What is the Longest Increasing Subarray problem and how can it be solved using Dynamic Programming?

Dynamic Programming Questions

What is the Longest Increasing Subarray problem and how can it be solved using Dynamic Programming?

The Longest Increasing Subarray problem is a problem where we need to find the length of the longest subarray in a given array such that all the elements in the subarray are in increasing order.

Dynamic Programming can be used to solve this problem efficiently. We can define a dynamic programming array, dp, where dp[i] represents the length of the longest increasing subarray ending at index i. Initially, all elements of dp are set to 1.

To solve this problem using dynamic programming, we iterate through the given array from left to right. For each element at index i, we compare it with all the previous elements (from 0 to i-1). If the current element is greater than the previous element, we update dp[i] as dp[i] = dp[i-1] + 1, indicating that the current element can be included in the longest increasing subarray ending at index i.

Finally, we find the maximum value in the dp array, which represents the length of the longest increasing subarray in the given array.

The time complexity of this dynamic programming solution is O(n), where n is the size of the given array.