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added Problem 25 to Euler #793

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Merged

raklaptudirm merged 13 commits into TheAlgorithms:master from byt3h3ad:master

Oct 21, 2021

Merged

added Problem 25 to Euler #793

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added Problem 25

byt3h3ad Oct 16, 2021

byt3h3ad Oct 16, 2021

byt3h3ad Oct 16, 2021

Merge branch 'TheAlgorithms:master' into master

byt3h3ad Oct 17, 2021

rewrote to improve runtime

byt3h3ad Oct 17, 2021

Update Problem025.js

byt3h3ad Oct 18, 2021

byt3h3ad Oct 18, 2021

Merge branch 'TheAlgorithms:master' into master

byt3h3ad Oct 21, 2021

added test file for Project-Euler/Problem025.js

byt3h3ad Oct 21, 2021

Update Project-Euler/test/Problem025.test.js

byt3h3ad Oct 21, 2021

Update Problem025.test.js

byt3h3ad Oct 21, 2021

Merge branch 'TheAlgorithms:master' into master

byt3h3ad Oct 21, 2021

Merge branch 'TheAlgorithms:master' into master

byt3h3ad Oct 21, 2021

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45 changes: 45 additions & 0 deletions Project-Euler/Problem025.js

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	/**
	* Problem 25 - 1000-digit Fibonacci number
	*
	* @see {@link https://projecteuler.net/problem=25}
	*
	* The Fibonacci sequence is defined by the recurrence relation:
	*
	* Fn = Fn−1 + Fn−2, where F1 = 1 and F2 = 1.
	*
	* Hence the first 12 terms will be:
	*
	* F1 = 1
	* F2 = 1
	* F3 = 2
	* F4 = 3
	* F5 = 5
	* F6 = 8
	* F7 = 13
	* F8 = 21
	* F9 = 34
	* F10 = 55
	* F11 = 89
	* F12 = 144
	* The 12th term, F12, is the first term to contain three digits.

	* What is the index of the first term in the Fibonacci sequence to contain 1000 digits?
	*/

	// brute force method

	function fibonacciIndex(t = 1000) {
	let digits = 10n**BigInt(t-1),
	fib0 = BigInt(0),
	fib1 = BigInt(1),
	index = 1
	while (fib1 < digits) { // using this to compare number of digits instead of .toString() significantly improved run time
	const tempfib = fib1
	fib1 = fib1 + fib0
	fib0 = tempfib
	index += 1
	}
	return(index)
	}

	export { fibonacciIndex }