Every newcomer in the Computer Science Course must face some of the beginner-level problems in the C Programming Language. The “Fibonacci Series Program in C Language” is one of such problems where you have to face challenges.
However, the concept of the Fibonacci Sequence does not originate from Computer Science. The Fibonacci Sequence is completely a concept of Mathematics. But with the C Language, we can implement the Fibonacci Sequence as well.
In this article, we will discuss all the necessary elements of the Fibonacci Sequence. We will start our discussion with the Mathematical Background of the Fibonacci Numbers. Later we will move to the development of the Fibonacci Series in C Language.
Summary Or Key Highlights:
The Fibonacci Series is one of the famous Mathematical Terms that can be implemented using C Language.
The Fibonacci Series is developed with the sum of the previous value along with the present value.
There is also a Direct Formula that exists to calculate the nth Fibonacci Number using C Language.
The Fibonacci Series in C can be developed with the help of the Iteration Function, Recursive Function, and Dynamic Programming.
There are many instances where the use of the Fibonacci Series can be seen in real life.
What Is The Fibonacci Series? Read Below
In Mathematics, we will find different series and sequences. Among them, the Fibonacci Series is one of the important ones. The Sum of the Previous Two Numbers will be considered the Next Number in the Fibonacci Series.
Is the concept appearing a bit more difficult to understand? Let’s make it simple.
In the Fibonacci Series, the first two numbers or first two terms are considered as Zero and One. The Next Number is the Sum of these first two terms which is Term 1. So, after the first two terms, the third term will be presented, and the number of terms will increase to 3.
ย We can understand that programming with mathematics can be a little difficult to understand, so you can always hire CodingZap experts if youย need any assistance with your C homework.
Now, the next number is the sum of the last two numbers, so the result will be 2. In this way, we have to move ahead for the first two terms. The formula for such calculation is the following.
Process To Get The nth Term In Series:
Fn = Fn-1 + Fn-2 [F0 will be 0 & F1 will be 1]
How To Implement Direct Formula Of nth Fibonacci Number In C Language?
Now, the above formula is to write the nth number of terms from the very beginning of the Fibonacci Series. In this case, the Complete Fibonacci Series will be printed on the screen. But, what if, you want to get a specific Fibonacci number to be printed without the entire Fibonacci series?
In that case, you have to use the Direct Formula to get any Fibonacci Numbers without printing the entire Fibonacci Series. There is a separate formula present to get such Fibonacci Numbers. The Formula to get any Fibonacci Numbers without the entire Fibonacci Series is the following.
Formula To Get The nth Term Directly Without Series: {[(โ5 + 1)/2] ^ (n-1)} / โ5
Now, it is time to implement the C Program with the help of the above formula. Then, we can see how a certain number is getting printed on the screen without the entire Fibonacci Series. For that purpose, check the following C Code Example.
#include<stdio.h>
#include<math.h> // Importing Package To Use Mathematical Functions
# define one (sqrt(5) + 1) / 2 // Defining The 1st Part Formula Of Fibonacci Numbers
int main ()
{
int n = 4; // nth Term Value
double phi = round(pow(one, n-1) / sqrt(5)); // Implementing Formula Using Variable Sum
printf("The %dth Term Is: %.0lf", n, phi); // Printing Value Using Term & Sum Variable
return 0;
}
Steps Of The Program:
First, we have imported one necessary library that will be used to handle the mathematical terms.
Now, we have defined one variable that will be used to implement the first part of the formula.
Now, the positive integer value will be provided inside the program. In this case, no User Input has been taken. And the remaining formula will be implemented.
We will print the value along with the term number that is taken inside the program.
Output:
From the above output, we can see that the direct Fibonacci number is coming. In this C Program, no Loop & Recursive Call is used to get the required output. Such a program helps to get a specific term without increasing Time Complexity & Space Complexity.
How To Implement Fibonacci Series Program In C Using Iteration?
Now, if we want to develop the Series of Fibonacci Numbers, there are different methods present. Among those different methods to get the nth number of terms as the Fibonacci Series, the Iteration Method can be useful where different Data Structures concepts can be utilized.
Here, we are going to use the Loop Concept first. We will use the While Loop and For Loop to implement the Series of Fibonacci Numbers. The probable flowchart of the entire process can be the following one.
ย Loops in Pythonย are used in an interesting way to make the condition satisfied.
How To Implement Fibonacci Series Program In C Using Recursive Function Calls?
Now, after discussing the important methods with Iteration or Dynamic Programming, we have to move to the Recursive Method. In the Recursive Approach, a function where the Recursion Logic is implemented will call itself multiple times.
To understand the Recursion Fibonacci Series, you should first understand the Recurrence Relation. In the recursion method, one function calls itself multiple times & one ending condition is provided there to terminate that.
If you wish to know about recursion, you can read out our article on Recursion in C to make things more clear.
#include<stdio.h>
void print(int n) // Function To Print Fibonacci Series Program In C
{
static int a1=0, a2=1, a3; // Initial Two Digits
if(n>0) // Conditional Ending Statement
{
a3 = a1 + a2; // Statement For Registered Marks
a1 = a2;
a2 = a3;
printf(", %d", a3); // Printing Number Of Terms
print(n-1); // Recursive Calling Function
}
}
int main()
{
int n = 10; Implementing the Int N to Ger Nth Term Value
int fib;
printf("The Fibonacci Series: 0, 1"); // Printing Initial Values
print(n-2); // Calling Function To Create Recursion Tree
return 0; // No Return Fibonacci Is Needed
}
Steps Of The Program:
To Implement the Fibonacci Series using Recursion, we have to take the term value inside of the int main() function.
Now, the previous two values will be printed in the program. These are the initial values that are needed to start the program.
Now, the function will be called from the int main() function. Inside the function, one conditional statement is used.
Inside that conditional statement, we will display the Fibonacci Sequence using the print statement. This function will be called recursively to print the remaining terms.
When the condition becomes false, the function will be finished along with the program.
Output:
From the output, we can see that along with the first two terms, further terms are also printed in the Fibonacci Series. So, the Fibonacci Series in C program is implemented without any error.
What Is The Time Complexity and Space Complexity Of The Fibonacci Series Program?
Now, before we end the discussion, we should discuss the Time Complexity and Space Complexity of the Fibonacci series program in c. The Space & Time Complexity will help to understand which process is better to utilize.
The Time Complexity of the Iterative Approach will be the O(n). The Space Complexity of the iteration Approach will be the O(1). So, this combination is looking good. However, let us check the combination for the Recursive Method.
For the Recursive Approach, the time complexity will be O(2^n). The Space Complexity will be the O(n). Space Complexity appears due to the Stack Size which we can’t much rely on. So, the best option is not to use the recursive method for small numbers.
Conclusion:
As we saw it is very important to know the “Fibonacci Series Program in C Language”.
The Fibonacci Sequence might be a concept from Mathematics, but it has one important role in the project management institute. Such problems help to grow the logical thinking & programming skills of the students.
Takeaways:
In the Fibonacci Sequence, the previous two values are added to receive the next new value.
In the Iteration Method, using the While Loop and For Loop will be the best to get the Fibonacci Sequence.
The Recursion can also be a good alternative to get Fibonacci Numbers without using Iteration.
The Best Time Complexity you can get when Lower Values are used in the Iteration Method of Fibonacci Series.
The Fibonacci Sequence can be used for Algorithms, Data Science & Problem-Solving.
