Handling Large Input for Longest Common Subsequence in Python - Memory scenarios
I've hit a wall trying to I tried several approaches but none seem to work. Quick question that's been bugging me - I'm currently implementing the Longest Common Subsequence (LCS) algorithm in Python using dynamic programming. My input sequences can be quite large, sometimes exceeding lengths of 1000 characters. I initially approached the question with a 2D list to store the lengths of the LCS, but I keep running into a `MemoryError` when trying to allocate space for the matrix. Here's the code I've written so far: ```python def longest_common_subsequence(X, Y): m = len(X) n = len(Y) # Create a 2D array to store lengths of longest common subsequence. L = [[0] * (n + 1) for _ in range(m + 1)] # Build the LCS length matrix. for i in range(m + 1): for j in range(n + 1): if i == 0 or j == 0: L[i][j] = 0 elif X[i - 1] == Y[j - 1]: L[i][j] = L[i - 1][j - 1] + 1 else: L[i][j] = max(L[i - 1][j], L[i][j - 1]) return L[m][n] ``` When I run this with two sequences of length 1000, it raises a `MemoryError`. I tried reducing the size of the matrix by switching to a 1D list approach, but I got confused about how to keep track of the previous row's values, which led to incorrect results. I've read up on some optimizations but I'm unsure how to implement them without losing the efficiency of the algorithm. Is there a more memory-efficient way to compute LCS that can handle larger sequences without running out of memory? Also, if possible, can you provide insights into maintaining correctness when switching from a 2D matrix to a 1D array? I'm working on a web app that needs to handle this. Has anyone else encountered this? This is part of a larger desktop app I'm building. Is there a simpler solution I'm overlooking? Is there a simpler solution I'm overlooking?