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Improved SieveOfEratosthenes.js
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@ -1,16 +1,24 @@
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function sieveOfEratosthenes (n) {
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/*
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* Calculates prime numbers till a number n
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* :param n: Number upto which to calculate primes
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* :return: A boolean list contaning only primes
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*/
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* Calculates prime numbers till a number n
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* :param n: Number upto which to calculate primes
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* :return: A boolean list contaning only primes
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*/
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const primes = new Array(n + 1)
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primes.fill(true) // set all as true initially
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primes[0] = primes[1] = false // Handling case for 0 and 1
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const sqrtn = Math.ceil(Math.sqrt(n))
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for (let i = 2; i <= sqrtn; i++) {
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if (primes[i]) {
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for (let j = 2 * i; j <= n; j += i) {
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for (let j = i * i; j <= n; j += i) {
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/*
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Optimization.
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Let j start from i * i, not 2 * i, because smaller multiples of i have been marked false.
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For example, let i = 4.
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We do not have to check from 8(4 * 2) to 12(4 * 3)
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because they have been already marked false when i=2 and i=3.
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*/
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primes[j] = false
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}
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}
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