#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;
}

#include <iostream>
#include <vector>

int longestIncreasingSubsequence(const std::vector<int>& nums) {
    int n = nums.size();
    if (n == 0) return 0;  // Empty array has LIS of length 0.

    // Initialize the dp array with all values set to 1.
    std::vector<int> dp(n, 1);

    // Iterate over each element in the array.
    for (int i = 1; i < n; ++i) {
        // Check all previous elements for increasing subsequence.
        for (int j = 0; j < i; ++j) {
            if (nums[i] > nums[j]) {
                dp[i] = std::max(dp[i], dp[j] + 1);
            }
        }
    }

    // Find the maximum value in dp, which represents the length of the LIS.
    int maxLIS = *std::max_element(dp.begin(), dp.end());

    return maxLIS;
}

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;
}