F(100)
- Input
- n=100
- Expected output
- 354.224.848.179.261.915.075
21 digits — impossible with float64.
Fibonacci algorithms in computing
Fibonacci Algorithms — Recursive vs Iterative
The naive recursive implementation costs O(2ⁿ). The iterative one costs O(n). This tool uses iterative BigInt to compute F(499) in milliseconds.
Fibonacci algorithm complexity
- Naive recursive: each call makes 2 recursive calls, creating a tree of 2ⁿ nodes. F(50) would require ~10¹⁵ operations. Not viable.
- Iterative with BigInt: two variables and a loop — O(n) time and O(d) space where d is the digit count of F(n). F(499) has 104 digits.
Examples
F(200)
- Input
- n=200
- Expected output
- 280.571.172.992.510.140.037.611.932.413.038.677.189.525
42 digits with exact precision.
Full tool FAQ
It is a sequence of integers where each term is the sum of the two preceding ones: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34… It was popularized by Leonardo of Pisa ('Fibonacci') in the 13th century.
Frequently asked questions
Why use BigInt instead of float?
Float64 has ~15–17 significant digits. F(79) already has 17 digits and exceeds float precision. BigInt has no precision limit.
Does this page replace official or professional review?
No. It helps explain the scenario and use the tool more safely, but real decisions should consider official sources, full context and qualified guidance when needed.