What is the space complexity of a recursive fibonacci algorithm?

Question

This is the recursive implementation of the Fibonacci sequence from Cracking the Coding Interview (5th Edition)

int fibonacci(int i) {
       if(i == 0) retu         


        

Answer 1

Here's a hint. Modify your code with a print statement as in the example below:

int fibonacci(int i, int stack) {
    printf("Fib: %d, %d\n", i, stack);
    if (i == 0) return 0;
    if (i == 1) return 1;
    return fibonacci(i - 1, stack + 1) + fibonacci(i - 2, stack + 1);
}

Now execute this line in main:

Fibonacci(6,1);

What's the highest value for "stack" that is printed out. You'll see that it's "6". Try other values for "i" and you'll see that the "stack" value printed never rises above the original "i" value passed in.

Since Fib(i-1) gets evaluated completely before Fib(i-2), there will never be more than i levels of recursion.

Hence, O(N).