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C Program for Fibonacci numbers

  • Last Updated : 04 Dec, 2018

The Fibonacci numbers are the numbers in the following integer sequence.

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, ……..

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In mathematical terms, the sequence Fn of Fibonacci numbers is defined by the recurrence relation

    Fn = Fn-1 + Fn-2

with seed values



   F0 = 0 and F1 = 1.

C




// Fibonacci Series using Recursion
#include <stdio.h>
int fib(int n)
{
    if (n <= 1)
        return n;
    return fib(n - 1) + fib(n - 2);
}
  
int main()
{
    int n = 9;
    printf("%d", fib(n));
    getchar();
    return 0;
}
Output:
34

Time Complexity: T(n) = T(n-1) + T(n-2) which is exponential.
We can observe that this implementation does a lot of repeated work (see the following recursion tree). So this is a bad implementation for nth Fibonacci number.

                         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)

Extra Space: O(n) if we consider the function call stack size, otherwise O(1).

Method 2 ( Use Dynamic Programming )
We can avoid the repeated work done is the method 1 by storing the Fibonacci numbers calculated so far.

C




// Fibonacci Series using Dynamic Programming
#include <stdio.h>
  
int fib(int n)
{
    /* Declare an array to store Fibonacci numbers. */
    int f[n + 1];
    int i;
  
    /* 0th and 1st number of the series are 0 and 1*/
    f[0] = 0;
    f[1] = 1;
  
    for (i = 2; i <= n; i++) {
        /* Add the previous 2 numbers in the series
         and store it */
        f[i] = f[i - 1] + f[i - 2];
    }
  
    return f[n];
}
  
int main()
{
    int n = 9;
    printf("%d", fib(n));
    getchar();
    return 0;
}
Output:
34

Time Complexity: O(n)
Extra Space: O(n)

Method 3 ( Space Optimized Method 2 )
We can optimize the space used in method 2 by storing the previous two numbers only because that is all we need to get the next Fibonacci number in series.

C/C++




// Fibonacci Series using Space Optimized Method
#include <stdio.h>
int fib(int n)
{
    int a = 0, b = 1, c, i;
    if (n == 0)
        return a;
    for (i = 2; i <= n; i++) {
        c = a + b;
        a = b;
        b = c;
    }
    return b;
}
  
int main()
{
    int n = 9;
    printf("%d", fib(n));
    getchar();
    return 0;
}
Output:
34

Please refer complete article on Program for Fibonacci numbers for more details!




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