# Large Fibonacci Numbers in Java

Given a number n, find n-th Fibonacci Number. Note that n may be large.

Examples:
```Input : 100
Output : 354224848179261915075

Input : 500
Output : 139423224561697880139724382870
407283950070256587697307264108962948325571622
863290691557658876222521294125
```

Prerequisite: BigInteger Class in Java, Fibonacci numbers
Fibonacci of large number may contain more than 100 digits, it can be easily handled by BigInteger in Java. BigInteger class is used for the mathematical operation which involves very big integer calculations that are outside the limit of all available primitive data types.

## JAVA

 `// Java program to compute n-th Fibonacci ``// number where n may be large. ``import` `java.io.*; ``import` `java.util.*; ``import` `java.math.*; `` ` `public` `class` `Fibonacci ``{ ``    ``// Returns n-th Fibonacci number ``    ``static` `BigInteger fib(``int` `n) ``    ``{ ``        ``BigInteger a = BigInteger.valueOf(``0``); ``        ``BigInteger b = BigInteger.valueOf(``1``); ``        ``BigInteger c = BigInteger.valueOf(``1``); ``        ``for` `(``int` `j=``2` `; j<=n ; j++) ``        ``{ ``            ``c =  a.add(b); ``            ``a = b; ``            ``b = c; ``        ``} `` ` `        ``return` `(b); ``    ``} `` ` `    ``public` `static` `void` `main(String[] args) ``    ``{ ``        ``int` `n = ``100``; ``        ``System.out.println(``"Fibonacci of "` `+ n + ``            ``"th term"` `+ ``" "` `+``"is"` `+``" "` `+ fib(n)); ``    ``} ``} `

Output
```Fibonacci of 100th term is 354224848179261915075
```

Note that the above solution takes O(n) time, we can find the n-th Fibonacci number in O(log n) time. As an exercise, find the n-th Fibonacci number for large n in O(log n) time.