Longest Increasing Subsequence: Given an array of integers, find the length of the longest increasing subsequence (LIS). A subsequence does not need to be contiguous but must maintain the order of elements. • Define Variables: Define the variables you will use to track the state of your dynamic programming solution. • Recurrence Relation: Derive a recurrence relation between variables. • Pseudocode: Write pseudocode to find the length and an actual longest increasing subsequence. • Example: For the input array [10, 22, 9, 33, 21, 50, 41, 60, 80], the output should be 6, corresponding to the subsequence [10, 22, 33, 50, 60, 80]. • Complexity Analysis: Analyze the time and space complexity of your solution

Longest Increasing Subsequence:

Given an array of integers, find the length of the longest increasing subsequence (LIS). A subsequence does not need to be contiguous but must maintain the order of elements.

• Define Variables: Define the variables you will use to track the state of your dynamic programming solution.

• Recurrence Relation: Derive a recurrence relation between variables.

• Pseudocode: Write pseudocode to find the length and an actual longest increasing subsequence.

• Example: For the input array [10, 22, 9, 33, 21, 50, 41, 60, 80], the output should be 6, corresponding to the subsequence [10, 22, 33, 50, 60, 80].

• Complexity Analysis: Analyze the time and space complexity of your solution