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18 lines
573 B
JavaScript
18 lines
573 B
JavaScript
const SQ5 = 5 ** 0.5
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//Square root of 5
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const PHI = (1 + SQ5) / 2
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// definition of PHI
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//theoretically it should take O(1) constant amount of time as long
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// arithmetic calculations are considered to be in constant amount of time
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function EvenFibonacci(limit) {
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const highestIndex = Math.floor(Math.log(limit * SQ5) / Math.log(PHI))
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const n = Math.floor(highestIndex / 3)
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return ((PHI ** (3 * n + 3) - 1) / (PHI ** 3 - 1) -
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((1 - PHI) ** (3 * n + 3) - 1) / ((1 - PHI) ** 3 - 1)) / SQ5
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}
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console.log(EvenFibonacci(4e6));
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// Sum of Even Fibonnaci upto 4 Million
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