Can you find the proof that finding all LCS is O(n^3)? The author was talking about "the standard algorithm for computing LCS". I was assuming the standard algorithm finds one LCS only.
Indeed, finding all LCSs requires exponential time: The strings "abcdefghijkl..." and "badcfehgjilk..." have the 2^(N/2) LCSs "[ab][cd][ef][gh][ij][kl]..." and no algorithm can ever run faster than the amount of time it takes to print its output.
