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Improved SieveOfEratosthenes.js

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JimmyJoo
2020-10-02 17:13:28 +09:00
parent 51cf96cf23
commit e23d09b4f1
1 changed files with 13 additions and 5 deletions
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18
Maths/SieveOfEratosthenes.js
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@ -1,16 +1,24 @@
function sieveOfEratosthenes (n) { function sieveOfEratosthenes (n) {
/* /*
* Calculates prime numbers till a number n * Calculates prime numbers till a number n
* :param n: Number upto which to calculate primes * :param n: Number upto which to calculate primes
* :return: A boolean list contaning only primes * :return: A boolean list contaning only primes
*/ */
const primes = new Array(n + 1) const primes = new Array(n + 1)
primes.fill(true) // set all as true initially primes.fill(true) // set all as true initially
primes[0] = primes[1] = false // Handling case for 0 and 1 primes[0] = primes[1] = false // Handling case for 0 and 1
const sqrtn = Math.ceil(Math.sqrt(n)) const sqrtn = Math.ceil(Math.sqrt(n))
for (let i = 2; i <= sqrtn; i++) { for (let i = 2; i <= sqrtn; i++) {
if (primes[i]) { if (primes[i]) {
for (let j = 2 * i; j <= n; j += i) { for (let j = i * i; j <= n; j += i) {
/*
Optimization.
Let j start from i * i, not 2 * i, because smaller multiples of i have been marked false.
For example, let i = 4.
We do not have to check from 8(4 * 2) to 12(4 * 3)
because they have been already marked false when i=2 and i=3.
*/
primes[j] = false primes[j] = false
} }
} }