# 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 ``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 `` ` `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;``    ``f = 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 ``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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