Given a number N, the task is to evaluate below expression. Expected time complexity is O(1).
f(n-1)*f(n+1) - f(n)*f(n)
Where f(n) is the n-th Fibonacci number with n >= 1. First few Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, ………..i.e. (considering 0 as 0th Fibonacci number)
Input : n = 5 Output : -1 f(5-1=4) = 3 f(5+1=6) = 8 f(5)*f(5)= 5*5 = 25 f(4)*f(6)- f(5)*f(5)= 24-25= -1
Although the task is simple i.e. find n-1th, nth and (n+1)-th Fibonacci numbers. Evaluate the expression and display the result. But this can be done in O(1) time using Cassini’s Identity which states that:
f(n-1)*f(n+1) - f(n*n) = (-1)^n
So, we don’t need to calculate any Fibonacci term,the only thing is to check whether n is even or odd.
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