implementing Dynamic Programming Approach for Longest Increasing Subsequence in Python
I'm refactoring my project and After trying multiple solutions online, I still can't figure this out. I'm working on a project and hit a roadblock. I'm currently implementing the Longest Increasing Subsequence (LIS) algorithm using dynamic programming in Python, but my solution seems to be returning incorrect results for certain edge cases. My implementation is based on a common O(n^2) dynamic programming approach, where I maintain an array `dp` that stores the length of the longest increasing subsequence ending at each index. However, I'm working with issues when testing with the input `[3, 2, 5, 6, 3, 7, 1, 8]` which should yield a LIS of length 5 (the subsequence being `[2, 5, 6, 7, 8]`). Here is a snippet of my code: ```python def length_of_lis(nums): if not nums: return 0 dp = [1] * len(nums) for i in range(1, len(nums)): for j in range(i): if nums[i] > nums[j]: dp[i] = max(dp[i], dp[j] + 1) return max(dp) ``` When I run this function with the provided input, it returns `4`, which is incorrect. I suspect the scenario might be related to how I'm updating the `dp` array. I've also tried adding print statements to debug and see the values of `dp` at each iteration, but I need to seem to identify the mistake clearly. Could someone guide to identify why my implementation is failing for this particular case, and if there are any best practices for debugging dynamic programming solutions like this one? My development environment is Linux. Could someone point me to the right documentation? For reference, this is a production desktop app. What's the correct way to implement this?