Given a number ‘n’, how to check if n is a Fibonacci number. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 141, ..
Examples :
Input : 8 Output : Yes Input : 34 Output : Yes Input : 41 Output : No
Following is an interesting property about Fibonacci numbers that can also be used to check if a given number is Fibonacci or not.
A number is Fibonacci if and only if one or both of (5*n2 + 4) or (5*n2 – 4) is a perfect square (Source: Wiki).
// C++ program to check if x is a perfect square #include <iostream> #include <math.h> using namespace std;
// A utility function that returns true if x is perfect square bool isPerfectSquare( int x)
{ int s = sqrt (x);
return (s * s == x);
} // Returns true if n is a Fibonacci Number, else false bool isFibonacci( int n)
{ // n is Fibonacci if one of 5*n*n + 4 or 5*n*n - 4 or both
// is a perfect square
return isPerfectSquare(5 * n * n + 4) || isPerfectSquare(5 * n * n - 4);
} // A utility function to test above functions int main()
{ for ( int i = 1; i <= 10; i++)
isFibonacci(i) ? cout << i << " is a Fibonacci Number \n"
: cout << i << " is a not Fibonacci Number \n";
return 0;
} |
1 is a Fibonacci Number 2 is a Fibonacci Number 3 is a Fibonacci Number 4 is a not Fibonacci Number 5 is a Fibonacci Number 6 is a not Fibonacci Number 7 is a not Fibonacci Number 8 is a Fibonacci Number 9 is a not Fibonacci Number 10 is a not Fibonacci Number
Time complexity: O(logn)
As sqrt() function takes O(logn) time.
Auxiliary space: O(1)
As constant extra space is used.
Please refer complete article on How to check if a given number is Fibonacci number? for more details!