: [ 9 9 10 6 1 7 5 2 ]
 
Stack empty.</pre>
 
=={{header|Racket}}==
Line 689 ⟶ 1,109:
{{trans|Tcl}} (which gives credit to [[#D]])
 
<langsyntaxhighlight lang="racket">#lang racket/base
(require (only-in racket/string string-join string-split))
 
Line 710 ⟶ 1,130:
(displayln loi)
(displayln rnk)
(displayln urk))</langsyntaxhighlight>
 
{{out}}
Line 717 ⟶ 1,137:
1828381281448726746426183460251416730347660304377387
(1 2 3 10 100 987654321 135792468107264516704251 7)</pre>
 
=={{header|Raku}}==
(formerly Perl 6)
Here is a cheap solution using a base-11 encoding and string operations:
<syntaxhighlight lang="raku" line>sub rank(*@n) { :11(@n.join('A')) }
sub unrank(Int $n) { $n.base(11).split('A') }
 
say my @n = (1..20).roll(12);
say my $n = rank(@n);
say unrank $n;</syntaxhighlight>
{{out}}
<pre>1 11 16 1 3 9 0 2 15 7 19 10
25155454474293912130094652799
1 11 16 1 3 9 0 2 15 7 19 10</pre>
 
Here is a bijective solution that does not use string operations.
 
<syntaxhighlight lang="raku" line>multi infix:<rad> () { 0 }
multi infix:<rad> ($a) { $a }
multi infix:<rad> ($a, $b) { $a * $*RADIX + $b }
multi expand(Int $n is copy, 1) { $n }
multi expand(Int $n is copy, Int $*RADIX) {
my \RAD = $*RADIX;
my @reversed-digits = gather while $n > 0 {
take $n % RAD;
$n div= RAD;
}
eager for ^RAD {
[rad] reverse @reversed-digits[$_, * + RAD ... *]
}
}
multi compress(@n where @n == 1) { @n[0] }
multi compress(@n is copy) {
my \RAD = my $*RADIX = @n.elems;
[rad] reverse gather while @n.any > 0 {
(state $i = 0) %= RAD;
take @n[$i] % RAD;
@n[$i] div= RAD;
$i++;
}
}
sub rank(@n) { compress (compress(@n), @n - 1)}
sub unrank(Int $n) { my ($a, $b) = expand $n, 2; expand $a, $b + 1 }
 
my @list = (^10).roll((2..20).pick);
my $rank = rank @list;
say "[$@list] -> $rank -> [{unrank $rank}]";
 
for ^10 {
my @unrank = unrank $_;
say "$_ -> [$@unrank] -> {rank @unrank}";
}</syntaxhighlight>
 
{{out}}
<pre>[7 1 4 7 7 0 2 7 7 0 7 7] -> 20570633300796394530947471 -> [7 1 4 7 7 0 2 7 7 0 7 7]
0 -> [0] -> 0
1 -> [1] -> 1
2 -> [0 0] -> 2
3 -> [1 0] -> 3
4 -> [2] -> 4
5 -> [3] -> 5
6 -> [0 1] -> 6
7 -> [1 1] -> 7
8 -> [0 0 0] -> 8
9 -> [1 0 0] -> 9</pre>
 
=={{header|REXX}}==
Line 722 ⟶ 1,213:
 
No checks are made that the numbers are non-negative integers or malformed integers.
<langsyntaxhighlight lang="rexx">/*REXX program assigns an integer for a finite list of arbitrary non-negative integers. */
parse arg $ /*obtain optional argument (int list).*/
if $='' | $="," then $=3 14 159 265358979323846 /*Not specified? Then use the default.*/
Line 735 ⟶ 1,226:
/*──────────────────────────────────────────────────────────────────────────────────────*/
rank: return x2d( translate( space( arg(1) ), 'c', ",") )
unrank: return space( translate( d2x( arg(1) ), ',', "C") )</langsyntaxhighlight>
{{out|output|text=&nbsp; when using the default input:}}
<pre>
Line 745 ⟶ 1,236:
=={{header|Ruby}}==
{{trans|Python}}
<langsyntaxhighlight lang="ruby">def rank(arr)
arr.join('a').to_i(11)
end
 
def unrank(n)
n.to_s(11).split('a').collect{|x| x.map(&:to_i})
end
 
Line 758 ⟶ 1,249:
p n
l = unrank(n)
p l</langsyntaxhighlight>
{{out}}
<pre>
Line 767 ⟶ 1,258:
=== Bijection ===
{{trans|Python}}
<langsyntaxhighlight lang="ruby">def unrank(n)
return [0] if n==1
n.to_s(2)[1..-1].split('0',-1).map(&:size)
Line 783 ⟶ 1,274:
puts
x = [1, 2, 3, 5, 8]
puts "#{x} => #{rank(x)} => #{unrank(rank(x))}"</langsyntaxhighlight>
{{out}}
<pre>
Line 800 ⟶ 1,291:
[1, 2, 3, 5, 8] => 14401279 => [1, 2, 3, 5, 8]
</pre>
 
=={{header|Scala}}==
{{Out}}Best seen in running your browser either by [https://scalafiddle.io/sf/7NvnU4t/0 ScalaFiddle (ES aka JavaScript, non JVM)] or [https://scastie.scala-lang.org/l0uAGyyCTDSAV9Q45vRGaA Scastie (remote JVM)].
<syntaxhighlight lang="scala">object IndexFiniteList extends App {
val (defBase, s) = (10, Seq(1, 2, 3, 10, 100, 987654321))
 
def rank(x: Seq[Int], base: Int = defBase) =
BigInt(x.map(Integer.toString(_, base)).mkString(base.toHexString), base + 1)
 
def unrank(n: BigInt, base: Int = defBase): List[BigInt] =
n.toString(base + 1).split((base).toHexString).map(BigInt(_)).toList
 
val ranked = rank(s)
 
println(s.mkString("[", ", ", "]"))
println(ranked)
println(unrank(ranked).mkString("[", ", ", "]"))
 
}</syntaxhighlight>
 
=={{header|Sidef}}==
{{trans|Ruby}}
<langsyntaxhighlight lang="ruby">func rank(Array arr) {
Number(arr.join('a'), 11)
}
Line 816 ⟶ 1,326:
say n
var l = unrank(n)
say l</langsyntaxhighlight>
{{out}}
<pre>[1, 2, 3, 10, 100, 987654321]
<pre>
[1, 2, 3, 10, 100, 987654321]
14307647611639042485573
[1, 2, 3, 10, 100, 987654321]</pre>
</pre>
 
'''Bijection:'''
<langsyntaxhighlight lang="ruby">func unrank(Number n) {
n == 1 ? [0]
: n.base(2).substr(1).split('0', -1).map{.len}
Line 841 ⟶ 1,349:
say ''
var x = [1, 2, 3, 5, 8]
say "#{x} => #{rank(x)} => #{unrank(rank(x))}"</langsyntaxhighlight>
{{out}}
<pre> 0 : [] : 0
<pre>
0 : [] : 0
1 : [0] : 1
2 : [0, 0] : 2
Line 856 ⟶ 1,363:
10 : [0, 1, 0] : 10
 
[1, 2, 3, 5, 8] => 14401279 => [1, 2, 3, 5, 8]</pre>
</pre>
 
=={{header|Tcl}}==
{{works with|Tcl|8.6}}
Inspired by the [[#D|D solution]].
<langsyntaxhighlight lang="tcl">package require Tcl 8.6
 
proc rank {integers} {
Line 870 ⟶ 1,376:
proc unrank {codedValue} {
lmap i [split $codedValue 8] {scan $i %llo}
}</langsyntaxhighlight>
Demonstrating:
<langsyntaxhighlight lang="tcl">set s {1 2 3 10 100 987654321 135792468107264516704251 7}
puts "prior: $s"
set c [rank $s]
puts "encoded: $c"
set t [unrank $c]
puts "after: $t"</langsyntaxhighlight>
{{out}}
<pre>
Line 883 ⟶ 1,389:
encoded: 1828381281448726746426183460251416730347660304377387
after: 1 2 3 10 100 987654321 135792468107264516704251 7
</pre>
 
=={{header|Wren}}==
{{trans|Kotlin}}
{{libheader|Wren-big}}
<syntaxhighlight lang="wren">import "./big" for BigInt
 
// Separates each integer in the list with an 'a' then encodes in base 11.
// Empty list mapped to '-1'.
var rank = Fn.new { |li|
if (li.count == 0) return BigInt.minusOne
return BigInt.fromBaseString(li.join("a"), 11)
}
 
var unrank = Fn.new { |r|
if (r == BigInt.minusOne) return []
return r.toBaseString(11).split("a").map { |d| (d != "") ? Num.fromString(d) : 0 }.toList
}
 
// Each integer n in the list mapped to '1' plus n '0's.
// Empty list mapped to '0'
var rank2 = Fn.new { |li|
if (li.isEmpty) return BigInt.zero
var sb = ""
for (i in li) sb = sb + "1" + ("0" * i)
return BigInt.fromBaseString(sb, 2)
}
 
var unrank2 = Fn.new { |r|
if (r == BigInt.zero) return []
return r.toBaseString(2)[1..-1].split("1").map { |d| d.count }.toList
}
 
var li = [0, 1, 2, 3, 10, 100, 987654321]
System.print("Before ranking : %(li)")
var r = rank.call(li)
System.print("Rank = %(r)")
li = unrank.call(r)
System.print("After unranking : %(li)")
System.print("\nAlternative approach (not suitable for large numbers)...\n")
li = li[0..-2]
System.print("Before ranking : %(li)")
r = rank2.call(li)
System.print("Rank = %(r)")
li = unrank2.call(r)
System.print("After unranking : %(li)")</syntaxhighlight>
 
{{out}}
<pre>
Before ranking : [0, 1, 2, 3, 10, 100, 987654321]
Rank = 828335141480036653618783
After unranking : [0, 1, 2, 3, 10, 100, 987654321]
 
Alternative approach (not suitable for large numbers)...
 
Before ranking : [0, 1, 2, 3, 10, 100]
Rank = 4364126777249122850009283661412696064
After unranking : [0, 1, 2, 3, 10, 100]
</pre>
 
=={{header|zkl}}==
Using GMP, base 11 and sometimes strings to represent big ints.
<langsyntaxhighlight lang="zkl">var BN=Import("zklBigNum");
fcn rank(ns) { BN(ns.concat("A"),11) }
fcn unrank(bn) { bn.toString(11).split("a").apply("toInt") }
fcn unrankS(bn){ bn.toString(11).split("a") }</langsyntaxhighlight>
<langsyntaxhighlight lang="zkl">fcn rankz(ns,S=False){
ns.println();
rank(ns).println();
Line 898 ⟶ 1,462:
}
rankz(T(1,2,3,10,100,987654321));
rankz(T(1,2,3,10,100,987654321,"135792468107264516704251",7),True);</langsyntaxhighlight>
{{out}}
<pre>
Peak
2,442

edits

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