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15 lines
589 B
JavaScript
15 lines
589 B
JavaScript
const SQ5 = 5 ** .5; // Square root of 5
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const PHI = (1 + SQ5) / 2; // 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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