How do I design a brute-force algorithm and a dynamic programming algorithm based on the given description to solve the stated problem and write its pseudocode?

Assume you have two sequences and of the same length > 1, where each sequence contains integer values. The goal of this problem is to find a subsequence which has the following properties: 1. The subsequence is common to both and . 2. The subsequence length is maximum among any other common subsequences. 3. The subsequence cannot be empty. 4. The values in subsequence S are consecutive values in X and Y.

Brute-force algorithm: Generate all possible subsequences of X, and all subsequences of Y. Then, for each subsequence sx in X, and for each subsequence sy in Y, check if sx and sy are equal. If so, then compare its length with the maximum common subsequence found so far and keep the maximum length subsequence.