Given a positive integer n, the task is to print the n’th non Fibonacci number. The Fibonacci numbers are defined as:
Fib(0) = 0 Fib(1) = 1 for n >1, Fib(n) = Fib(n-1) + Fib(n-2)
First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ……..
Input : n = 2 Output : 6 Input : n = 5 Output : 10
A naive solution is to find find Fibonacci numbers and then print first n numbers not present in the found Fibonacci numbers.
A better solution is to use the formula of Fibonacci numbers and keep adding of gap between two consecutive Fibonacci numbers. Value of sum of gap is count of non-fibonacci numbers seen so far. Below is implementation of above idea.
Time Complexity : O(n)
Auxiliary Space : O(1)
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