Solution for this please. be attention to the written notes.

Solution must be in C programming language. Please provide a brief explanation of the codes and the efficiency analysis with comments. Question ONE: Devise a dynamic programming algorithm that takes a sequence Sofn integers a!...., a! as input, and outputs the longest and strictly increasing subsequence. Note that the numbers in the subsequence don't need to be successive. Also, all the inputs given to the algorithm are assumed to be legitimate, i.e. the users are assumed to provide only integers. Input: output: 5 11 22 33 12 13 11 22 33 Input: 10 9 99 12 45 56 78 98 101 100 97 9 12 45 56 78 98 101