Python Program to Find Fibonacci Series

You can find the Fibonacci series in Python by using a loop that starts with 0 and 1 and adds the last two numbers to get the next one, like this: for i in range(n): print(a, end=' '); a, b = b, a + b.

Examples

Input5

Output0 1 1 2 3

Input1

Output0

Input0

Output

How to Think About It

To find the Fibonacci series, start with the first two numbers 0 and 1. Then, keep adding the last two numbers to get the next number in the series. Repeat this process until you reach the desired length.

Algorithm

1

Get the number of terms to generate, n.

2

Initialize two variables with 0 and 1 as the first two Fibonacci numbers.

3

Loop from 0 to n-1.

4

In each loop, print the current number and update the two variables to the next two Fibonacci numbers.

5

Stop when n numbers are printed.

Code

python

n = int(input('Enter number of terms: '))
a, b = 0, 1
for _ in range(n):
    print(a, end=' ')
    a, b = b, a + b

Output

Enter number of terms: 5
0 1 1 2 3 

Dry Run

Let's trace the input 5 through the code

1

Initialize

a = 0, b = 1

2

Iteration 1

Print 0, update a=1, b=1

3

Iteration 2

Print 1, update a=1, b=2

4

Iteration 3

Print 1, update a=2, b=3

5

Iteration 4

Print 2, update a=3, b=5

6

Iteration 5

Print 3, update a=5, b=8

Iteration	a (printed)	b (next)
1	0	1
2	1	1
3	1	2
4	2	3
5	3	5

Why This Works

Step 1: Start with first two numbers

The Fibonacci series always begins with 0 and 1, so we set a = 0 and b = 1.

Step 2: Print current number

In each loop, we print the current number a which is the next number in the series.

Step 3: Update numbers

We update a and b to the next two Fibonacci numbers by setting a = b and b = a + b (using the old values).

Alternative Approaches

Using recursion

python

def fib(n):
    if n <= 1:
        return n
    else:
        return fib(n-1) + fib(n-2)

n = int(input('Enter number of terms: '))
for i in range(n):
    print(fib(i), end=' ')

Simple but inefficient for large n due to repeated calculations.

Using dynamic programming (memoization)

python

def fib(n, memo={}):
    if n in memo:
        return memo[n]
    if n <= 1:
        memo[n] = n
    else:
        memo[n] = fib(n-1, memo) + fib(n-2, memo)
    return memo[n]

n = int(input('Enter number of terms: '))
for i in range(n):
    print(fib(i), end=' ')

Faster than plain recursion by storing results but uses extra memory.

Complexity: O(n) time, O(1) space

Time Complexity

The loop runs n times, so the time grows linearly with n.

Space Complexity

Only a few variables are used, so space stays constant regardless of n.

Which Approach is Fastest?

The iterative loop approach is fastest and uses least memory compared to recursion or memoization.

Approach	Time	Space	Best For
Iterative loop	O(n)	O(1)	Most efficient for large n
Recursion	O(2^n)	O(n)	Simple but slow, small n only
Memoization	O(n)	O(n)	Faster recursion with extra memory