How can I efficiently find the longest increasing subsequence in a large array with duplicates in Java?
I'm stuck on something that should probably be simple... I'm sure I'm missing something obvious here, but I'm currently working on a project that involves analyzing large datasets, and I've been tasked with finding the longest increasing subsequence (LIS) from an array that may contain duplicates. I've implemented a solution using dynamic programming, but I'm running into performance optimization with larger datasets where the array length can exceed 10,000 elements. Here’s my current approach: ```java public int lengthOfLIS(int[] nums) { if (nums.length == 0) return 0; int[] dp = new int[nums.length]; int maxLength = 1; Arrays.fill(dp, 1); for (int i = 1; i < nums.length; i++) { for (int j = 0; j < i; j++) { if (nums[i] > nums[j]) { dp[i] = Math.max(dp[i], dp[j] + 1); } } maxLength = Math.max(maxLength, dp[i]); } return maxLength; } ``` This solution has a time complexity of O(n^2), which is proving to be too slow for larger arrays. I’ve read about using binary search to improve the efficiency of the LIS question, especially with the `List` class from `java.util`, but I’m unsure how to implement that with duplicates. Additionally, I'm working with issues when the array has many elements with the same value. For instance, given the input `[10, 9, 2, 10, 3, 7, 101, 18]`, my current method correctly identifies the LIS length as `4` (for the subsequence `[2, 3, 7, 101]`), but I'd like to ensure that my approach can handle more complex cases involving duplicates without missing valid subsequences. Are there effective ways to implement a more efficient algorithm for this question? Any guidance on how to integrate binary search in this context while still managing duplicates would be greatly appreciated. This is part of a larger CLI tool I'm building. Any help would be greatly appreciated! Thanks in advance! I'm working in a Windows 11 environment. Any feedback is welcome!