implementing Optimizing Dynamic Programming Solution for Longest Common Subsequence in C# - Running Out of Memory
I'm working on a project and hit a roadblock... I'm stuck on something that should probably be simple. I'm currently working on an implementation of the Longest Common Subsequence (LCS) algorithm using dynamic programming in C#. My input strings can be quite large (up to 2000 characters each), and while my initial implementation works correctly, it consumes an enormous amount of memory and sometimes runs into `OutOfMemoryException`. Here's the code snippet I'm using for the LCS calculation: ```csharp public int LongestCommonSubsequence(string text1, string text2) { int m = text1.Length; int n = text2.Length; int[,] dp = new int[m + 1, n + 1]; for (int i = 1; i <= m; i++) { for (int j = 1; j <= n; j++) { if (text1[i - 1] == text2[j - 1]) { dp[i, j] = dp[i - 1, j - 1] + 1; } else { dp[i, j] = Math.Max(dp[i - 1, j], dp[i, j - 1]); } } } return dp[m, n]; } ``` I've tried optimizing the memory usage by switching to a one-dimensional array instead of a two-dimensional array since I only need the previous row to compute the current row. However, I need to seem to get it right, and my results are incorrect when I implement it. Here's my modified approach: ```csharp public int LongestCommonSubsequenceOptimized(string text1, string text2) { int m = text1.Length; int n = text2.Length; int[] dp = new int[n + 1]; for (int i = 1; i <= m; i++) { int prev = 0; for (int j = 1; j <= n; j++) { int temp = dp[j]; if (text1[i - 1] == text2[j - 1]) { dp[j] = prev + 1; } else { dp[j] = Math.Max(dp[j], dp[j - 1]); } prev = temp; } } return dp[n]; } ``` Unfortunately, the optimized version still returns incorrect results in some cases, and I suspect it has to do with how I'm handling the previous value. The original implementation works fine on smaller inputs, but with larger strings, it just doesn't complete or runs out of memory. Can anyone guide to pinpoint where I'm going wrong or suggest further optimizations? I'm using .NET 6.0 for this implementation. This is part of a larger CLI tool I'm building. Thanks in advance! How would you solve this?