Given a positive integer N, the task is to find Fib(N)2 – (Fib(N-1) * Fib(N+1)) where Fib(N) returns the Nth Fibonacci number.
Examples:
Input: N = 3
Output: 1
Fib(3) * Fib(3) – Fib(2) * Fib(4) = 4 – 3 = 1
Input: N = 2
Output: -1
Fib(2) * Fib(2) – Fib(1) * Fib(3) = 1 – 2 = -1
Approach: This question can be approached by first trying out a few test cases. Let’s take a few examples:
For N = 1 : Fib(1) * Fib(1) – Fib(0) * Fib(2) = 1 – 0 = 1
For N = 2 : Fib(2) * Fib(2) – Fib(1) * Fib(3) = 1 – 2 = -1
For N = 3 : Fib(3) * Fib(3) – Fib(2) * Fib(4) = 4 – 3 = 1
For N = 4 : Fib(4) * Fib(4) – Fib(3) * Fib(5) = 9 – 10 = -1
We observe here that when N is even then the answer will be -1 and when the N is odd then the answer will be 1.
Below is the implementation of the above approach:
// C++ implementation of the approach #include <iostream> using namespace std;
int getResult( int n)
{ if (n & 1)
return 1;
return -1;
} // Driver code int main()
{ int n = 3;
cout << getResult(n);
} |
//Java implementation of the approach import java.io.*;
class GFG {
static int getResult( int n)
{ if ((n & 1 )> 0 )
return 1 ;
return - 1 ;
} // Driver code public static void main (String[] args) {
int n = 3 ;
System.out.println(getResult(n));
}
//This code is contributed by @Tushil. } |
# Python 3 implementation of # the approach def getResult(n):
if n & 1 :
return 1
return - 1
# Driver code n = 3
print (getResult(n))
# This code is contributed # by Shrikant13 |
//C# implementation of the approach using System;
class GFG {
static int getResult( int n)
{ if ((n & 1)>0)
return 1;
return -1;
} // Driver code public static void Main () {
int n = 3;
Console.WriteLine(getResult(n));
}
//This code is contributed by anuj_67.. } |
<?php // PHP implementation of the approach function getResult( $n )
{ if ( $n & 1)
return 1;
return -1;
} // Driver code $n = 3;
echo getResult( $n );
// This code is contributed by akt_mit ?> |
<script> // Javascript implementation of the approach
function getResult(n)
{
if ((n & 1)>0)
return 1;
return -1;
}
let n = 3;
document.write(getResult(n));
</script> |
1
Time Complexity: O(1)
Auxiliary Space: O(1)