What is dynamic programming and how does it relate to arrays?

What is dynamic programming and how does it relate to arrays?

Dynamic programming is a method for solving complex problems by breaking them down into simpler subproblems. It is particularly useful in optimization problems and can be applied to arrays to improve efficiency.

Can you give me an example of a problem that uses dynamic programming with arrays?

Sure! A classic example is the Fibonacci sequence. Instead of calculating each Fibonacci number recursively, which can be inefficient, dynamic programming allows us to store previously computed values in an array to avoid redundant calculations.

How do I implement dynamic programming for the Fibonacci sequence in Python?

You can implement it using an array to store Fibonacci numbers. Here's a simple example:

def fibonacci(n):
    fib = [0] * (n + 1)
    fib[1] = 1
    for i in range(2, n + 1):
        fib[i] = fib[i - 1] + fib[i - 2]
    return fib[n]

What are some other problems that can be solved using dynamic programming?

Other problems include the Knapsack problem, Longest Common Subsequence, and Coin Change problem. Each of these can be efficiently solved using dynamic programming techniques.