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GFact | Finding nth Fibonacci Number using Golden Ratio

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We have discussed different methods to find nth Fibonacci Number. Following is another mathematically correct way to find the same. nth Fibonacci Number :  F(n) = \left \lfloor \frac{\varphi^n}{\sqrt5} + \frac{1}{2} \right \rfloor, n >= 0 Here φ is golden ratio with value as (\sqrt 5+1)/2 The above formula seems to be good for finding nth Fibonacci Number in O(Logn) time as integer power of a number can be calculated in O(Logn) time. But this solution doesn’t work practically because φ is stored as a floating point number and when we calculate powers of φ, important bits may be lost in the process and we may get incorrect answer. References: https://www.youtube.com/watch?v=-EQTVuAhSFY http://en.wikipedia.org/wiki/Fibonacci_number

Last Updated : 17 Oct, 2023
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