I have an algorithm analysis project where I'm supposed to make a new improved algorithm with a better asymptotic upper bound.

The original bryte force algoritm is supposed to take two sequences X and Y with the same length and find the longest common subsequence between them.

the out put will be the LCM and the start index of it from both X and Y.

How can I make a new algorithm with a better upper bound?

below is the brute force algoritm I wrote for the problem with O(n^4)

*the elements in the subsequence must be cosecutive

*LCS*