# Shortest common supersequence

For two input sequences, an scs can be formed from a longest common subsequence (lcs) easily. For example, if X$[1..m] = abcbdab$ and Y$[1..n] = bdcaba$, the lcs is Z$[1..r] = bcba$. By inserting the non-lcs symbols while preserving the symbol order, we get the scs: U$[1..t] = abdcabdab$.
It is quite clear that $r + t = m + n$ for two input sequences. However, for three or more input sequences this does not hold. Note also, that the lcs and the scs problems are not dual problems.