Question

The terms in the Fibonacci sequence are given by : F? = 1, F? = 1; F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub> Consider the following recursive algorithm to calculate the nth Fibonacci number. int Fib(int n) { if (n <= 1) return n; return Fib(n-1) + Fib(n-2); } What is the running time of the recursive Fib? What is the running time of an efficient DP algorithm to calculate the nth Fibonacci number? Both algorithms are O(n) Recursive: O(n^2) and DP: O(n) Recursive: Theta(2^n) and DP: Theta(n^2) Recursive: O(2^n) and DP: Theta(n) Recursive O(4^n) and DP: O(Ign)

          The terms in the Fibonacci sequence are
given by :
F? = 1, F? = 1; F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub>
Consider the following recursive algorithm
to calculate the nth Fibonacci number.
int Fib(int n)
{
if (n <= 1)
return n;
return Fib(n-1) + Fib(n-2);
}
What is the running time of the recursive
Fib? What is the running time of an
efficient DP algorithm to calculate the nth
Fibonacci number?
Both algorithms are O(n)
Recursive: O(n^2) and DP: O(n)
Recursive: Theta(2^n) and DP: Theta(n^2)
Recursive: O(2^n) and DP: Theta(n)
Recursive O(4^n) and DP: O(Ign)

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The terms in the Fibonacci sequence are
given by :
F? = 1, F? = 1; F<sub>n</sub> = F<sub>n-1</sub> + F<sub>n-2</sub>
Consider the following recursive algorithm
to calculate the nth Fibonacci number.
int Fib(int n)

if (n <= 1)
return n;
return Fib(n-1) + Fib(n-2);

What is the running time of the recursive
Fib? What is the running time of an
efficient DP algorithm to calculate the nth
Fibonacci number?
Both algorithms are O(n)
Recursive: O(n^2) and DP: O(n)
Recursive: Theta(2^n) and DP: Theta(n^2)
Recursive: O(2^n) and DP: Theta(n)
Recursive O(4^n) and DP: O(Ign)

Added by Jennifer M.

Computer Science and Information Technology

Trishna Knowledge Systems 2018 Edition

Instant Answer

Solved by Expert Deepak Kumar

Step 1

This is because for each call to the Fib function, it makes two recursive calls to calculate Fib(n-1) and Fib(n-2). Each of these calls then makes two more recursive calls, and so on. This results in an exponential growth in the number of function calls, leading Show more…

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The terms in the Fibonacci sequence are given by: F1 = 1, F2 = 1; Fn = Fn-1 + Fn-2 Consider the following recursive algorithm to calculate the nth Fibonacci number: return Fib(n-1) + Fib(n-2); What is the running time of the recursive Fib? What is the running time of an efficient DP algorithm to calculate the nth Fibonacci number? Both algorithms are O(n) Recursive: O(n^2) and DP: O(n) Recursive: Theta(2^n) and DP: Theta(n^2) Recursive: O(2^n) and DP: Theta(n) Recursive: O(4^n) and DP: O(1)

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