How does the fibonacci recursive function "work"?

How does the fibonacci recursive function "work"?

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I'm new to Javascript and was reading up on it, when I came to a chapter that described function recursion. It used an example function to find the nth number of the Fibonacci sequence. The code is as follows:

function fibonacci(n) {
   if (n < 2){
     return 1;
   }else{
     return fibonacci(n-2) + fibonacci(n-1);
   }
}

console.log(fibonacci(7));
//Returns 21

I'm having trouble grasping exactly what this function is doing. Can someone explain what's going on here? I'm getting stuck on the 5th line, where the function calls itself. What's happening here?


Fibonacci series using recursion in C, because each term after the second term is the sum of the previous two terms. Our first two terms are 1 and 1. The third term is the previous two terms added together, or 1+1=2. During the section where we learn about recursion, the Fibonacci sequence is used to illustrate the concept. Below is a recursive method, written in Ruby, to find the nth number in the Fibonacci sequence. I will attempt to explain how this method works using the code as well as a tree diagram as presented in the Launch School course.


There are many good answers here, but I made this diagram which helps better explain the outcome of the function. The only values that will ever be returned are 1 or 0 (your example returns 1 for n < 2, but should instead return n).

This means that each recursive call will eventually wind up returning either a 0 or 1. Those end up being "cached" in the stack and "carried up" into the original invocation and added together.

So if you were to draw this same diagram out for each value of 'n' you could manually find the answer.

This diagram roughly illustrates how every function is returned for fib(5).

This shows the control flow, i.e. the order of execution for the functions. Remember code is always executed left->right and top-> bottom. So whenever a new function is called it is paused and then the next invocation occurs.

The following illustrates the actual control flow based on your original post. Please note the base condition is if (n <= 0) {return 0} else if (n <= 2) {return 1;} for simplification:

1. fib(5) {
    return fib(4) + fib(3);
2.   fib(4) {
      return fib(3) + fib(2);
3.     fib(3) {
        return fib(2) + fib(1);
4.       fib(2) {
A=        return 1;
         };
5.       fib(1) {
B=        return 1;
         };
C=      return 2; // (1 + 1)
       };
6.     fib(2) {
D=      return 1;
       };
E=    return 3; // (2 + 1)
     };
7.   fib(3) {
      return fib(2) + fib(1);
8.     fib(2) {
F=      return 1;
       };
9.     fib(1) {
G=      return 1;
       };
H=    return 2; // (1 + 1)
     };
I=  return 5; // (3 + 2)
   };

CSci 160 Session 29: Recursion, Fibonacci numbers, What is the Fibonacci sequence and how can you program that using recursion? Recursive fibonacci method in Java. The fibonacci series is a series in which each number is the sum of the previous two numbers. The number at a particular position in the fibonacci series can be obtained using a recursive method.


Step 1) When fibonacci(7) is called imagine the following (notice how I changed all the n's to 7):

function fibonacci(7) {
    if (7 < 2){
        return 1;
    }else{
        return fibonacci(7-2) + fibonacci(7-1);
    }
}

Step 2) Since (7 < 2) is obviously false, we go to fibonacci(7-2) + fibonacci(7-1); which translates to fibonacci(5) + fibonacci(6); Since fibonacci(5) comes first, that get called (changes the n's to 5 this time):

function fibonacci(5) {
    if (5 < 2){
        return 1;
    }else{
        return fibonacci(5-2) + fibonacci(5-1);
    }
}

Step 3) And or course fibonacci(6) also gets called, so what happened is for everyone call of fibonacci 2 new fibonacci get called.

Visualization:

      fibonacci(7)
      ____|_____
     |          |
fibonacci(5)  fibonacci(6)
____|____     ____|_____
|        |    |         |
fib(3)  fib(4) fib(4)   fib(5)

See how it branches? When is it going to stop? When n becomes less than 2, thats why you have if (n < 2). At that point the branching stops and everything gets added together.

Recursive Sequence: Formula & Overview, Recursive functions are those functions which, basically, call themselves. I want to note that this isn't the best method to do it — in fact, it could be  · A recursive function F (F for Fibonacci): to compute the value of the next term. · Nothing else: I warned you it was quite basic. Our function will take n as an input, which will refer to the nth term of the sequence that we want to be computed. So, F(4) should return the fourth term of the sequence.


Hopefully the following helps. Calling:

fibonacci(3)

will get to line 5 and do:

return fibonacci(1) + fibonacci(2);

the first expression calls the function again and returns 1 (since n < 2).

The second calls the function again, gets to the 5th line and does:.

return fibonacci(0) + fibonacci(1);

both expressions return 1 (since n < 2 for both), so this call to the function returns 2.

So the answer is 1 + 2, which is 3.

Fibonacci Series Program in Java using Loops & Recursion, You're defining a function in terms of itself. In general, fibonnaci(n) = fibonnaci(n - 2) + fibonnaci(n - 1) . We're just representing this relationship  Recursive functions achieve this goal by re-using the same logic with different parameters every time the function is recursively called. Recursion and the Fibonacci Sequence. With this in mind, it’s easy to see why the Fibonacci sequence is a good example of recursion. In the Fibonacci sequence, each number is recursively defined as the sum


I think that these two functions gave a much clearer explanation of recursion to me (from this blog post):

function fibDriver(n) {
  return n === 0 ? 0 : fib(0, 1, n);
}

function fib(a, b, n) {
  return n === 1 ? b : fib(b, a + b, n-1);
}

How to use recursive functions to create the Fibonacci Sequence in , The Fibonacci numbers are the numbers in the following integer sequence. Write a Duration: 2:14 Posted: Sep 10, 2011 A recursive function recur_fibo() is used to calculate the nth term of the sequence. We use a for loop to iterate and calculate each term recursively. Visit here to know more about recursion in Python .


How does the fibonacci recursive function "work"?, available right now. Please try again later. Published on Jun 30, 2011. Understanding why Duration: 8:04 Posted: Jun 30, 2011 Now, we want to find out the number of recursive calls made to calculate F (n). We use G (n) to denote the number of calls made by the recursive program in calculating F (n). Let's examine the output above. We see that G (0) = G (1) = 1 and to compute G (n) for arbitrary n,


Program for Fibonacci numbers, Code : Compute fibonacci numbers using recursion method important to recursion function, i.e n == 0 and n == 1 or the recursive call would be infinite leading  This matches the time for computing the n th Fibonacci number from the closed-form matrix formula, but with fewer redundant steps if one avoids recomputing an already computed Fibonacci number (recursion with memoization). Identification. The question may arise whether a positive integer x is a Fibonacci number.


Stepping Through Recursive Fibonacci Function, For example, the Fibonacci numbers are often defined recursively. And Java allows you to do this - all you have to do is to use the function within its own  Recursive Functions A recursive function (DEF) is a function which either calls itself or is in a potential cycle of function calls. As the definition specifies, there are two types of recursive functions. Consider a function which calls itself: we call this type of recursion immediate recursion.