What are some advanced dynamic programming problems in C++?

What are some advanced dynamic programming problems I can solve using C++?

Here are a few advanced dynamic programming problems you can try:

1. Longest Increasing Subsequence
2. Edit Distance
3. 0/1 Knapsack Problem
4. Matrix Chain Multiplication
5. Coin Change Problem Would you like to dive deeper into any of these?

Can you explain the Longest Increasing Subsequence problem?

Sure! The Longest Increasing Subsequence (LIS) problem involves finding the longest subsequence in a sequence of numbers where the subsequence's elements are in increasing order. For example, in the sequence [10, 22, 9, 33, 21, 50, 41, 60, 80], the LIS is [10, 22, 33, 50, 60, 80]. The problem can be solved using dynamic programming with a time complexity of O(n^2) or O(n log n) using binary search. Would you like to see a code example?

Yes, please provide a C++ implementation for the LIS problem.

Here's a simple C++ implementation for the Longest Increasing Subsequence problem:

#include <iostream>
#include <vector>
#include <algorithm>

int longestIncreasingSubsequence(std::vector<int>& nums) {
    std::vector<int> dp(nums.size(), 1);
    for (int i = 1; i < nums.size(); i++) {
        for (int j = 0; j < i; j++) {
            if (nums[i] > nums[j]) {
                dp[i] = std::max(dp[i], dp[j] + 1);
            }
        }
    }
    return *std::max_element(dp.begin(), dp.end());
}

int main() {
    std::vector<int> nums = {10, 22, 9, 33, 21, 50, 41, 60, 80};
    std::cout << "Length of LIS is " << longestIncreasingSubsequence(nums) << std::endl;
    return 0;
}

This code calculates the length of the longest increasing subsequence. Would you like to know more about the algorithm?