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Fibonacci Series : C Program To Find The Index Of an Input Number

What is Fibonacci Series

The problem is to find the index of a number that occurs in the Fibonacci series. Fibonacci series starts from zero. Sequence such as 0 1 1 2 3 5 8 13 21 34 55.......etc. The sequence is the sum of two previous values in the series.
                                                                               

Algorithm :-

  1. Enter the number, you want to find the index in the Fibonacci series, read as n.
  2. Declare three integer variable, read as a, b, c, res, these variables are used to find the Fibonacci series.
  3. Initialize the variable a=0, series start from zero, b=1, c=1 and res=1,here res is the index of the Fibonacci series.
  4. We have to check, if n is less than or equal to one then return 1; else run the while loop in the next.
  5. For while loop variables a, b, c are used to find the Fibonacci series and res is used to calculate the index of n.
  6. whenever c is equal to or greater than the n, while loop while will be terminated, else while loop executes.
  7. First a+b is stored in c and res will be incremented, b value initialized to a and c value initialized to b, after firs loop completed, it will check the value of c and compare with n, if value of c is greater than the n then while loop terminates and return will return res which is the index to the main function.
  8. Inside the main function, index of the program is printed.

Program:-

#include<stdio.h>
#include<conio.h>

int fibo(int n)
{
  int a, b, c, res;
  a=0;
  b=1;
  c=1;
  
  res=1;

  if(n<=1)
   return n;

  while(c<n)
  {
     c=a+b;
     res++;
     a=b;
     b=c;
   }
   return res;
}

int main()
{
  int n,p;
  printf("Enter a number:-);
  scanf("%d",&n);
  
  p=fibo(n);
  printf("Index of %d is %d",n,res);
}

Output:-

Enter a number:-
21
Index of 21 is 8

Explanation:-
In this program, Finding the index of a number in The Fibonacci series, required number is entered as input by the user. A function used inside the main function fibo(), to pass the value that is fibo(n). It passes the enter input to the prototype function.

Some header files are used to execute the build in function in the c programming such as #include<stdio.h> and #include<conio.h>. In both, #include is including both the library files in the program. stdio.h and conio.h are two headers files, stio.h stands for standard input output in the c program.

Int fibo(int n), it takes the integer value n and passes inside the function to find the Fibonacci series and the index of number n. Variables a, b, c are used to calculate the Fibonacci series and res is used to find the index value of the entered input n.
Example:-
Enter n=21
Fibonacci series : 0 1 1 2 3 5 8 13 21 ......, so 21 comes at 8th position in the series,since 1 comes two times, but it is counted as 1, starts from zero as 1st position and position of 1 is first position of 1 is 2nd, position of 2 is 3rd, similarly position of 21, you will get 8th.

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