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/**
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* Problem 25 - 1000-digit Fibonacci number
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*
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* @see {@link https://projecteuler.net/problem=25}
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*
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* The Fibonacci sequence is defined by the recurrence relation:
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*
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* Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
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*
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* Hence the first 12 terms will be:
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*
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* F1 = 1
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* F2 = 1
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* F3 = 2
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* F4 = 3
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* F5 = 5
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* F6 = 8
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* F7 = 13
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* F8 = 21
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* F9 = 34
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* F10 = 55
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* F11 = 89
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* F12 = 144
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* The 12th term, F12, is the first term to contain three digits.
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* What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
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*/
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// brute force method
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2021-10-22 09:38:10 +05:30
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function fibonacciIndex (t = 1000) {
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const digits = 10n ** BigInt(t - 1)
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let fib0 = BigInt(0)
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let fib1 = BigInt(1)
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let index = 1
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while (fib1 < digits) { // using this to compare number of digits instead of .toString() significantly improved run time
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const tempfib = fib1
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fib1 = fib1 + fib0
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fib0 = tempfib
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index += 1
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}
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return (index)
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}
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export { fibonacciIndex }
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