How can I solve the Fibonacci sequence using dynamic programming?

How can I solve the Fibonacci sequence using dynamic programming?

You can solve the Fibonacci sequence using dynamic programming by storing previously computed values to avoid redundant calculations.

Can you show me a simple implementation in Python?

Sure! Here's a simple implementation:

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]

This function computes the nth Fibonacci number efficiently.

What is the time complexity of this approach?

The time complexity of this dynamic programming approach is O(n), as it computes each Fibonacci number once and stores it.

Are there any other methods to solve the Fibonacci sequence?

Yes, you can also solve it using recursion, memoization, or even matrix exponentiation for more efficient calculations.