Question

(b) Prove that at each step of the Fibonacci search algorithm, p<q Hint: Prove the cases k-n (Step 2), k-n - 1,n - 2,...,3 (Step 3), and k -2 (Step 4) separately For the Step 3 case consider how the length of the interval is being reduced at each iteration. You will also need to use (and prove) 〉 -when Fk = , ,3 Alternative, correct proofs that do not use the hint are also acceptable

Fibonacci search algorithm

Proof required

Answer 1

i didn't understand what you want

c code for fibonacci series is with different conditions

#include <stdio.h>
int main()
{
  int Number, i = 0, Next, First_Value = 0, Second_Value = 1;

  printf("\n Please Enter the Range Number: ");
  scanf("%d",&Number);
  
  while(i < Number) 
  {
        if(i <= 1)
        {
                Next = i;
        }
        else
        {
                Next = First_Value + Second_Value;
                First_Value = Second_Value;
                Second_Value = Next;
        }
    printf("%d \t", Next);
        i++;  
  }
  return 0;
}

//2
#include <stdio.h>

int main() {
   int a, b, c, i, n;

   n = 4;

   a = b = 1;
   
   printf("%d %d ",a,b);

   for(i = 1; i <= n-2; i++) {
      c = a + b;
      printf("%d ", c);
      
      a = b;
      b = c;
   }
   
   return 0;
}

//3

// Fibonacci Series using Recursion
#include <stdio.h>
int fib(int n)
{
   if (n <= 1)
       return n;
   return fib(n - 1) + fib(n - 2);
}

int main()
{
   int n = 9;
   printf("%d", fib(n));
   getchar();
   return 0;
}