add code for goldbach conjecture algorithms

maths/goldbach_conjecture.ts

@@ -0,0 +1,55 @@
+import {
+  takeLeft,
+} from 'fp-ts/lib/Array'
+
+import { isPrime } from './primes'
+
+function range(start: number, end: number, step: number = 1): number[] {
+  const result: number[] = [];
+  for (let i = start; i < end; i += step) {
+    result.push(i);
+  }
+  return result;
+}
+
+/**
+ * @function goldbachNumbers
+ * @description Return the goldbach numbers for a given even number
+ * @param {Number} n - a positive even number
+ * @return {Number} - an array of two numbers representing the goldbach numbers for N
+ * @see https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
+ * @example goldbachNumbers(28) = [5, 23]
+ * @example goldbachNumbers(16) = [5, 11]
+ * @example goldbachNumbers(20) = [3, 17]
+ */
+export const goldbachNumbers = (n: number): number[] => {
+  const primes = range(2,n).filter( (m: number): Boolean => isPrime(m) && isPrime(n - m))
+  if (primes.length == 0) {
+    []
+  }
+  let m = takeLeft(1)(primes)[0]
+  return [m, n-m]
+}
+
+
+/**
+ * @function goldbachCompositions
+ * @description Return the goldbach numbers for all even numbers in a given range of positive integers, low and high
+ * @param {Number, Number} low and high, low < high
+ * @return {Number} - an array of tuples with the first element representing the even number, and the second is the two primes that sum to it.
+ * @see https://en.wikipedia.org/wiki/Goldbach%27s_conjecture
+ * @example goldbachCompositiions(20, 30) = [
+ *    [20,[3,17]],
+ *    [22,[3,19]],
+ *    [24,[5,19]],
+ *    [26,[3,23]],
+ *    [28,[3,25]]
+ * ]
+ */
+export const goldbachCompositions = (low: number, high: number): [number, number[]][] => {
+  let lo = (low % 2 == 0) ? low : low + 1
+  let hi = (high % 2 == 0) ? high : high - 1
+
+
+  return range(lo, hi, 2).map((n: number) => [n, goldbachNumbers(n)] )
+}

package.json

@@ -19,5 +19,8 @@
     "prepare": "husky install"
   },
   "author": "TheAlgorithms",
-  "license": "MIT"
+  "license": "MIT",
+  "dependencies": {
+    "fp-ts": "^2.16.9"
+  }
 }