Shortest uncommon subseqence - algorithm

Question

Given two strings s and t, determine length of shortest string z such that z is a subsequence of s and not a subsequence of t.
example :
s :babab,
t :babba
sol :
3 (aab)
not looking for copy pastable code, please if anybody can help with intution for solving this.
thanks a lot !

Answer 1

Here you go. I created on IEnumarable method which gives back all possible combinations. This is compared with t. I optimized the solution to loop only once over the not match String t.
using System;
using System.Collections.Generic;
namespace GuessTheNumber
{
public class Element:IComparable<Element>
{
public string Seq { get; set; }
public int Id { get; set; }
public int CompareTo(Element other)
{
return this.Seq.CompareTo(other.Seq);
}
}
class Program
{
static void Main(string[] args)
{
string s = "babab";
string t = "babba";
string z = ShortestUncommonSuqsequence(s, t);
}
static public string ShortestUncommonSuqsequence(string SubSequenceOf, string NotSubSequenceOf)
{
var uniqueSeq = new SortedList<Element, int>();
uniqueSeq.Add(new Element() { Seq = "", Id = -1 }, -1);
foreach (Element oneSequence in GetNextUniqueSequences(uniqueSeq, SubSequenceOf))
{
int index = oneSequence.Id + 1;
while (index < NotSubSequenceOf.Length)
{
char NotChar = NotSubSequenceOf[index];
if (oneSequence.Seq[oneSequence.Seq.Length - 1] == NotChar) break;
index++;
}
if (index == NotSubSequenceOf.Length)
{
return oneSequence.Seq;
}
else
{
oneSequence.Id = index;
}
}
return null;
}
static public IEnumerable<Element> GetNextUniqueSequences(SortedList<Element, int> UniqueSeq, string Input)
{
SortedList<Element, int> results = new SortedList<Element, int>();
foreach (var prevResult in UniqueSeq)
{
for (int i = 0; i < Input.Length; i++)
{
if (prevResult.Value < prevResult.Key.Seq.Length + i)
{
string nextStr = prevResult.Key.Seq + Input[i].ToString();
Element newElem = new Element() { Seq = nextStr, Id = prevResult.Key.Id };
if (!results.Keys.Contains(newElem))
{
results.Add(newElem, prevResult.Key.Seq.Length + i);
yield return newElem;
}
}
}
}
if (Input.Length > 1)
{
foreach (Element res in GetNextUniqueSequences(results, Input.Substring(1)))
{
yield return res;
}
}
}
}
}