The Longest Common Subsequence (LCS) problem is a classic problem in dynamic programming. Given two sequences, the goal is to find the longest subsequence that is common to both sequences. A subsequence is a sequence that can be derived by deleting some or no elements from the original sequence while maintaining the relative order of the remaining elements.

Here's the algorithm to solve the Longest Common Subsequence problem using dynamic programming:

1. Define the problem:

- Given two sequences, X of length m and Y of length n.
- Determine the length of the longest common subsequence (LCS) of X and Y.

2. Create a dynamic programming table:

- Create a 2D table `L` of size (m+1) x (n+1), where L[i][j] represents the length of the LCS of the prefixes X[0...i-1] and Y[0...j-1].
- Initialize the first row and the first column of `L` with zeros.

3. Fill in the table:

- For each position (i, j) in the table, compare the elements X[i-1] and Y[j-1].
- If X[i-1] equals Y[j-1], it means the elements are common, so the length of the LCS at this position is 1 plus the length of the LCS without these elements, i.e., L[i][j] = L[i-1][j-1] + 1.
- If X[i-1]

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