Dynamic Programming Questions Medium
Dynamic Programming can be used to solve the Fibonacci sequence problem by using a technique called memoization.
In the Fibonacci sequence, each number is the sum of the two preceding ones. The traditional recursive approach to solve this problem has an exponential time complexity, as it recalculates the same Fibonacci numbers multiple times.
To optimize this, we can use dynamic programming and store the previously calculated Fibonacci numbers in an array or a dictionary. This way, when we need to calculate a Fibonacci number, we first check if it has already been calculated and stored. If it has, we simply retrieve it from the storage, avoiding redundant calculations. If it hasn't been calculated yet, we calculate it and store it for future use.
Here is an example implementation in Python:
def fibonacci(n):
fib = [0, 1] # Initialize the Fibonacci sequence with the first two numbers
for i in range(2, n+1):
fib.append(fib[i-1] + fib[i-2]) # Calculate the next Fibonacci number and store it
return fib[n] # Return the nth Fibonacci number
By using dynamic programming and memoization, this implementation has a time complexity of O(n), significantly improving the efficiency compared to the traditional recursive approach.