Shortest common supersequence: Difference between revisions
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{{
;;Task:
Given two strings <math>u</math> and <math>v</math>, find the shortest possible sequence <math>s</math>, which is the shortest common super-sequence of <math>u</math> and <math>v</math> where both <math>u</math> and <math>v</math> are a subsequence of <math>s</math>. Defined as such, <math>s</math> is not necessarily unique.
Demonstrate this by printing <math>s</math> where <math>u = </math>“<tt>abcbdab</tt>” and <math>v = </math>“<tt>bdcaba</tt>”.
<!-- This example is taken from the Wikipedia page. -->
;Also see:
* [[wp:Shortest_common_supersequence_problem|Wikipedia: shortest common supersequence]]
<br><br>
=={{header|11l}}==
{{trans|C++}}
<syntaxhighlight lang="11l">F scs(String x, y)
I x.empty
R y
I y.empty
R x
I x[0] == y[0]
R x[0]‘’scs(x[1..], y[1..])
I scs(x, y[1..]).len <= scs(x[1..], y).len
R y[0]‘’scs(x, y[1..])
E
R x[0]‘’scs(x[1..], y)
print(scs(‘abcbdab’, ‘bdcaba’))</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Ada}}==
{{trans|C++}}
<syntaxhighlight lang="ada">with Ada.Text_IO;
procedure Shortest is
function Scs (Left, Right : in String) return String is
Left_Tail : String renames Left (Left'First + 1 .. Left'Last);
Right_Tail : String renames Right (Right'First + 1 .. Right'Last);
begin
if Left = "" then return Right; end if;
if Right = "" then return Left; end if;
if Left (Left'First) = Right (Right'First) then
return Left (Left'First) & Scs (Left_Tail, Right_Tail);
end if;
declare
S1 : constant String := Scs (Left, Right_Tail);
S2 : constant String := Scs (Left_Tail, Right);
begin
return (if S1'Length <= S2'Length
then Right (Right'First) & S1
else Left (Left'First) & S2);
end;
end Scs;
procedure Exercise (Left, Right : String) is
use Ada.Text_Io;
begin
Put ("scs ( "); Put (Left); Put (" , "); Put (Right); Put ( " ) -> ");
Put (Scs (Left, Right));
New_Line;
end Exercise;
begin
Exercise ("abcbdab", "bdcaba");
Exercise ("WEASELS", "WARDANCE");
end Shortest;</syntaxhighlight>
{{out}}
<pre>
scs ( abcbdab , bdcaba ) -> abdcabdab
scs ( WEASELS , WARDANCE ) -> WARDEANCSELS
</pre>
=={{header|ALGOL 68}}==
{{Trans|C++}}
<syntaxhighlight lang="algol68">BEGIN
PRIO SCS = 1;
# returns the shortest common supersequence of x and y #
OP SCS = ( STRING x, y )STRING:
IF x = "" THEN y
ELIF y = "" THEN x
ELIF x[ LWB x ] = y[ LWB y ]
THEN x[ LWB x ] + ( x[ LWB x + 1 : ] SCS y[ LWB y + 1 : ] )
ELIF STRING x y sub = x SCS y[ LWB y + 1 : ];
STRING x sub y = x[ LWB x + 1 : ] SCS y;
INT x y sub size = ( UPB x y sub - LWB x y sub ) + 1;
INT x sub y size = ( UPB x sub y - LWB x sub y ) + 1;
x y sub size <= x sub y size
THEN y[ LWB y ] + x y sub
ELSE x[ LWB x ] + x sub y
FI # SCS # ;
print( ( "abcbdab" SCS "bdcaba", newline ) )
END</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|C}}==
The C99 code here isn't all that different from Levenstein distance calculation.
<syntaxhighlight lang="c">#include <stdio.h>
#include <string.h>
typedef struct link link_t;
struct link {
int len;
char letter;
link_t *next;
};
// Stores a copy of a SCS of x and y in out. Caller needs to make sure out is long enough.
int scs(char *x, char *y, char *out)
{
int lx = strlen(x), ly = strlen(y);
link_t lnk[ly + 1][lx + 1];
for (int i = 0; i < ly; i++)
lnk[i][lx] = (link_t) {ly - i, y[i], &lnk[i + 1][lx]};
for (int j = 0; j < lx; j++)
lnk[ly][j] = (link_t) {lx - j, x[j], &lnk[ly][j + 1]};
lnk[ly][lx] = (link_t) {0};
for (int i = ly; i--; ) {
for (int j = lx; j--; ) {
link_t *lp = &lnk[i][j];
if (y[i] == x[j]) {
lp->next = &lnk[i+1][j+1];
lp->letter = x[j];
} else if (lnk[i][j+1].len < lnk[i+1][j].len) {
lp->next = &lnk[i][j+1];
lp->letter = x[j];
} else {
lp->next = &lnk[i+1][j];
lp->letter = y[i];
}
lp->len = lp->next->len + 1;
}
}
for (link_t *lp = &lnk[0][0]; lp; lp = lp->next)
*out++ = lp->letter;
return 0;
}
int main(void)
{
char x[] = "abcbdab", y[] = "bdcaba", res[128];
scs(x, y, res);
printf("SCS(%s, %s) -> %s\n", x, y, res);
return 0;
}</syntaxhighlight>
{{out}}
<pre>
SCS(abcbdab, bdcaba) -> abdcabdab
</pre>
=={{header|C sharp}}==
{{trans|Java}}This is based on the Java version, but with added caching.
<syntaxhighlight lang="csharp">public class ShortestCommonSupersequence
{
Dictionary<(string, string), string> cache = new();
public string scs(string x, string y)
{
if (x.Length == 0) return y;
if (y.Length == 0) return x;
if (cache.TryGetValue((x, y), out var result)) return result;
if (x[0] == y[0])
{
return cache[(x, y)] = x[0] + scs(x.Substring(1), y.Substring(1));
}
var xr = scs(x.Substring(1), y);
var yr = scs(x, y.Substring(1));
if (yr.Length <= xr.Length)
{
return cache[(x, y)] = y[0] + yr;
}
else
{
return cache[(x, y)] = x[0] + xr;
}
}
public static void Main(string[] args)
{
var scs = new ShortestCommonSupersequence();
Console.WriteLine(scs.scs("abcbdab", "bdcaba"));
}
}
</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|C++}}==
{{trans|Java}}
<syntaxhighlight lang="cpp">#include <iostream>
std::string scs(std::string x, std::string y) {
if (x.empty()) {
return y;
}
if (y.empty()) {
return x;
}
if (x[0] == y[0]) {
return x[0] + scs(x.substr(1), y.substr(1));
}
if (scs(x, y.substr(1)).size() <= scs(x.substr(1), y).size()) {
return y[0] + scs(x, y.substr(1));
} else {
return x[0] + scs(x.substr(1), y);
}
}
int main() {
auto res = scs("abcbdab", "bdcaba");
std::cout << res << '\n';
return 0;
}</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|D}}==
{{trans|Racket}}
<syntaxhighlight lang="d">import std.stdio, std.functional, std.array, std.range;
dstring scs(in dstring x, in dstring y) nothrow @safe {
alias mScs = memoize!scs;
if (x.empty) return y;
if (y.empty) return x;
if (x.front == y.front)
return x.front ~ mScs(x.dropOne, y.dropOne);
if (mScs(x, y.dropOne).length <= mScs(x.dropOne, y).length)
return y.front ~ mScs(x, y.dropOne);
else
return x.front ~ mScs(x.dropOne, y);
}
void main() @safe {
scs("abcbdab", "bdcaba").writeln;
}</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|EasyLang}}==
{{trans|C++}}
<syntaxhighlight>
func$ car x$ .
return substr x$ 1 1
.
func$ cdr x$ .
return substr x$ 2 9999
.
func$ scs x$ y$ .
if x$ = ""
return y$
.
if y$ = ""
return x$
.
if car x$ = car y$
return car x$ & scs cdr x$ cdr y$
.
r1$ = scs x$ cdr y$
r2$ = scs cdr x$ y$
if len r1$ <= len r2$
return car y$ & r1$
else
return car x$ & r2$
.
.
print scs "abcbdab" "bdcaba"
</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Elixir}}==
{{trans|Ruby}}
{{works with|Elixir|1.3}}
uses 'LCS' from [[Longest common subsequence#Elixir|here]]
<syntaxhighlight lang="elixir">defmodule SCS do
def scs(u, v) do
lcs = LCS.lcs(u, v) |> to_charlist
scs(to_charlist(u), to_charlist(v), lcs, []) |> to_string
end
defp scs(u, v, [], res), do: Enum.reverse(res) ++ u ++ v
defp scs([h|ut], [h|vt], [h|lt], res), do: scs(ut, vt, lt, [h|res])
defp scs([h|_]=u, [vh|vt], [h|_]=lcs, res), do: scs(u, vt, lcs, [vh|res])
defp scs([uh|ut], v, lcs, res), do: scs(ut, v, lcs, [uh|res])
end
u = "abcbdab"
v = "bdcaba"
IO.puts "SCS(#{u}, #{v}) = #{SCS.scs(u, v)}"</syntaxhighlight>
{{out}}
<pre>
SCS(abcbdab, bdcaba) = abdcabdab
</pre>
=={{header|Factor}}==
{{trans|Julia}}
<syntaxhighlight lang="factor">USING: combinators io kernel locals math memoize sequences ;
MEMO:: scs ( x y -- seq )
{
{ [ x empty? ] [ y ] }
{ [ y empty? ] [ x ] }
{ [ x first y first = ]
[ x rest y rest scs x first prefix ] }
{ [ x y rest scs length x rest y scs length <= ]
[ x y rest scs y first prefix ] }
[ x rest y scs x first prefix ]
} cond ;
"abcbdab" "bdcaba" scs print</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|FreeBASIC}}==
<syntaxhighlight lang="vbnet">Function LCS(a As String, b As String) As String
Dim As String x, y
If Len(a) = 0 Or Len(b) = 0 Then
Return ""
Elseif Right(a, 1) = Right(b, 1) Then
LCS = LCS(Left(a, Len(a) - 1), Left(b, Len(b) - 1)) + Right(a, 1)
Else
x = LCS(a, Left(b, Len(b) - 1))
y = LCS(Left(a, Len(a) - 1), b)
If Len(x) > Len(y) Then Return x Else Return y
End If
End Function
Function SCS(u As String, v As String) As String
Dim lcsStr As String = LCS(u, v)
Dim As Integer i, ui = 0, vi = 0
Dim As String sb = ""
For i = 1 To Len(lcsStr)
While ui < Len(u) Andalso Mid(u, ui + 1, 1) <> Mid(lcsStr, i, 1)
sb += Mid(u, ui + 1, 1)
ui += 1
Wend
While vi < Len(v) Andalso Mid(v, vi + 1, 1) <> Mid(lcsStr, i, 1)
sb += Mid(v, vi + 1, 1)
vi += 1
Wend
sb += Mid(lcsStr, i, 1)
ui += 1
vi += 1
Next
If ui < Len(u) Then sb += Right(u, Len(u) - ui)
If vi < Len(v) Then sb += Right(v, Len(v) - vi)
Return sb
End Function
Print SCS("abcbdab", "bdcaba")
Print SCS("WEASELS", "WARDANCE")
Sleep</syntaxhighlight>
{{out}}
<pre>abdcabdab
WEASRDANCELS</pre>
=={{header|Go}}==
{{trans|Kotlin}}
<syntaxhighlight lang="go">package main
import (
"fmt"
"strings"
)
func lcs(x, y string) string {
xl, yl := len(x), len(y)
if xl == 0 || yl == 0 {
return ""
}
x1, y1 := x[:xl-1], y[:yl-1]
if x[xl-1] == y[yl-1] {
return fmt.Sprintf("%s%c", lcs(x1, y1), x[xl-1])
}
x2, y2 := lcs(x, y1), lcs(x1, y)
if len(x2) > len(y2) {
return x2
} else {
return y2
}
}
func scs(u, v string) string {
ul, vl := len(u), len(v)
lcs := lcs(u, v)
ui, vi := 0, 0
var sb strings.Builder
for i := 0; i < len(lcs); i++ {
for ui < ul && u[ui] != lcs[i] {
sb.WriteByte(u[ui])
ui++
}
for vi < vl && v[vi] != lcs[i] {
sb.WriteByte(v[vi])
vi++
}
sb.WriteByte(lcs[i])
ui++
vi++
}
if ui < ul {
sb.WriteString(u[ui:])
}
if vi < vl {
sb.WriteString(v[vi:])
}
return sb.String()
}
func main() {
u := "abcbdab"
v := "bdcaba"
fmt.Println(scs(u, v))
}</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Haskell}}==
{{trans|C++}}
<syntaxhighlight lang="haskell">scs :: Eq a => [a] -> [a] -> [a]
scs [] ys = ys
scs xs [] = xs
scs xss@(x:xs) yss@(y:ys)
| x == y = x : scs xs ys
| otherwise = ws
where
us = scs xs yss
vs = scs xss ys
ws | length us < length vs = x : us
| otherwise = y : vs
main = putStrLn $ scs "abcbdab" "bdcaba"</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|Java}}==
{{trans|D}}
<syntaxhighlight lang="java">public class ShortestCommonSuperSequence {
private static boolean isEmpty(String s) {
return null == s || s.isEmpty();
}
private static String scs(String x, String y) {
if (isEmpty(x)) {
return y;
}
if (isEmpty(y)) {
return x;
}
if (x.charAt(0) == y.charAt(0)) {
return x.charAt(0) + scs(x.substring(1), y.substring(1));
}
if (scs(x, y.substring(1)).length() <= scs(x.substring(1), y).length()) {
return y.charAt(0) + scs(x, y.substring(1));
} else {
return x.charAt(0) + scs(x.substring(1), y);
}
}
public static void main(String[] args) {
System.out.println(scs("abcbdab", "bdcaba"));
}
}</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|jq}}==
{{trans|Wren}}
{{works with|jq}}
'''Works with gojq, the Go implementation of jq'''
<syntaxhighlight lang="jq"># largest common substring
# Uses recursion, taking advantage of jq's TCO
def lcs:
. as [$x, $y]
| if ($x|length == 0) or ($y|length == 0) then ""
else $x[:-1] as $x1
| $y[:-1] as $y1
| if $x[-1:] == $y[-1:] then ([$x1, $y1] | lcs) + $x[-1:]
else ([$x, $y1] | lcs) as $x2
| ([$x1, $y] | lcs) as $y2
| if ($x2|length) > ($y2|length) then $x2 else $y2 end
end
end;
def scs:
def eq($s;$i; $t;$j): $s[$i:$i+1] == $t[$j:$j+1];
. as [$u, $v]
| lcs as $lcs
| reduce range(0; $lcs|length) as $i ( { ui: 0, vi: 0, sb: "" };
until( .ui == ($u|length) or eq($u;.ui; $lcs;$i);
.ui as $ui
| .sb += $u[$ui:$ui+1]
| .ui += 1 )
| until(.vi == ($v|length) or eq($v;.vi; $lcs;$i);
.vi as $vi
| .sb += $v[$vi:$vi+1]
| .vi += 1 )
| .sb += $lcs[$i:$i+1]
| .ui += 1
| .vi += 1
)
| if .ui < ($u|length) then .sb = .sb + $u[.ui:] else . end
| if .vi < ($v|length) then .sb = .sb + $v[.vi:] else . end
| .sb ;
[ "abcbdab", "bdcaba" ] | scs</syntaxhighlight>
{{out}}
<pre>
"abdcabdab"
</pre>
=={{header|Julia}}==
{{trans|D}}
<syntaxhighlight lang="julia">using Memoize
@memoize function scs(x, y)
if x == ""
return y
elseif y == ""
return x
elseif x[1] == y[1]
return "$(x[1])$(scs(x[2:end], y[2:end]))"
elseif length(scs(x, y[2:end])) <= length(scs(x[2:end], y))
return "$(y[1])$(scs(x, y[2:end]))"
else
return "$(x[1])$(scs(x[2:end], y))"
end
end
println(scs("abcbdab", "bdcaba"))
</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Kotlin}}==
Uses 'lcs' function from [[Longest common subsequence#Kotlin]]:
<syntaxhighlight lang="scala">// version 1.1.2
fun lcs(x: String, y: String): String {
if (x.length == 0 || y.length == 0) return ""
val x1 = x.dropLast(1)
val y1 = y.dropLast(1)
if (x.last() == y.last()) return lcs(x1, y1) + x.last()
val x2 = lcs(x, y1)
val y2 = lcs(x1, y)
return if (x2.length > y2.length) x2 else y2
}
fun scs(u: String, v: String): String{
val lcs = lcs(u, v)
var ui = 0
var vi = 0
val sb = StringBuilder()
for (i in 0 until lcs.length) {
while (ui < u.length && u[ui] != lcs[i]) sb.append(u[ui++])
while (vi < v.length && v[vi] != lcs[i]) sb.append(v[vi++])
sb.append(lcs[i])
ui++; vi++
}
if (ui < u.length) sb.append(u.substring(ui))
if (vi < v.length) sb.append(v.substring(vi))
return sb.toString()
}
fun main(args: Array<String>) {
val u = "abcbdab"
val v = "bdcaba"
println(scs(u, v))
}</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Mathematica}}/{{header|Wolfram Language}}==
<syntaxhighlight lang="mathematica">ClearAll[RosettaShortestCommonSuperSequence]
RosettaShortestCommonSuperSequence[aa_String, bb_String] :=
Module[{lcs, scs, a = aa, b = bb},
lcs = LongestCommonSubsequence[aa, bb];
scs = "";
While[StringLength[lcs] > 0,
If[StringTake[a, 1] == StringTake[lcs, 1] \[And] StringTake[b, 1] == StringTake[lcs, 1],
scs = StringJoin[scs, StringTake[lcs, 1]];
lcs = StringDrop[lcs, 1];
a = StringDrop[a, 1];
b = StringDrop[b, 1];
,
If[StringTake[a, 1] == StringTake[lcs, 1],
scs = StringJoin[scs, StringTake[b, 1]];
b = StringDrop[b, 1];
,
scs = StringJoin[scs, StringTake[a, 1]];
a = StringDrop[a, 1];
]
]
];
StringJoin[scs, a, b]
]
RosettaShortestCommonSuperSequence["abcbdab", "bdcaba"]
RosettaShortestCommonSuperSequence["WEASELS", "WARDANCE"]</syntaxhighlight>
{{out}}
<pre>bdcabcbdaba
WEASELSARDANCE</pre>
=={{header|Nim}}==
{{trans|Kotlin}}
<syntaxhighlight lang="nim">proc lcs(x, y: string): string =
if x.len == 0 or y.len == 0: return
let x1 = x[0..^2]
let y1 = y[0..^2]
if x[^1] == y[^1]: return lcs(x1, y1) & x[^1]
let x2 = lcs(x, y1)
let y2 = lcs(x1, y)
result = if x2.len > y2.len: x2 else: y2
proc scs(u, v: string): string =
let lcs = lcs(u, v)
var ui, vi = 0
for ch in lcs:
while ui < u.len and u[ui] != ch:
result.add u[ui]
inc ui
while vi < v.len and v[vi] != ch:
result.add v[vi]
inc vi
result.add ch
inc ui
inc vi
if ui < u.len: result.add u.substr(ui)
if vi < v.len: result.add v.substr(vi)
when isMainModule:
let u = "abcbdab"
let v = "bdcaba"
echo scs(u, v)</syntaxhighlight>
{{out}}
<pre>abdcabdab</pre>
=={{header|Perl}}==
<syntaxhighlight lang="perl">sub lcs { # longest common subsequence
my( $u, $v ) = @_;
return '' unless length($u) and length($v);
my $longest = '';
for my $first ( 0..length($u)-1 ) {
my $char = substr $u, $first, 1;
my $i = index( $v, $char );
next if -1==$i;
my $next = $char;
$next .= lcs( substr( $u, $first+1), substr( $v, $i+1 ) ) unless $i==length($v)-1;
$longest = $next if length($next) > length($longest);
}
return $longest;
}
sub scs { # shortest common supersequence
my( $u, $v ) = @_;
my @lcs = split //, lcs $u, $v;
my $pat = "(.*)".join("(.*)",@lcs)."(.*)";
my @u = $u =~ /$pat/;
my @v = $v =~ /$pat/;
my $scs = shift(@u).shift(@v);
$scs .= $_.shift(@u).shift(@v) for @lcs;
return $scs;
}
my $u = "abcbdab";
my $v = "bdcaba";
printf "Strings %s %s\n", $u, $v;
printf "Longest common subsequence: %s\n", lcs $u, $v;
printf "Shortest common supersquence: %s\n", scs $u, $v;
</syntaxhighlight>
{{out}}
<pre>Strings abcbdab bdcaba
Longest common subsequence: bcba
Shortest common supersquence: abdcabdab
</pre>
=={{header|Phix}}==
{{trans|Python}}
<!--<syntaxhighlight lang="phix">(phixonline)-->
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
<span style="color: #008080;">function</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[$]=</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[$]</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">],</span><span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">..-</span><span style="color: #000000;">2</span><span style="color: #0000FF;">])&</span><span style="color: #000000;">a</span><span style="color: #0000FF;">[$]</span>
<span style="color: #008080;">else</span>
<span style="color: #004080;">sequence</span> <span style="color: #000000;">l</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span><span style="color: #000000;">b</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;">r</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</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;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008080;">iff</span><span style="color: #0000FF;">(</span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">l</span><span style="color: #0000FF;">)></span><span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)?</span><span style="color: #000000;">l</span><span style="color: #0000FF;">:</span><span style="color: #000000;">r</span><span style="color: #0000FF;">)</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</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;">function</span> <span style="color: #000000;">shortest_common_supersequence</span><span style="color: #0000FF;">(</span><span style="color: #004080;">string</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
<span style="color: #004080;">string</span> <span style="color: #000000;">lcs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">),</span>
<span style="color: #000000;">scs</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
<span style="color: #000080;font-style:italic;">-- Consume lcs</span>
<span style="color: #008080;">while</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">lcs</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">do</span>
<span style="color: #004080;">integer</span> <span style="color: #000000;">c</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lcs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">c</span> <span style="color: #008080;">and</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
<span style="color: #000080;font-style:italic;">-- Part of the lcs, so consume from all strings</span>
<span style="color: #000000;">scs</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">c</span>
<span style="color: #000000;">lcs</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">lcs</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">elsif</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]==</span><span style="color: #000000;">c</span> <span style="color: #008080;">then</span>
<span style="color: #000000;">scs</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">b</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">else</span>
<span style="color: #000000;">scs</span> <span style="color: #0000FF;">&=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">1</span><span style="color: #0000FF;">]</span>
<span style="color: #000000;">a</span> <span style="color: #0000FF;">=</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[</span><span style="color: #000000;">2</span><span style="color: #0000FF;">..$]</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">if</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">while</span>
<span style="color: #000080;font-style:italic;">-- append remaining characters</span>
<span style="color: #008080;">return</span> <span style="color: #000000;">scs</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">a</span> <span style="color: #0000FF;">&</span> <span style="color: #000000;">b</span>
<span style="color: #008080;">end</span> <span style="color: #008080;">function</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">shortest_common_supersequence</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"abcbdab"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"bdcaba"</span><span style="color: #0000FF;">)</span>
<span style="color: #0000FF;">?</span><span style="color: #000000;">shortest_common_supersequence</span><span style="color: #0000FF;">(</span><span style="color: #008000;">"WEASELS"</span><span style="color: #0000FF;">,</span> <span style="color: #008000;">"WARDANCE"</span><span style="color: #0000FF;">)</span>
<!--</syntaxhighlight>-->
{{out}}
<pre>
"abdcabdab"
"WEASRDANCELS"
</pre>
=={{header|Python}}==
<syntaxhighlight lang="python">
# Use the Longest Common Subsequence algorithm
def shortest_common_supersequence(a, b):
lcs = longest_common_subsequence(a, b)
scs = ""
# Consume lcs
while len(lcs) > 0:
if a[0]==lcs[0] and b[0]==lcs[0]:
# Part of the LCS, so consume from all strings
scs += lcs[0]
lcs = lcs[1:]
a = a[1:]
b = b[1:]
elif a[0]==lcs[0]:
scs += b[0]
b = b[1:]
else:
scs += a[0]
a = a[1:]
# append remaining characters
return scs + a + b
</syntaxhighlight>
{{out}}
<pre>
Seq1: WEASELS
Seq2: WARDANCE
SCS: WEASRDANCELS
</pre>
=={{header|Racket}}==
{{trans|C}}This program is based on the C implementation, but use memorization instead of dynamic programming. More explanations about the memorization part in http://blog.racket-lang.org/2012/08/dynamic-programming-versus-memoization.html .
<syntaxhighlight lang="racket">#lang racket
(struct link (len letters))
(define (link-add li n letter)
(link (+ n (link-len li))
(cons letter (link-letters li))))
(define (memoize f)
(local ([define table (make-hash)])
(lambda args
(dict-ref! table args (λ () (apply f args))))))
(define scs/list
(memoize
(lambda (x y)
(cond
[(null? x)
(link (length y) y)]
[(null? y)
(link (length x) x)]
[(eq? (car x) (car y))
(link-add (scs/list (cdr x) (cdr y)) 1 (car x))]
[(<= (link-len (scs/list x (cdr y)))
(link-len (scs/list (cdr x) y)))
(link-add (scs/list x (cdr y)) 1 (car y))]
[else
(link-add (scs/list (cdr x) y) 1 (car x))]))))
(define (scs x y)
(list->string (link-letters (scs/list (string->list x) (string->list y)))))
(scs "abcbdab" "bdcaba")</syntaxhighlight>
{{out}}
<pre>"abdcabdab"</pre>
=={{header|Raku}}==
(formerly Perl 6)
Using 'lcs' routine from [[Longest_common_subsequence#Raku|Longest common subsequence task]]
<syntaxhighlight lang="raku" line>sub lcs(Str $xstr, Str $ystr) { # longest common subsequence
return "" unless $xstr && $ystr;
my ($x, $xs, $y, $ys) = $xstr.substr(0, 1), $xstr.substr(1), $ystr.substr(0, 1), $ystr.substr(1);
return $x eq $y
?? $x ~ lcs($xs, $ys)
!! max(:by{ $^a.chars }, lcs($xstr, $ys), lcs($xs, $ystr) );
}
sub scs ($u, $v) { # shortest common supersequence
my @lcs = (lcs $u, $v).comb;
my $pat = '(.*)' ~ join('(.*)',@lcs) ~ '(.*)';
my $regex = "rx/$pat/".EVAL;
my @u = ($u ~~ $regex).list;
my @v = ($v ~~ $regex).list;
my $scs = shift(@u) ~ shift(@v);
$scs ~= $_ ~ shift(@u) ~ shift(@v) for @lcs;
return $scs;
}
my $u = 'abcbdab';
my $v = 'bdcaba';
printf "Strings: %s %s\n", $u, $v;
printf "Longest common subsequence: %s\n", lcs $u, $v;
printf "Shortest common supersquence: %s\n", scs $u, $v;</syntaxhighlight>
{{out}}
<pre>Strings: abcbdab bdcaba
Longest common subsequence: bcba
Shortest common supersquence: abdcabdab</pre>
=={{header|REXX}}==
{{trans|RING}}
<syntaxhighlight lang="rexx">/*REXX program finds the Shortest common supersequence (SCS) of two character strings.*/
parse arg u v . /*obtain optional arguments from the CL*/
if u=='' | u=="," then u= 'abcbdab' /*Not specified? Then use the default.*/
if v=='' | v=="," then v= 'bdcaba' /* " " " " " " */
say ' string u=' u /*echo the value of string U to term.*/
say ' string v=' v /* " " " " " V " " */
$= u /*define initial value for the output. */
do n=1 to length(u) /*process the whole length of string U.*/
do m=n to length(v) - 1 /* " right─ish part " " V.*/
p= pos( substr(v, m, 1), $) /*position of mTH V char in $ string.*/
_= substr(v, m+1, 1) /*obtain a single character of string V*/
if p\==0 & _\==substr($, p+1, 1) then $= insert(_, $, p)
end /*m*/ /* [↑] insert _ in $ after position P.*/
end /*n*/
say
say 'shortest common supersequence=' $ /*stick a fork in it, we're all done. */</syntaxhighlight>
{{out|output|text= when using the default inputs:}}
<pre>
string u= abcbdab
string v= bdcaba
shortest common supersequence= abdcabdab
</pre>
{{out|output|text= when using the inputs values: <tt> ab ac </tt>}}
<pre>
string u= ab
string v= ac
shortest common supersequence= acb
</pre>
{{out|output|text= when using the inputs values: <tt> ac ab </tt>}}
<pre>
string u= ac
string v= ab
shortest common supersequence= abc
</pre>
=={{header|Ring}}==
<syntaxhighlight lang="ring">
# Project : Shortest common supersequence
str1 = "a b c b d a b"
str2 = "bdcaba"
str3 = str2list(substr(str1, " ", nl))
for n = 1 to len(str3)
for m = n to len(str2)-1
pos = find(str3, str2[m])
if pos > 0 and str2[m+1] != str3[pos+1]
insert(str3, pos, str2[m+1])
ok
next
next
showarray(str3)
func showarray(vect)
svect = ""
for n = 1 to len(vect)
svect = svect + vect[n]
next
see svect
</syntaxhighlight>
Output:
<pre>
Shortest common supersequence: abdcabdab
</pre>
=={{header|Ruby}}==
{{trans|Tcl}}
uses 'lcs' from [[Longest common subsequence#Ruby|here]]
<syntaxhighlight lang="ruby">require 'lcs'
def scs(u, v)
lcs = lcs(u, v)
u, v = u.dup, v.dup
scs = ""
# Iterate over the characters until LCS processed
until lcs.empty?
if u[0]==lcs[0] and v[0]==lcs[0]
# Part of the LCS, so consume from all strings
scs << lcs.slice!(0)
u.slice!(0)
v.slice!(0)
elsif u[0]==lcs[0]
# char of u = char of LCS, but char of LCS v doesn't so consume just that
scs << v.slice!(0)
else
# char of u != char of LCS, so consume just that
scs << u.slice!(0)
end
end
# append remaining characters, which are not in common
scs + u + v
end
u = "abcbdab"
v = "bdcaba"
puts "SCS(#{u}, #{v}) = #{scs(u, v)}"</syntaxhighlight>
{{out}}
<pre>
SCS(abcbdab, bdcaba) = abcbdcaba
</pre>
=={{header|Sidef}}==
{{trans|Perl}}
Uses the ''lcs'' function defined [http://rosettacode.org/wiki/Longest_common_subsequence#Sidef here].
<syntaxhighlight lang="ruby">func scs(u, v) {
var ls = lcs(u, v).chars
var pat = Regex('(.*)'+ls.join('(.*)')+'(.*)')
u.scan!(pat)
v.scan!(pat)
var ss = (u.shift + v.shift)
ls.each { |c| ss += (c + u.shift + v.shift) }
return ss
}
say scs("abcbdab", "bdcaba")</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|Tcl}}==
This example uses either of the <code>lcs</code> implementations from [[longest common subsequence#Tcl|here]], assumed renamed to <tt>lcs</tt>…
<syntaxhighlight lang="tcl">proc scs {u v} {
set lcs [lcs $u $v]
set scs ""
# Iterate over the characters until LCS processed
for {set ui [set vi [set li 0]]} {$li<[string length $lcs]} {} {
set uc [string index $u $ui]
set vc [string index $v $vi]
set lc [string index $lcs $li]
if {$uc eq $lc} {
if {$vc eq $lc} {
# Part of the LCS, so consume from all strings
append scs $lc
incr ui
incr li
} else {
# char of u = char of LCS, but char of LCS v doesn't so consume just that
append scs $vc
}
incr vi
} else {
# char of u != char of LCS, so consume just that
append scs $uc
incr ui
}
}
# append remaining characters, which are not in common
append scs [string range $u $ui end] [string range $v $vi end]
return $scs
}</syntaxhighlight>
Demonstrating:
<syntaxhighlight lang="tcl">set u "abcbdab"
set v "bdcaba"
puts "SCS($u,$v) = [scs $u $v]"</syntaxhighlight>
{{out}}
<pre>SCS(abcbdab,bdcaba) = abdcabdab</pre>
=={{header|Wren}}==
{{trans|Kotlin}}
<syntaxhighlight lang="wren">var lcs // recursive
lcs = Fn.new { |x, y|
if (x.count == 0 || y.count == 0) return ""
var x1 = x[0...-1]
var y1 = y[0...-1]
if (x[-1] == y[-1]) return lcs.call(x1, y1) + x[-1]
var x2 = lcs.call(x, y1)
var y2 = lcs.call(x1, y)
return (x2.count > y2.count) ? x2 : y2
}
var scs = Fn.new { |u, v|
var lcs = lcs.call(u, v)
var ui = 0
var vi = 0
var sb = ""
for (i in 0...lcs.count) {
while (ui < u.count && u[ui] != lcs[i]) {
sb = sb + u[ui]
ui = ui + 1
}
while (vi < v.count && v[vi] != lcs[i]) {
sb = sb + v[vi]
vi = vi + 1
}
sb = sb + lcs[i]
ui = ui + 1
vi = vi + 1
}
if (ui < u.count) sb = sb + u[ui..-1]
if (vi < v.count) sb = sb + v[vi..-1]
return sb
}
var u = "abcbdab"
var v = "bdcaba"
System.print(scs.call(u, v))</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
=={{header|zkl}}==
{{trans|C}}
<syntaxhighlight lang="zkl">class Link{ var len,letter,next;
fcn init(l=0,c="",lnk=Void){ len,letter,next=l,c,lnk; }
}
fcn scs(x,y,out){
lx,ly:=x.len(),y.len();
lnk:=(ly+1).pump(List,'wrap(_){ (lx+1).pump(List(),Link.create) });
foreach i in (ly){ lnk[i][lx]=Link(ly-i, y[i]) }
foreach j in (lx){ lnk[ly][j]=Link(lx-j, x[j]) }
foreach i,j in ([ly-1..0,-1],[lx-1..0,-1]){
lp:=lnk[i][j];
if (y[i]==x[j]){
lp.next =lnk[i+1][j+1];
lp.letter=x[j];
}else if(lnk[i][j+1].len < lnk[i+1][j].len){
lp.next =lnk[i][j+1];
lp.letter=x[j];
}else{
lp.next =lnk[i+1][j];
lp.letter=y[i];
}
lp.len=lp.next.len + 1;
}
lp:=lnk[0][0]; while(lp){ out.write(lp.letter); lp=lp.next; }
out.close()
}</syntaxhighlight>
<syntaxhighlight lang="zkl">scs("abcbdab","bdcaba", Sink(String)).println();</syntaxhighlight>
{{out}}
<pre>
abdcabdab
</pre>
{{omit from|Brlcad}}
{{omit from|GUISS}}
{{omit from|Lilypond}}
{{omit from|Openscad}}
{{omit from|TPP}}
| |||