What are some examples of iterative and recursive algorithms?

What are some examples of iterative and recursive algorithms?

Iterative algorithms solve problems by repeating a set of instructions until a condition is met. Examples include loops for calculating factorials or Fibonacci numbers. Recursive algorithms, on the other hand, solve problems by calling themselves with a subset of the original problem. Classic examples are the Tower of Hanoi and quicksort.

Can you explain how the Fibonacci sequence can be calculated using both methods?

Sure! For the iterative method, you can use a loop to calculate Fibonacci numbers by keeping track of the last two numbers. For the recursive method, you define a function that calls itself to calculate Fibonacci(n) as Fibonacci(n-1) + Fibonacci(n-2) until it reaches the base cases.

What are the advantages of using recursion over iteration?

Recursion can lead to simpler and more readable code, especially for problems that have a natural recursive structure, like tree traversals. However, it can be less efficient due to function call overhead and potential stack overflow for deep recursions.

Are there any downsides to using recursive algorithms?

Yes, recursive algorithms can consume more memory due to the call stack and may be slower than their iterative counterparts. Additionally, they can lead to stack overflow errors if the recursion depth is too high.