What are some examples of dynamic programming in C++?

What are some examples of dynamic programming in C++?

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. Here are a few examples in C++:

1. Fibonacci Sequence: Using memoization to store previously computed values.
2. Knapsack Problem: Finding the maximum value that can be carried in a knapsack of a given capacity.
3. Longest Common Subsequence: Determining the longest subsequence present in two sequences.

Would you like to see code examples for any of these?

Yes, can you show me the Fibonacci sequence example?

Sure! Here's a simple implementation of the Fibonacci sequence using dynamic programming in C++:

#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 = 10; // Example input
    std::cout << "Fibonacci of " << n << " is " << fibonacci(n) << std::endl;
    return 0;
}

This code calculates the nth Fibonacci number using a bottom-up approach. Would you like to explore another example?

Can you explain the knapsack problem?

Absolutely! The knapsack problem is a classic optimization problem. The goal is to maximize the total value of items placed in a knapsack without exceeding its weight capacity. Here's a brief overview:

• Input: A set of items, each with a weight and a value, and a maximum weight capacity of the knapsack.
• Output: The maximum value that can be achieved within the given weight limit.

Would you like to see a C++ implementation of the knapsack problem?