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Improved SieveOfEratosthenes.js #351

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Merged
merged 1 commit into from May 23, 2021
Merged

Improved SieveOfEratosthenes.js #351

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18 changes: 13 additions & 5 deletions Maths/SieveOfEratosthenes.js
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Original file line number Diff line number Diff line change
@@ -1,16 +1,24 @@
function sieveOfEratosthenes (n) {
/*
* Calculates prime numbers till a number n
* :param n: Number upto which to calculate primes
* :return: A boolean list contaning only primes
*/
* Calculates prime numbers till a number n
* :param n: Number upto which to calculate primes
* :return: A boolean list contaning only primes
*/
const primes = new Array(n + 1)
primes.fill(true) // set all as true initially
primes[0] = primes[1] = false // Handling case for 0 and 1
const sqrtn = Math.ceil(Math.sqrt(n))
for (let i = 2; i <= sqrtn; 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
}
}
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