recursive function fibonacci javascript

How does the fibonacci recursive function "work"?

stackoverflow.com › questions › 8845154 › how-does-the-fibonacci-recursive-function-work

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 in code. So, for fibonnaci(7) we can observe:

fibonacci(7) is equal to fibonacci(6) + fibonacci(5)
fibonacci(6) is equal to fibonacci(5) + fibonacci(4)
fibonacci(5) is equal to fibonacci(4) + fibonacci(3)
fibonacci(4) is equal to fibonacci(3) + fibonacci(2)
fibonacci(3) is equal to fibonacci(2) + fibonacci(1)
fibonacci(2) is equal to fibonacci(1) + fibonacci(0)
fibonacci(1) is equal to 1
fibonacci(0) is equal to 1

We now have all the parts needed to evaluate fibonacci(7), which was our original goal. Notice that the base case -- return 1 when n < 2 -- is what makes this possible. This is what stops the recursion, so that we can can start the process of unrolling the stack and summing the values we're returning at each step. Without this step, we'd continue calling fibonacci on smaller and smaller values right up until the program finally crashed.

It might help to add some logging statements that illustrate this:

function fibonacci(n, c) {
    var indent = "";
    for (var i = 0; i < c; i++) {
        indent += " ";
    }
    console.log(indent + "fibonacci(" + n + ")");
    if (n < 2) {
        return 1;
    } else {
        return fibonacci(n - 2, c + 4) + fibonacci(n - 1, c + 4);
    }
}

console.log(fibonacci(7, 0));

Output:

fibonacci(7)
    fibonacci(5)
        fibonacci(3)
            fibonacci(1)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
        fibonacci(4)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
    fibonacci(6)
        fibonacci(4)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
        fibonacci(5)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
            fibonacci(4)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
                fibonacci(3)
                    fibonacci(1)
                    fibonacci(2)
                        fibonacci(0)
                        fibonacci(1)

Values at the same level of indentation are summed to produce the result for the previous level of indentation.

Answer from Wayne on Stack Overflow

Stack Overflow

stackoverflow.com › questions › 8845154 › how-does-the-fibonacci-recursive-function-work

recursion - How does the fibonacci recursive function "work"? - Stack Overflow

Top answer

1 of 14

121

fibonacci(7) is equal to fibonacci(6) + fibonacci(5)
fibonacci(6) is equal to fibonacci(5) + fibonacci(4)
fibonacci(5) is equal to fibonacci(4) + fibonacci(3)
fibonacci(4) is equal to fibonacci(3) + fibonacci(2)
fibonacci(3) is equal to fibonacci(2) + fibonacci(1)
fibonacci(2) is equal to fibonacci(1) + fibonacci(0)
fibonacci(1) is equal to 1
fibonacci(0) is equal to 1

It might help to add some logging statements that illustrate this:

function fibonacci(n, c) {
    var indent = "";
    for (var i = 0; i < c; i++) {
        indent += " ";
    }
    console.log(indent + "fibonacci(" + n + ")");
    if (n < 2) {
        return 1;
    } else {
        return fibonacci(n - 2, c + 4) + fibonacci(n - 1, c + 4);
    }
}

console.log(fibonacci(7, 0));

Output:

fibonacci(7)
    fibonacci(5)
        fibonacci(3)
            fibonacci(1)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
        fibonacci(4)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
    fibonacci(6)
        fibonacci(4)
            fibonacci(2)
                fibonacci(0)
                fibonacci(1)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
        fibonacci(5)
            fibonacci(3)
                fibonacci(1)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
            fibonacci(4)
                fibonacci(2)
                    fibonacci(0)
                    fibonacci(1)
                fibonacci(3)
                    fibonacci(1)
                    fibonacci(2)
                        fibonacci(0)
                        fibonacci(1)

Values at the same level of indentation are summed to produce the result for the previous level of indentation.

2 of 14

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)
   };

Programiz

programiz.com › javascript › examples › fibonacci-recursion

JavaScript Program to Display Fibonacci Sequence Using Recursion

// program to display fibonacci sequence using recursion function fibonacci(num) { if(num < 2) { return num; } else { return fibonacci(num-1) + fibonacci(num - 2); } } // take nth term input from the user const nTerms = prompt('Enter the number of terms: '); if(nTerms <=0) { console.log('Enter ...

Discussions

Can you explain the logic behind a recursive fibonacci function?

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r/javahelp

November 23, 2022

Can I get clarification on the fibonacci javascript exercise?

You can do all of that inside of one function. -Take the given number and check if it should be accept. -Then iterate through the sequence until the given position. For this, the calculation should be simple, 1 + 1 = 2, 1 + 2 = 3, and so on. -Return the member of the sequence in that position. You'll need at least one temp variable and because of the way fibonacci works, you'll need to adjust the loop properly. More on reddit.com

r/theodinproject

November 21, 2022

I just implemented the Fibonacci sequence as a one-liner, arrow function as a Javascript newbie, feeling VERY happy and proud of it

Nice! :) Here is one in Clojure, defining the infinite Fibonacci sequence. > (def fib (lazy-cat [0 1] (map + fib (rest fib)))) > fib (0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610 987 1597 2584 4181 ...) More on reddit.com

r/learnprogramming

585

December 14, 2019

Fibonacci recursion is wrecking my brain. What's going on with the console.log here? I thought I understood what this code was doing but I was wrong. Here I am trying to evaluate what the fibonacci number is at the 5th position (i.e. 5th position of this fibonnaci sequence 1, 2, 3, 5, 8).

This subreddit is for anyone who wants to learn JavaScript or help others do so. Questions and posts about frontend development in general are welcome, as are all posts pertaining to JavaScript on the backend · Create your account and connect with a world of communities More on reddit.com

r/learnjavascript

July 23, 2017

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