Dynamic Programming Challenge: Longest Increasing Subsequence

Given an array of integers, find the length of the longest increasing subsequence. A subsequence is a sequence that can be derived from another sequence by deleting some or no elements without changing the order of the remaining elements.
For example:
#include <iostream> #include <vector> int longestIncreasingSubsequence(const std::vector<int>& nums) { // Your dynamic programming solution goes here. // Return the length of the longest increasing subsequence. } int main() { std::vector<int> sequence = {10, 22, 9, 33, 21, 50, 41, 60, 80}; int result = longestIncreasingSubsequence(sequence); std::cout << "Length of the longest increasing subsequence: " << result << std::endl; return 0; }
I'm specifically interested in implementing this using dynamic programming techniques. How can I approach this problem using dynamic programming, and what would be the C++ code for solving it? Any insights, code snippets, or explanations would be incredibly helpful in mastering dynamic programming for this particular challenge. Thank you for your assistance!

@SachinBhatt
I had to look up what "dynamic programming" is! They like their labels for things, don't they?Am I missing something, or is this real easy? You start by setting a variable for the longest subsequence to 0. You count from left to right while the numbers increase. So for
10, 22
and then9
the longest so far is 2 (10, 22), terminated by 9 (because it is less than the preceding 22). You note that 2 is the longest so far, because it is more than 0, and so update the count variable. You know that you can resume looking from the9
. You encounter9, 33
and then21, 50
, both terminated by smaller numbers, and those are also of length 2, no better then before. Finally you meet41, 60, 80
, terminated by end of input, that is length 3, and so is the highest. So that is what you return....