In the Fibonacci sequence, each number of the series is the sum of the previous two values. Given a starting number of 0 and 1, the sequence goes on to print; `0, 1, 1, 2, 3, 5 ...`

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In Java, we can implement the Fibonacci sequence using loops and recursion. We will be going through both implementations in detail.

For both snippets, try changing the value of `total`

to print out more numbers in the sequence.

To implement the Fibonacci sequence in Java using loops we can use either the `for`

or the `while`

loop. For each implementation, the time complexity is simply * O(total)* i.e. the number of times the loop is run. The code snippet below shows both ways to write the code

class for_Fibonacci {public static void main( String args[] ) {int number1 = 0;int number2 = 1;int sum;int total = 15;System.out.print(number1);for(int i=1;i<total;++i){sum = number1 + number2;System.out.print(", " + number2);number1 = number2;number2= sum;}}}

Another method of implementing the Fibonacci sequence in Java is to use recursion. In this way, we first create a method that calls itself recursively to print the sequence, until a base case is reached. The time complexity of this code is * O(2^total)*. The code snippet below shows how to do this.

A fibonacci recursive tree for total = 5

class recurse_Fibonacci {static int fib(int total){//Base Caseif (total <= 1){return total;}return fib(total-1) + fib(total-2);}public static void main( String args[] ) {int total = 15;for (int i= 0; i < total; i++){System.out.print(fib(i) + " ");}}}

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