Non-continuous subsequences: Difference between revisions

A ''continuous'' subsequence is one in which no elements are missing between the first and last elements of the subsequence.

 

 

 

 

=={{header|Ada}}==

===Recursive===

 

procedure Test_Non_Continuous is

Put_NCS ((1,2,3,4)); New_Line;

Put_NCS ((1,2,3,4,5)); New_Line;

 

<pre style="height:30ex;overflow:scroll"> 1 3

 

2 5

3 5</pre>

=={{header|ALGOL 68}}==

===Recursive===

 

{{works with|ELLA ALGOL 68|Any (with appropriate job cards) - tested with release [http://sourceforge.net/projects/algol68/files/algol68toc/algol68toc-1.8.8d/algol68toc-1.8-8d.fc9.i386.rpm/download 1.8-8d]}}

MODE SEQMODE = CHAR;

MODE SEQ = [1:0]SEQMODE;

print((seq, new line))

# OD # )

<pre>

aeiu

 

Note: This specimen can only handle sequences of length less than ''bits width'' of '''bits'''.

MODE SEQ = [1:0]SEQMODE;

MODE YIELDSEQ = PROC(SEQ)VOID;

print((seq, new line))

# OD # )

<pre>

iu

ahk forum: [http://www.autohotkey.com/forum/viewtopic.php?p=277328#277328 discussion]

 

MsgBox % noncontinuous("1,2,3,4", ",")

 

ToBin(n,W=16) { ; LS W-bits of Binary representation of n

Return W=1 ? n&1 : ToBin(n>>1,W-1) . n&1

 

=={{header|Bracmat}}==

 

=={{header|C}}==

Note: This specimen can only handle lists of length less than the number of bits in an '''int'''.

#include <stdio.h>

 

Example use:

<pre>

$ ./noncont 1 2 3 4

2 4

1 4

$ ./noncont 1 2 3 4 5 6 7 8 9 0 | wc -l

968

</pre>

 

===Recursive method===

Using recursion and a state transition table.

 

typedef unsigned char sint;

pick(c - 1, 0, s_blnk, v + 1, 0);

return 0;

<pre>% ./a.out 1 2 3 4

1 3

% ./a.out 1 2 3 4 5 6 7 8 9 0 | wc -l

968</pre>

 

=={{header|Clojure}}==

Here's a simple approach that uses the clojure.contrib.combinatorics library to generate subsequences, and then filters out the continuous subsequences using a naïve subseq test:

 

(use '[clojure.contrib.combinatorics :only (subsets)])

 

 

(filter (of-min-length 2) (non-continuous-subsequences [:a :b :c :d]))

 

=={{header|CoffeeScript}}==

Use binary bitmasks to enumerate our sequences.

is_contigous_binary = (n) ->

# return true if binary representation of n is

num_solutions = non_contig_subsequences(arr).length

console.log "for n=#{n} there are #{num_solutions} solutions"

 

> coffee non_contig_subseq.coffee

[ [ 1, 3 ],

for n=9 there are 466 solutions

for n=10 there are 968 solutions

 

=={{header|Common Lisp}}==

looking at the screen wondering what's wrong for about half an hour -->

 

(labels ((subsequences (tail &optional (acc '()) (result '()))

"Return a list of the subsequence designators of the

(map-into subsequence-d 'first subsequence-d)))

(let ((nc-subsequences (delete-if #'continuous-p (subsequences list))))

 

{{trans|Scheme}}

 

(labels ((recurse (s list)

(if (endp list)

(recurse s xs))

(recurse (+ s 1) xs)))))))

 

=={{header|D}}==

===Recursive Version===

{{trans|Python}}

if (seq.length) {

aux ~= seq[0] ~ ys;

} else

}

 

{{out}}

<pre>[[1, 3]]

[2, 5]

[3, 5]</pre>

===Faster Lazy Version===

This version doesn't copy the sub-arrays.

T[] seq;

 

int result;

 

bool nc = false;

if (k == 0) {

if (nc) {

result = dg(auxS);

if (result)

}

break;

} else if (k % 2) {

nc = true;

}

void main() {

import std.array, std.range;

foreach (s; Ncsub!int(r))

counter++;

assert(counter == 16_776_915);

 

=={{header|Go}}==

Generate the power set (power sequence, actually) with a recursive function, but keep track of the state of the subsequence on the way down. When you get to the bottom, if state == non-continuous, then include the subsequence. It's just filtering merged in with generation.

 

import "fmt"

fmt.Println(" ", s)

}

<pre>

5 non-continuous subsequences:

===Generalized monadic filter===

 

 

fenceM p q s [] = guard (q s) >> return []

return $ f x ys

 

 

<pre>*Main> ncsubseq [1..3]

[[1,3]]

This implementation works by computing templates of all possible subsequences of the given length of sequence, discarding the continuous ones, then applying the remaining templates to the input list.

 

ncs xs = map (map fst . filter snd . zip xs) $

filter (not . continuous) $

 

===Recursive===

Recursive method with powerset as helper function.

 

 

poset = foldr (\x p -> p ++ map (x:) p) [[]]

nc [_] [] = [[]]

nc (_:x:xs) [] = nc [x] xs

 

*Main> ncsubs "aaa"

["aa"]

[]

(0.00 secs, 0 bytes)

 

=={{header|J}}==

We select those combinations where the end of the first continuous subsequence appears before the start of the last continuous subsequence:

 

firstend=:1 0 i.&1@E."1 ]

laststart=: 0 1 {:@I.@E."1 ]

 

Example use:

┌───┬───┬───┬─────┬─────┐

│2 4│1 4│1 3│1 3 4│1 2 4│

└──┴──┴──┴───┴───┴──┴──┴───┴──┴───┴───┴────┴───┴───┴────┴────┘

#noncont i.10

 

Alternatively, since there are relatively few continuous sequences, we could specifically exclude them:

 

 

=={{header|JavaScript}}==

 

{{works with|SpiderMonkey}}

var non_continuous = new Array();

for (var i = 0; i < ary.length; i++) {

load('json2.js'); /* http://www.json.org/js.html */

 

 

<pre>[[1,3],[1,4],[2,4],[1,2,4],[1,3,4]]</pre>

 

 

n=5

 

 

 

=={{header|OCaml}}==

{{trans|Generalized monadic filter}}

 

[] ->

if s >= 3 then

fence (s + 1) xs

 

 

<pre># ncsubseq [1;2;3];;

- : int list list = [[1; 3]]

=={{header|Oz}}==

A nice application of finite set constraints. We just describe what we want and the constraint system will deliver it:

fun {NCSubseq SeqList}

Seq = {FS.value.make SeqList}

end

in

 

=={{header|Perl}}==

sub non_continuous {

 

for ($idx .. $max) {

}

 

 

 

 

 

=={{header|PicoLisp}}==

{{trans|Scheme}}

(let S 0

(recur (S Lst)

(mapcar '((YS) (cons X YS))

(recurse S XS) )

 

=={{header|Pop11}}==

variables to keep track if subsequence is continuous.

 

lvars acc = [], gap_started = false, is_continuous = true;

define do_it(l1, l2);

enddefine;

 

 

 

=={{header|PowerShell}}==

{

$sc = $S.count

}

 

 

=={{header|Prolog}}==

We explain to Prolog how to build a non continuous subsequence of a list L, then we ask Prolog to fetch all the subsequences.

 

% fetch all the subsequences

ncsubs(L, LNCSL) :-

reverse(L, [_|SL1]),

reverse(SL1, SL)).

Example :

 

=={{header|Python}}==

{{trans|Scheme}}

 

if seq:

x = seq[:1]

return [x + ys for ys in ncsub(xs, s + p1)] + ncsub(xs, s + p2)

else:

 

<pre>>>> ncsub(range(1, 4))

[[1, 3]]

A faster Python + Psyco JIT version:

 

import psyco

 

psyco.full()

n = 10 if len(argv) < 2 else int(argv[1])

 

=={{header|R}}==

The idea behind this is to loop over the possible lengths of subsequence, finding all subsequences then discarding those which are continuous.

 

{

n <- length(x)

# Example usage

ncsub(1:4)

 

=={{header|REXX}}==

 

 

 

 

</pre>

 

 

</pre>

 

 

</pre>

 

 

</pre>

 

Uses code from [[Power Set]].

 

def func_power_set

inject([[]]) { |ps,item| # for each item in the Array

}

end

def non_continuous_subsequences

end

true

end

p (1..3).to_a.non_continuous_subsequences

p (1..4).to_a.non_continuous_subsequences

 

<pre>[[1, 3]]

[[1, 3], [1, 4], [2, 4], [1, 2, 4], [1, 3, 4]]

[[1, 3], [1, 4], [2, 4], [1, 2, 4], [1, 3, 4], [1, 5], [2, 5], [1, 2, 5], [3, 5], [1, 3, 5],

 

 

 

(let recurse ((s 0)

(lst lst))

(map (lambda (ys) (cons x ys))

(recurse s xs))

 

<pre>> (ncsubseq '(1 2 3))

((1 3))

> (ncsubseq '(1 2 3 4 5))

((1 2 3 5) (1 2 4 5) (1 2 4) (1 2 5) (1 3 4 5) (1 3 4) (1 3 5) (1 3) (1 4 5) (1 4) (1 5) (2 3 5) (2 4 5) (2 4) (2 5) (3 5))</pre>

 

=={{header|Standard ML}}==

{{trans|Generalized monadic filter}}

 

if s >= 3 then

[[]]

fence (s + 1) xs

 

 

<pre>- ncsubseq [1,2,3];

val it = [[1,3]] : int list list

This Tcl implementation uses the ''subsets'' function from [[Power Set]], which is acceptable as that conserves the ordering, as well as a problem-specific test function ''is_not_continuous'' and a generic list filter ''lfilter'':

 

set res [list [list]]

foreach e $l {

 

% lfilter is_not_continuous [subsets {1 2 3 4}]

 

=={{header|Ursala}}==

To do it the lazy programmer way, apply the powerset library function to the list, which will generate all continuous and non-continuous subsequences of it, and then delete the subsequences that are also substrings (hence continuous) using a judicious combination of the built in substring predicate (K3), negation (Z), and distributing filter (K17) operator suffixes. This function will work on lists of any type. To meet the requirement for structural equivalence, the list items are first uniquely numbered (num), and the numbers are removed afterwards (rSS).

 

 

noncontinuous = num; ^rlK3ZK17rSS/~& powerset

#show+

 

 

<pre>abce

abd

be

ce</pre>