In Arithmetic, the Fibonacci Collection is a sequence of numbers such that every quantity within the sequence is a sum of the previous numbers. The sequence begins with 0 and 1. This weblog will train us the best way to create the Fibonacci Collection in Python utilizing a loop, recursion, and dynamic programming.

**What is Fibonacci Series****Fibonacci Series Logic****Fibonacci Series Formula****Fibonacci Spiral****Fibonacci series algorithm****Fibonacci Series in Python**

a. Fibonacci Series Using loop

b. Fibonacci Series using Recursion

c. Fibonacci Series using Dynamic Programming**FAQs**

Leonardo Pisano Bogollo was an Italian mathematician from the Republic of Pisa and was thought-about essentially the most gifted Western mathematician of the Center Ages. He lived between 1170 and 1250 in Italy. “Fibonacci” was his nickname, which means “Son of Bonacci.” Fibonacci was not the primary to know concerning the sequence, and it was identified in India lots of of years earlier than!

**What’s **Fibonacci Collection ?

Fibonacci Collection is a sample of numbers the place every quantity outcomes from including the final two consecutive numbers. The primary 2 numbers begin with 0 and 1, and the third quantity within the sequence is 0+1=1. The 4th quantity is the addition of the 2nd and third quantity, i.e., 1+1=2, and so forth.

The Fibonacci Sequence is the sequence of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

**The logic of the Fibonacci Collection**

The next quantity is a sum of the 2 numbers earlier than it.

The third factor is (1+0) = 1

The 4th factor is (1+1) = 2

The fifth factor is (2+1) = 3

**Fibonacci Collection Method**

Therefore, the method for calculating the sequence is as follows:

x_{n} = x_{n-1} + x_{n-2} ; the place

x_{n} is the time period quantity “n”

x_{n-1} is the earlier time period (n-1)

x_{n-2} is the time period earlier than that

**Fibonacci Spiral**

An thrilling property about these numbers is that we get a spiral once we make squares with these widths. A Fibonacci spiral is a sample of quarter-circles related inside a block of squares with Fibonacci numbers written in every of the blocks. The quantity within the big sq. is a sum of the next 2 smaller squares. This can be a excellent association the place every block is denoted the next quantity than the earlier two blocks. The principle thought has been derived from the Logarithmic sample, which additionally seems related. These numbers are additionally associated to the golden ratio.

Learn to discover if a String is a Palindrome in Python

**Fibonacci Collection Algorithm**

**Iterative Strategy**

- Initialize variables a,b to 1
- Initialize for loop in vary[1,n) # n exclusive
- Compute next number in series; total = a+b
- Store previous value in b
- Store total in a

**Recursive Approach**

- If n equals 1 or 0; return 1
- Else return fib(n-1) + fib(n-2)

**Dynamic Programming Approach**

- Initialize an array arr of size n to zeros
- If n equals 0 or 1; return 1 Else
- Initialize arr[0] and arr[1] to 1
- Run for loop in vary[2,num]
- Compute the worth arr[I]=arr[I-1] +arr[I-2]
- The array has the sequence computed until n

Therefore, the answer could be to compute the worth as soon as and retailer it in an array from the place it may be accessed the following time it’s required. Due to this fact, we use dynamic programming in such circumstances. The circumstances for implementing dynamic programming are

1. overlapping sub-problems

2. optimum substructure

### Iterative Strategy

```
def fib_iter(n):
a=1
b=1
if n==1:
print('0')
elif n==2:
print('0','1')
else:
print("Iterative Strategy: ", finish=' ')
print('0',a,b,finish=' ')
for i in vary(n-3):
whole = a + b
b=a
a= whole
print(whole,finish=' ')
print()
return b
fib_iter(5)
```

Output : Iterative Strategy : 0 1 1 2 3

### Recursive Strategy

```
def fib_rec(n):
if n == 1:
return [0]
elif n == 2:
return [0,1]
else:
x = fib_rec(n-1)
# the brand new factor the sum of the final two components
x.append(sum(x[:-3:-1]))
return x
x=fib_rec(5)
print(x)
```

Output – 0, 1, 1, 2, 3

**Dynamic Programming Strategy**

```
There's a slight modification to the iterative method. We use an extra array.
def fib_dp(num):
arr = [0,1]
print("Dynamic Programming Strategy: ",finish= ' ')
if num==1:
print('0')
elif num==2:
print('[0,','1]')
else:
whereas(len(arr)<num):
arr.append(0)
if(num==0 or num==1):
return 1
else:
arr[0]=0
arr[1]=1
for i in vary(2,num):
arr[i]=arr[i-1]+arr[i-2]
print(arr)
return arr[num-2]
fib_dp(5)
```

Output – 0, 1, 1, 2, 3

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**FAQs**

**What are the properties of the Fibonacci sequence?**

The Fibonacci sequence has a number of properties, together with:

-Every quantity within the sequence is the sum of the 2 previous numbers.

-The primary two numbers within the sequence are 0 and 1.

**What are some purposes of the Fibonacci sequence?**

The Fibonacci sequence has a number of purposes, together with:

-It may be used to mannequin the expansion of populations of animals.

-It may be used to calculate the Golden Ratio, which is utilized in structure and artwork.

-It may be utilized in pc programming to generate environment friendly algorithms.

**What’s the time complexity of producing the Fibonacci sequence?**

The time complexity of producing the Fibonacci sequence is O(n).

**What’s the house complexity of storing the Fibonacci sequence?**

The Fibonacci sequence is an infinite sequence, so the house complexity is infinite.

**Additional Studying**

- Factorial of a quantity in Python
- Palindrome in Python
- Convert Record to String in Python
- Eval Operate in Python