# Designing Code for Fibonacci Sequence without Recursion

Fibonacci sequence:

The Fibonacci sequence is a sequence type in which the sum of the previous two numbers is each consecutive number.

First few Fibonacci numbers are 0 1 1 2 3 5 8 …..etc.

## Fibonacci sequence without recursion:

Let us now write code to display this sequence without recursion. Because recursion is simple, i.e. just use the concept,

Fib(i) = Fib(i-1) + Fib(i-2)

However, because of the repeated calculations in recursion, large numbers take a long time.

So, without recursion, let’s do it.

Approach:

• Create two variables to hold the values of the previous and second previous numbers.
• Set both variables to 0 to begin.
• Begin a loop until N is reached, and for each i-th index
• Print the sum of the previous and second most previous i.e sum= previous + second previous
• Assign previous to second previous i.e. second previous= previous
• Assign sum to previous i.e previous=sum

Below is the implementation:

1)C++ implementation of above approach.

#include <iostream>
using namespace std;
int main()
{ // given number
int n = 10;
// initializing previous and second previous to 0
int previous = 0;
int secondprevious = 0;
int i;
// loop till n
for (i = 0; i < n; i++) {
// initializing sum to previous + second previous
int sum = previous + secondprevious;
cout << sum << " ";
if (!sum)
previous = 1;
secondprevious = previous;
previous = sum;
}
return 0;
}


2)Python implementation of above approach.

# given number
n = 10
# initializing previous and second previous to 0
previous = 0
secondprevious = 0
# loop till n
for i in range(n):
sum = previous + secondprevious
print(sum, end=" ")
if (not sum):
previous = 1
# initializing value to previous to second previous
secondprevious = previous
previous = sum


Output:

0 1 1 2 3 5 8 13 21 34

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