What are some dynamic programming challenges in C++?

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

Here are a few dynamic programming challenges you can try in C++: 1. Fibonacci Sequence 2. Longest Common Subsequence 3. 0/1 Knapsack Problem 4. Coin Change Problem 5. Edit Distance.

Can you explain the 0/1 Knapsack Problem?

Sure! The 0/1 Knapsack Problem involves a knapsack with a maximum weight capacity. You have a set of items, each with a weight and a value, and you need to determine the maximum value you can carry without exceeding the weight limit. You can either take an item or leave it (hence 0/1).

What is the time complexity of solving the Longest Common Subsequence problem?

The time complexity of the Longest Common Subsequence problem using dynamic programming is O(m * n), where m and n are the lengths of the two sequences.

Can you provide a sample code for the Coin Change Problem?

Certainly! Here's a simple C++ implementation for the Coin Change Problem:

#include <iostream>
#include <vector>
using namespace std;

int coinChange(vector<int>& coins, int amount) {
    vector<int> dp(amount + 1, amount + 1);
    dp[0] = 0;
    for (int i = 1; i <= amount; i++) {
        for (int coin : coins) {
            if (i - coin >= 0) {
                dp[i] = min(dp[i], dp[i - coin] + 1);
            }
        }
    }
    return dp[amount] > amount ? -1 : dp[amount];
}

This code calculates the minimum number of coins needed to make a given amount.