Adding Sieve of Eratosthenes (trekhleb#46)

jpvg10 · trekhleb · commit 943f83492a46 · 2018-06-03T09:25:15.000+03:00
* Adding Sieve of Eratosthenes

* Typo
diff --git a/src/algorithms/math/sieve-of-eratosthenes/README.md b/src/algorithms/math/sieve-of-eratosthenes/README.md
@@ -0,0 +1,29 @@
+# Sieve of Eratosthenes
+
+The Sieve of Eratosthenes is an algorithm for finding all prime numbers up to some limit `n`.
+
+It is attributed to Eratosthenes of Cyrene, an ancient Greek mathematician.
+
+## How it works
+
+1. Create a boolean array of `n+1` positions (to represent the numbers `0` through `n`)
+2. Set positions `0` and `1` to `false`, and the rest to `true`
+3. Start at position `p = 2` (the first prime number)
+4. Mark as `false` all the multiples of `p` (that is, positions `2*p`, `3*p`, `4*p`... until you reach the end of the array)
+5. Find the first position greater than `p` that is `true` in the array. If there is no such position, stop. Otherwise, let `p` equal this new number (which is the next prime), and repeat from step 4
+
+When the algorithm terminates, the numbers remaining `true` in the array are all the primes below `n`.
+
+An improvement of this algorithm is, in step 4, start marking multiples of `p` from `p*p`, and not from `2*p`. The reason why this works is because, at that point, smaller multiples of `p` will have already been marked `false`.
+
+## Example
+
+![Sieve](https://upload.wikimedia.org/wikipedia/commons/b/b9/Sieve_of_Eratosthenes_animation.gif)
+
+## Complexity
+
+The algorithm has a complexity of `O(n log(log n))`.
+
+## References
+
+[Wikipedia](https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes)
diff --git a/src/algorithms/math/sieve-of-eratosthenes/__test__/sieveOfEratosthenes.test.js b/src/algorithms/math/sieve-of-eratosthenes/__test__/sieveOfEratosthenes.test.js
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+import sieveOfEratosthenes from '../sieveOfEratosthenes';
+
+describe('factorial', () => {
+  it('should find all primes less than or equal to n', () => {
+    expect(sieveOfEratosthenes(5)).toEqual([2, 3, 5]);
+    expect(sieveOfEratosthenes(10)).toEqual([2, 3, 5, 7]);
+    expect(sieveOfEratosthenes(100)).toEqual([
+      2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
+      43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97,
+    ]);
+  });
+});
diff --git a/src/algorithms/math/sieve-of-eratosthenes/sieveOfEratosthenes.js b/src/algorithms/math/sieve-of-eratosthenes/sieveOfEratosthenes.js
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+/**
+ * @param {number} n
+ * @return {number[]}
+ */
+export default function sieveOfEratosthenes(n) {
+  const isPrime = new Array(n + 1).fill(true);
+  isPrime[0] = false;
+  isPrime[1] = false;
+  const primes = [];
+
+  for (let i = 2; i <= n; i += 1) {
+    if (isPrime[i] === true) {
+      primes.push(i);
+
+      // Warning: When working with really big numbers, the following line may cause overflow
+      // In that case, it can be changed to:
+      // let j = 2 * i;
+      let j = i * i;
+
+      while (j <= n) {
+        isPrime[j] = false;
+        j += i;
+      }
+    }
+  }
+
+  return primes;
+}
