C++ Dynamic Programming Exercises

Can you give me some dynamic programming exercises in C++?

Sure! Here are a few exercises you can try:

1. Fibonacci Sequence
2. Coin Change Problem
3. Longest Common Subsequence
4. 0/1 Knapsack Problem
5. Edit Distance Problem Which one would you like to start with?

Let's start with the Fibonacci Sequence. How do I implement it?

You can implement the Fibonacci sequence using dynamic programming like this:

#include <iostream>
#include <vector>

int fibonacci(int n) {
    std::vector<int> fib(n + 1);
    fib[0] = 0;
    fib[1] = 1;
    for (int i = 2; i <= n; ++i) {
        fib[i] = fib[i - 1] + fib[i - 2];
    }
    return fib[n];
}

int main() {
    int n;
    std::cout << "Enter a number: ";
    std::cin >> n;
    std::cout << "Fibonacci of " << n << " is " << fibonacci(n) << std::endl;
    return 0;
}

This code uses a vector to store Fibonacci numbers up to n.

What is the time complexity of this implementation?

The time complexity of this dynamic programming implementation of the Fibonacci sequence is O(n), as it computes each Fibonacci number once and stores it in a vector.

Can you explain the space complexity as well?

Certainly! The space complexity of this implementation is also O(n) due to the vector used to store the Fibonacci numbers. If you want to optimize it, you can reduce the space complexity to O(1) by only storing the last two Fibonacci numbers.