How to quickly find the longest increasing subsequence in a large integer array using Python?
I'm stuck on something that should probably be simple. I'm building a feature where I'm trying to debug I'm working on a project and hit a roadblock... I've searched everywhere and can't find a clear answer. I'm working on a project where I need to find the longest increasing subsequence in a large array of integers. The input can be quite large (up to 10^5 elements), and I'm looking for an efficient solution that runs in O(n log n) time complexity. I've tried the dynamic programming approach, which is O(n^2), but it's too slow for my use case. Here’s the code I’ve written so far using the dynamic programming method: ```python def longest_increasing_subsequence(arr): n = len(arr) if n == 0: return 0 dp = [1] * n for i in range(1, n): for j in range(0, i): if arr[i] > arr[j]: dp[i] = max(dp[i], dp[j] + 1) return max(dp) arr = [10, 22, 9, 33, 21, 50, 41, 60, 80] print(longest_increasing_subsequence(arr)) # Output: 6 ``` This works fine for smaller arrays, but I get a time limit exceeded behavior when I test it with larger inputs. I’ve read that using a binary search can optimize this process. I believe I could use a list to keep track of the current longest subsequence and apply binary search to find positions of elements. However, I'm unsure how to implement that efficiently. Any help on how to refactor my code to achieve the desired time complexity or clarify the binary search method for this question would be greatly appreciated. I'm using Python 3.9.1 and also would like to know if I need any specific libraries for the binary search implementation. I'm working on a CLI tool that needs to handle this. Any ideas what could be causing this? Any help would be greatly appreciated! Any pointers in the right direction? How would you solve this? For context: I'm using Python on Windows 11. Any ideas what could be causing this? I'm developing on Windows 11 with Python.