Answers for "Fibonacci"

fibonacci

# WARNING: this program assumes the
# fibonacci sequence starts at 1
def fib(num):
	"""return the number at index `num` in the fibonacci sequence"""
    if num <= 2:
        return 1
    return fib(num - 1) + fib(num - 2)

# method 2: use `for` loop
def fib2(num):
	a, b = 1, 1
	for _ in range(num - 1):
		a, b = b, a + b
	return a


print(fib(6))  # 8
print(fib2(6))  # same result, but much faster

fibonacci

# Easy fibonacci exercise
# Method #1
def fibonacci(n):
    # 1th: 0
    # 2th: 1
    # 3th: 1 ...
    if n == 1:
        return 0
    elif n == 2:
        return 1
    else:
        return fibonacci(n - 1) + fibonacci(n - 2)

# Method #2
def fibonacci2(n):
    if n == 0: return 0
    n1 = 1
    n2 = 1
    # (1, n - 2) because start by 1, 2, 3... not 0, 1, 1, 2, 3....
    for i in range(1, n - 2):
        n1 += n2
        n2 = n1 - n2
    return n1


print(fibonacci(13))
# return the nth element in the fibonacci sequence

fibonacci

f(n) = f(n-1) + f(n-2) 
                                  f(6)
                                   ^
  			                       /\
                f(5)               +                       f(4)
                ^
               /\                   +                        /\
                
        f(4)    +           f(3)                     f(3)    +    f(2)
       ^                       ^                     ^              ^
      /\                       /\                    /\            /\
   
 f(3)   +       f(2)            f(2) +f(1)       f(2) + f(1)   f(1) +  f(0)             
   ^              ^                ^                ^
   /\             /\                /\              /\
    
f(2) + f(1)      f(1) +  f(0)     f(1)+ f(0)       f(1) + f(0)         
  ^
  /\
f(1) +  f(0) 
  
//f(6) = 8   ==>  f(1)*8    f(1) appears 8 times 
 double feb  = (1/Math.pow(5,0.5)) * (Math.pow((1+Math.pow(5,0.5))/2,n)) - (1/Math.pow(5,0.5))* (Math.pow((1-Math.pow(5,0.5))/2,n));  
  
f(1) == 1;

Fibonacci

import java.util.Scanner;
public class Fibonacci 
{
    public static void main(String[] args) 
    {
        int n, a = 0, b = 0, c = 1;
        Scanner s = new Scanner(System.in);
        System.out.print("Enter value of n:");
        n = s.nextInt();
        System.out.print("Fibonacci Series:");
        for(int i = 1; i <= n; i++)
        {
            a = b;
            b = c;
            c = a + b;
            System.out.print(a+" ");
        }
    }
}

fibonacci

// program to generate fibonacci series up to n terms

// take input from the user
const number = parseInt(prompt('Enter the number of terms: '));
let n1 = 0, n2 = 1, nextTerm;

console.log('Fibonacci Series:');

for (let i = 1; i <= number; i++) {
    console.log(n1);
    nextTerm = n1 + n2;
    n1 = n2;
    n2 = nextTerm;
}Copied

fibonacci

def fibonacci(n):
    if n == 0:
        return 0
    elif n == 1:
        return 1
    return fibonacci(n - 1) + fibonacci(n - 2)

fibonacci

Each test case will contains a single integer n where n >=1.

fibonacci

fib(5)   
                     /                  
               fib(4)                fib(3)   
             /                      /     
         fib(3)      fib(2)         fib(2)    fib(1)
        /             /           /      
  fib(2)   fib(1)  fib(1) fib(0) fib(1) fib(0)
  /    
fib(1) fib(0)