SDE - Intern

Recursively called the react component that renders the comments.

Step 1: Define the approach
We will use dynamic programming to solve this problem. We'll create an array dp of the same length as the input array, where dp[i] represents the length of the longest increasing subsequence ending at index i.

Step 2: Initialize the DP array
You can initialize the dp array with all elements set to 1 since a single element is the most minor possible increasing subsequence.

Step 3: Iterate through the array
Start iterating through the input array numbers. For each element at index i, we will check all elements before it (from 0 to i-1) to find more minor elements than the element at index i. These are potential candidates to extend the increasing subsequence ending at index i.

Step 4: Update the DP array
For each index i, iterate through all indices j before it. If the element at index i (nums[i]) is greater than the element at index j (nums[j]), it means we can extend the increasing subsequence ending at index j by including the element at index i. In that case, update dp[i] to be the maximum of its current value and dp[j] + 1.

Step 5: Find the maximum value in the DP array
After iterating through all elements of the input array, the length of the longest increasing subsequence will be the maximum value in the dp array.

Step 6: Return the result
Return the maximum value found in the dp array, which represents the length of the longest increasing subsequence.