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This is a problem from COCI 2003, here I left you the link. The problem name is VOKI (it is the third in the pdf).
http://hsin.hr/2003/national/second_day/juniors/problems.pdf
So far I have a DP approach that works in O(n * m * max(n, m)) which is too slow, could you help me to improve this?
What I understood from the problem is find the shortest sequence that exists in VOKI and dose not exist in TOKI.
It can be done in O(n * m * logm ) whenever you decide to include the ith letter of VOKI , do binary search to find the same letter in TOKI after or equal the jth letter . here is my solution http://ideone.com/bMBs68
Can be done in O(n * m) also now nxt[i][j] denotes the next appearance of the ith letter after or equal to the jth index
http://ideone.com/chXExW
Could you explain it a little more? What I don't get is how do you guarantee that the subsequence isn't in TOKI. Also from your solution i and j are prefixes of VOKI and TOKI, right?