Fibonacci Series
In Mathematics, Fibonacci Series or Fibonacci Numbers are the numbers that are displayed in following sequence
Fibonacci Series = 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 …
If you observe the above pattern, First Value is 0, Second Value is 1 and the subsequent number is the result of sum of the previous two numbers. For example, Third value is (0 + 1), Fourth value is (1 + 1) so on and so forth.
In this article we will show you, How to Write Python Fibonacci Series program using While Loop, For Loop and Recursion.
Python Fibonacci Series program Using While Loop
This Python program allows the user to enter any positive integer and then, this program will display the fibonacci series of number from 0 to user specified number using the Python While Loop
PYTHON CODE
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# Python Fibonacci series Program using While Loop # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Initializing First and Second Values of a Series i = 0 First_Value = 0 Second_Value = 1 # Find & Displaying Fibonacci series while(i < Number): if(i <= 1): Next = i else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next) i = i + 1 |
OUTPUT
ANALYSIS
This program allows the user to enter any positive integer and then, that number is assigned to variable Number. Next, We declared three integer variables i, First_Value and Second_Value and assigned values as we shown above.
Below While loop will make sure that, the loop will start from 0 and it is less than the user given number. Within the While loop, we used If statement.
- If i value is less than or equal to 1 then, Next will be i
- If i value is greater than 1, perform calculations inside the Else block.
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while(i < Number): if(i <= 1): Next = i else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next) i = i + 1 |
Let us see the working principle of this while loop in iteration wise.
User Entered value: Number = 4 and i = 0, First_Value = 0, Second_Value = 1
First Iteration
- While (0 < 4) is TRUE so, program will start executing statements inside the while loop
- Within the while loop we have If statement and the condition if (0 <= 1) is TRUE so Next = 0 and compiler will exit from if statement block
- Print statement print(Next) will print the value 0
- Lastly, i will be incremented to 1
Second Iteration
- While (1 < 4) is TRUE so, program will start executing statements inside the while loop
- Within the while loop we have If statement and the condition if (1 <= 1) is TRUE so Next = 1 and compiler will exit from if statement block
- Print statement print(Next) will print the value 1
- Lastly, i will be incremented to 1
Third Iteration
While (2 < 4) is TRUE so, program will start executing statements inside the while loop. Within the while loop we have If statement and the condition if (2 <= 1) is FALSE so statements inside the else block will start executing
Next = First_Value + Second_Value
Next = 0 + 1 = 1
First_Value = Second_Value = 1
Second_Value = Next = 1
Next, Print statement print(Next) will print the value 1. Lastly, i will be incremented to 1
Fourth Iteration
While (3 < 4) is TRUE so, program will start executing statements inside the while loop. Within the while loop we have If statement and the condition if (3 <= 1) is FALSE so statements inside the else block will start executing
Next = First_Value + Second_Value
Next = 1 + 1 = 2
First_Value = Second_Value = 1
Second_Value = Next = 2
Next, Print statement print(Next) will print the value 2. Lastly, i will be incremented to 1
Fifth Iteration
While (4 < 4) is FALSE so, program will exit from the while loop.
From the above, Our final output of Next values are: 0 1 1 2
Python Fibonacci Series program Using For Loop
This Python program allows the user to enter any positive integer and then, this program will display the fibonacci series of number from 0 to user specified number using Python For Loop
PYTHON CODE
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# Python Fibonacci series Program using For Loop # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Initializing First and Second Values of a Series First_Value = 0 Second_Value = 1 # Find & Displaying Fibonacci series for Num in range(0, Number): if(Num <= 1): Next = Num else: Next = First_Value + Second_Value First_Value = Second_Value Second_Value = Next print(Next) |
OUTPUT
We just replaced the While loop in the above example with the For loop. If you don’t understand the for loop then please refer For Loop article here: Python For Loop
Python Fibonacci Series program Using Recursion
This Python program allows the user to enter any positive integer and then, this program will display the fibonacci series of number from 0 to user specified number using Recursion concept.
PYTHON CODE
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# Python Fibonacci series Program using Recursion # Recursive Function Beginning def Fibonacci_series(Number): if(Number == 0): return 0 elif(Number == 1): return 1 else: return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1)) # End of the Function # Fibonacci series will start at 0 and travel upto below number Number = int(input("\nPlease Enter the Range Number: ")) # Find & Displaying Fibonacci series for Num in range(0, Number): print(Fibonacci_series(Num)) |
OUTPUT
ANALYSIS
In this example we defined a function. Following function will accept integer values as parameter value and return value
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def Fibonacci_series(Number): |
Lets see the ElIf statement inside the above specified functions
- if (Number == 0) will check whether the given number is 0 or not. If it is TRUE, function will return the value Zero.
- if (Number == 1) will check whether the given number is 1 or not. If it is TRUE, function will return the value One.
- If the number is greater than 1 then the statements inside the else block will be executed.
Within the Else block we called the function recursively to display the Fibonacci series.
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return (Fibonacci_series(Number - 2)+ Fibonacci_series(Number - 1)) |
For example, Number = 2
(Fibonacci_series(Number – 2)+ Fibonacci_series(Number – 1))
(Fibonacci_series(2 – 2)+ Fibonacci_series(2 – 1)), It means
(Fibonacci_series(0)+ Fibonacci_series(1))
return (0 + 1) = return 1
NOTE: For Recursive functions it is very important to place a condition before using the function recursively otherwise, we will end up in infinite execution (Same like infinite Loop).
Please be careful 🙂
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