Fibonacci problem (Value of Fib(N)*Fib(N) – Fib(N-1) * Fib(N+1))

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++

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// 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);
}

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Java














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//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.     


} 



















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Python3














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# 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 



















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C#














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//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.. 


} 



















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PHP














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<?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 


?> 



















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Output:


1







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