The longest increasing subsequence (LIS) problem can be solved using dynamic programming. In TypeScript, you can use a DP array to keep track of subsequence lengths.

The longest increasing subsequence (LIS) problem involves finding the longest subsequence within a sequence of numbers such that the subsequence is strictly increasing. One common approach to solve this problem is using dynamic programming (DP), which has a time complexity of O(n^2). In TypeScript, you can implement the LIS solution by maintaining an array dp, where dp[i] represents the length of the longest increasing subsequence ending at index i. As you iterate through the array, you update the dp array by checking for any previous elements that are smaller than the current one, and if found, you update the subsequence length. A more optimized solution uses binary search to maintain a running list of the longest subsequences, which reduces the time complexity to O(n log n). Understanding how to implement the LIS in TypeScript is useful in various real-world applications such as version control, ranking algorithms, and genetic sequence analysis. By mastering LIS, developers can apply these techniques in optimization problems where sequences and order play a critical role.