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2
Task/Shortest-common-supersequence/00-META.yaml
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2
Task/Shortest-common-supersequence/00-META.yaml
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---
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from: http://rosettacode.org/wiki/Shortest_common_supersequence
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14
Task/Shortest-common-supersequence/00-TASK.txt
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Task/Shortest-common-supersequence/00-TASK.txt
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The '''[[wp:shortest common supersequence|shortest common supersequence]]''' is a problem closely related to the [[longest common subsequence]], which you can use as an external function for this task.
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;;Task:
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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.
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Demonstrate this by printing <math>s</math> where <math>u = </math>“<tt>abcbdab</tt>” and <math>v = </math>“<tt>bdcaba</tt>”.
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<!-- This example is taken from the Wikipedia page. -->
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;Also see:
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* [[wp:Shortest_common_supersequence_problem|Wikipedia: shortest common supersequence]]
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<br><br>
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F scs(String x, y)
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I x.empty
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R y
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I y.empty
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R x
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I x[0] == y[0]
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R x[0]‘’scs(x[1..], y[1..])
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I scs(x, y[1..]).len <= scs(x[1..], y).len
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R y[0]‘’scs(x, y[1..])
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E
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R x[0]‘’scs(x[1..], y)
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print(scs(‘abcbdab’, ‘bdcaba’))
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BEGIN
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PRIO SCS = 1;
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# returns the shortest common supersequence of x and y #
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OP SCS = ( STRING x, y )STRING:
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IF x = "" THEN y
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ELIF y = "" THEN x
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ELIF x[ LWB x ] = y[ LWB y ]
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THEN x[ LWB x ] + ( x[ LWB x + 1 : ] SCS y[ LWB y + 1 : ] )
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ELIF STRING x y sub = x SCS y[ LWB y + 1 : ];
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STRING x sub y = x[ LWB x + 1 : ] SCS y;
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INT x y sub size = ( UPB x y sub - LWB x y sub ) + 1;
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INT x sub y size = ( UPB x sub y - LWB x sub y ) + 1;
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x y sub size <= x sub y size
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THEN y[ LWB y ] + x y sub
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ELSE x[ LWB x ] + x sub y
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FI # SCS # ;
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print( ( "abcbdab" SCS "bdcaba", newline ) )
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END
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with Ada.Text_IO;
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procedure Shortest is
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function Scs (Left, Right : in String) return String is
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Left_Tail : String renames Left (Left'First + 1 .. Left'Last);
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Right_Tail : String renames Right (Right'First + 1 .. Right'Last);
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begin
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if Left = "" then return Right; end if;
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if Right = "" then return Left; end if;
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if Left (Left'First) = Right (Right'First) then
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return Left (Left'First) & Scs (Left_Tail, Right_Tail);
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end if;
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declare
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S1 : constant String := Scs (Left, Right_Tail);
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S2 : constant String := Scs (Left_Tail, Right);
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begin
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return (if S1'Length <= S2'Length
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then Right (Right'First) & S1
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else Left (Left'First) & S2);
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end;
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end Scs;
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procedure Exercise (Left, Right : String) is
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use Ada.Text_Io;
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begin
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Put ("scs ( "); Put (Left); Put (" , "); Put (Right); Put ( " ) -> ");
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Put (Scs (Left, Right));
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New_Line;
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end Exercise;
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begin
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Exercise ("abcbdab", "bdcaba");
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Exercise ("WEASELS", "WARDANCE");
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end Shortest;
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#include <iostream>
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std::string scs(std::string x, std::string y) {
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if (x.empty()) {
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return y;
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}
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if (y.empty()) {
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return x;
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}
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if (x[0] == y[0]) {
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return x[0] + scs(x.substr(1), y.substr(1));
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}
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if (scs(x, y.substr(1)).size() <= scs(x.substr(1), y).size()) {
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return y[0] + scs(x, y.substr(1));
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} else {
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return x[0] + scs(x.substr(1), y);
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}
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}
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int main() {
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auto res = scs("abcbdab", "bdcaba");
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std::cout << res << '\n';
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return 0;
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}
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public class ShortestCommonSupersequence
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{
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Dictionary<(string, string), string> cache = new();
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public string scs(string x, string y)
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{
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if (x.Length == 0) return y;
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if (y.Length == 0) return x;
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if (cache.TryGetValue((x, y), out var result)) return result;
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if (x[0] == y[0])
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{
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return cache[(x, y)] = x[0] + scs(x.Substring(1), y.Substring(1));
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}
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var xr = scs(x.Substring(1), y);
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var yr = scs(x, y.Substring(1));
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if (yr.Length <= xr.Length)
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{
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return cache[(x, y)] = y[0] + yr;
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}
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else
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{
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return cache[(x, y)] = x[0] + xr;
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}
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}
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public static void Main(string[] args)
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{
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var scs = new ShortestCommonSupersequence();
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Console.WriteLine(scs.scs("abcbdab", "bdcaba"));
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}
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}
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#include <stdio.h>
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#include <string.h>
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typedef struct link link_t;
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struct link {
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int len;
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char letter;
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link_t *next;
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};
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// Stores a copy of a SCS of x and y in out. Caller needs to make sure out is long enough.
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int scs(char *x, char *y, char *out)
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{
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int lx = strlen(x), ly = strlen(y);
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link_t lnk[ly + 1][lx + 1];
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for (int i = 0; i < ly; i++)
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lnk[i][lx] = (link_t) {ly - i, y[i], &lnk[i + 1][lx]};
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for (int j = 0; j < lx; j++)
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lnk[ly][j] = (link_t) {lx - j, x[j], &lnk[ly][j + 1]};
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lnk[ly][lx] = (link_t) {0};
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for (int i = ly; i--; ) {
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for (int j = lx; j--; ) {
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link_t *lp = &lnk[i][j];
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if (y[i] == x[j]) {
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lp->next = &lnk[i+1][j+1];
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lp->letter = x[j];
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} else if (lnk[i][j+1].len < lnk[i+1][j].len) {
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lp->next = &lnk[i][j+1];
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lp->letter = x[j];
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} else {
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lp->next = &lnk[i+1][j];
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lp->letter = y[i];
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}
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lp->len = lp->next->len + 1;
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}
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}
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for (link_t *lp = &lnk[0][0]; lp; lp = lp->next)
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*out++ = lp->letter;
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return 0;
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}
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int main(void)
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{
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char x[] = "abcbdab", y[] = "bdcaba", res[128];
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scs(x, y, res);
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printf("SCS(%s, %s) -> %s\n", x, y, res);
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return 0;
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}
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import std.stdio, std.functional, std.array, std.range;
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dstring scs(in dstring x, in dstring y) nothrow @safe {
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alias mScs = memoize!scs;
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if (x.empty) return y;
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if (y.empty) return x;
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if (x.front == y.front)
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return x.front ~ mScs(x.dropOne, y.dropOne);
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if (mScs(x, y.dropOne).length <= mScs(x.dropOne, y).length)
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return y.front ~ mScs(x, y.dropOne);
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else
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return x.front ~ mScs(x.dropOne, y);
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}
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void main() @safe {
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scs("abcbdab", "bdcaba").writeln;
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}
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defmodule SCS do
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def scs(u, v) do
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lcs = LCS.lcs(u, v) |> to_charlist
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scs(to_charlist(u), to_charlist(v), lcs, []) |> to_string
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end
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defp scs(u, v, [], res), do: Enum.reverse(res) ++ u ++ v
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defp scs([h|ut], [h|vt], [h|lt], res), do: scs(ut, vt, lt, [h|res])
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defp scs([h|_]=u, [vh|vt], [h|_]=lcs, res), do: scs(u, vt, lcs, [vh|res])
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defp scs([uh|ut], v, lcs, res), do: scs(ut, v, lcs, [uh|res])
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end
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u = "abcbdab"
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v = "bdcaba"
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IO.puts "SCS(#{u}, #{v}) = #{SCS.scs(u, v)}"
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USING: combinators io kernel locals math memoize sequences ;
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MEMO:: scs ( x y -- seq )
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{
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{ [ x empty? ] [ y ] }
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{ [ y empty? ] [ x ] }
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{ [ x first y first = ]
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[ x rest y rest scs x first prefix ] }
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{ [ x y rest scs length x rest y scs length <= ]
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[ x y rest scs y first prefix ] }
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[ x rest y scs x first prefix ]
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} cond ;
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"abcbdab" "bdcaba" scs print
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package main
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import (
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"fmt"
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"strings"
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)
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func lcs(x, y string) string {
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xl, yl := len(x), len(y)
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if xl == 0 || yl == 0 {
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return ""
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}
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x1, y1 := x[:xl-1], y[:yl-1]
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if x[xl-1] == y[yl-1] {
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return fmt.Sprintf("%s%c", lcs(x1, y1), x[xl-1])
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}
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x2, y2 := lcs(x, y1), lcs(x1, y)
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if len(x2) > len(y2) {
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return x2
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} else {
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return y2
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}
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}
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func scs(u, v string) string {
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ul, vl := len(u), len(v)
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lcs := lcs(u, v)
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ui, vi := 0, 0
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var sb strings.Builder
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for i := 0; i < len(lcs); i++ {
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for ui < ul && u[ui] != lcs[i] {
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sb.WriteByte(u[ui])
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ui++
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}
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for vi < vl && v[vi] != lcs[i] {
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sb.WriteByte(v[vi])
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vi++
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}
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sb.WriteByte(lcs[i])
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ui++
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vi++
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}
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if ui < ul {
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sb.WriteString(u[ui:])
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}
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if vi < vl {
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sb.WriteString(v[vi:])
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}
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return sb.String()
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}
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func main() {
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u := "abcbdab"
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v := "bdcaba"
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fmt.Println(scs(u, v))
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}
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scs :: Eq a => [a] -> [a] -> [a]
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scs [] ys = ys
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scs xs [] = xs
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scs xss@(x:xs) yss@(y:ys)
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| x == y = x : scs xs ys
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| otherwise = ws
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where
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us = scs xs yss
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vs = scs xss ys
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ws | length us < length vs = x : us
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| otherwise = y : vs
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main = putStrLn $ scs "abcbdab" "bdcaba"
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public class ShortestCommonSuperSequence {
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private static boolean isEmpty(String s) {
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return null == s || s.isEmpty();
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}
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private static String scs(String x, String y) {
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if (isEmpty(x)) {
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return y;
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}
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if (isEmpty(y)) {
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return x;
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}
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if (x.charAt(0) == y.charAt(0)) {
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return x.charAt(0) + scs(x.substring(1), y.substring(1));
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}
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if (scs(x, y.substring(1)).length() <= scs(x.substring(1), y).length()) {
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return y.charAt(0) + scs(x, y.substring(1));
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} else {
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return x.charAt(0) + scs(x.substring(1), y);
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}
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}
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public static void main(String[] args) {
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System.out.println(scs("abcbdab", "bdcaba"));
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}
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}
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# largest common substring
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# Uses recursion, taking advantage of jq's TCO
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def lcs:
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. as [$x, $y]
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| if ($x|length == 0) or ($y|length == 0) then ""
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else $x[:-1] as $x1
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| $y[:-1] as $y1
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| if $x[-1:] == $y[-1:] then ([$x1, $y1] | lcs) + $x[-1:]
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else ([$x, $y1] | lcs) as $x2
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| ([$x1, $y] | lcs) as $y2
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| if ($x2|length) > ($y2|length) then $x2 else $y2 end
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end
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end;
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def scs:
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def eq($s;$i; $t;$j): $s[$i:$i+1] == $t[$j:$j+1];
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. as [$u, $v]
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| lcs as $lcs
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| reduce range(0; $lcs|length) as $i ( { ui: 0, vi: 0, sb: "" };
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until( .ui == ($u|length) or eq($u;.ui; $lcs;$i);
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.ui as $ui
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| .sb += $u[$ui:$ui+1]
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| .ui += 1 )
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| until(.vi == ($v|length) or eq($v;.vi; $lcs;$i);
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.vi as $vi
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| .sb += $v[$vi:$vi+1]
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| .vi += 1 )
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| .sb += $lcs[$i:$i+1]
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| .ui += 1
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| .vi += 1
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)
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| if .ui < ($u|length) then .sb = .sb + $u[.ui:] else . end
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| if .vi < ($v|length) then .sb = .sb + $v[.vi:] else . end
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| .sb ;
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[ "abcbdab", "bdcaba" ] | scs
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using Memoize
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@memoize function scs(x, y)
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if x == ""
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return y
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elseif y == ""
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return x
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elseif x[1] == y[1]
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return "$(x[1])$(scs(x[2:end], y[2:end]))"
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elseif length(scs(x, y[2:end])) <= length(scs(x[2:end], y))
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return "$(y[1])$(scs(x, y[2:end]))"
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else
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return "$(x[1])$(scs(x[2:end], y))"
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end
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end
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println(scs("abcbdab", "bdcaba"))
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// version 1.1.2
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fun lcs(x: String, y: String): String {
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if (x.length == 0 || y.length == 0) return ""
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val x1 = x.dropLast(1)
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val y1 = y.dropLast(1)
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if (x.last() == y.last()) return lcs(x1, y1) + x.last()
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val x2 = lcs(x, y1)
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val y2 = lcs(x1, y)
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return if (x2.length > y2.length) x2 else y2
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}
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fun scs(u: String, v: String): String{
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val lcs = lcs(u, v)
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var ui = 0
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var vi = 0
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val sb = StringBuilder()
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for (i in 0 until lcs.length) {
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while (ui < u.length && u[ui] != lcs[i]) sb.append(u[ui++])
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while (vi < v.length && v[vi] != lcs[i]) sb.append(v[vi++])
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sb.append(lcs[i])
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ui++; vi++
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}
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if (ui < u.length) sb.append(u.substring(ui))
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if (vi < v.length) sb.append(v.substring(vi))
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return sb.toString()
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}
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||||
|
||||
fun main(args: Array<String>) {
|
||||
val u = "abcbdab"
|
||||
val v = "bdcaba"
|
||||
println(scs(u, v))
|
||||
}
|
||||
|
|
@ -0,0 +1,25 @@
|
|||
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"]
|
||||
|
|
@ -0,0 +1,29 @@
|
|||
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)
|
||||
|
|
@ -0,0 +1,31 @@
|
|||
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, $v;
|
||||
|
|
@ -0,0 +1,43 @@
|
|||
(phixonline)-->
|
||||
<span style="color: #008080;">with</span> <span style="color: #008080;">javascript_semantics</span>
|
||||
<span style="color: #008080;">function</span> <span style="color: #000000;">longest_common_subsequence</span><span style="color: #0000FF;">(</span><span style="color: #004080;">sequence</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">,</span> <span style="color: #000000;">b</span><span style="color: #0000FF;">)</span>
|
||||
<span style="color: #004080;">sequence</span> <span style="color: #000000;">res</span> <span style="color: #0000FF;">=</span> <span style="color: #008000;">""</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">a</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">and</span> <span style="color: #7060A8;">length</span><span style="color: #0000FF;">(</span><span style="color: #000000;">b</span><span style="color: #0000FF;">)</span> <span style="color: #008080;">then</span>
|
||||
<span style="color: #008080;">if</span> <span style="color: #000000;">a</span><span style="color: #0000FF;">[$]=</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>
|
||||
<!--
|
||||
|
|
@ -0,0 +1,21 @@
|
|||
# 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
|
||||
|
|
@ -0,0 +1,16 @@
|
|||
/*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. */
|
||||
|
|
@ -0,0 +1,33 @@
|
|||
#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")
|
||||
|
|
@ -0,0 +1,24 @@
|
|||
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;
|
||||
|
|
@ -0,0 +1,21 @@
|
|||
# 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
|
||||
|
|
@ -0,0 +1,28 @@
|
|||
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)}"
|
||||
|
|
@ -0,0 +1,11 @@
|
|||
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")
|
||||
|
|
@ -0,0 +1,31 @@
|
|||
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 $scs
|
||||
}
|
||||
|
|
@ -0,0 +1,3 @@
|
|||
set u "abcbdab"
|
||||
set v "bdcaba"
|
||||
puts "SCS($u,$v) = [scs $u $v]"
|
||||
|
|
@ -0,0 +1,37 @@
|
|||
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))
|
||||
|
|
@ -0,0 +1,28 @@
|
|||
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()
|
||||
}
|
||||
|
|
@ -0,0 +1 @@
|
|||
scs("abcbdab","bdcaba", Sink(String)).println();
|
||||
Loading…
Add table
Add a link
Reference in a new issue