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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
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)
![image text in transcribed](https://s3.amazonaws.com/si.experts.images/answers/2024/08/66d0b062b11c2_67466d0b06244c0f.jpg)
*the elements in the subsequence must be cosecutive
*LCS*
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