From ece543acf7e4d2c1c7faf38f49a89c9fe39e0c11 Mon Sep 17 00:00:00 2001
From: Darius Liddell <darius@carerev.com>
Date: Tue, 10 Dec 2024 18:31:47 +0100
Subject: [PATCH] add code for goldbach conjecture algorithms

---
 maths/goldbach_conjecture.ts | 55 ++++++++++++++++++++++++++++++++++++
 package-lock.json            | 14 +++++++++
 package.json                 |  5 +++-
 3 files changed, 73 insertions(+), 1 deletion(-)
 create mode 100644 maths/goldbach_conjecture.ts

diff --git a/maths/goldbach_conjecture.ts b/maths/goldbach_conjecture.ts
new file mode 100644
index 00000000..b4b8f14b
--- /dev/null
+++ b/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)] )
+}
\ No newline at end of file
diff --git a/package-lock.json b/package-lock.json
index ad263744..c047bbab 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -8,6 +8,9 @@
       "name": "typescript",
       "version": "1.0.0",
       "license": "MIT",
+      "dependencies": {
+        "fp-ts": "^2.16.9"
+      },
       "devDependencies": {
         "@types/jest": "^29.0.3",
         "husky": "^8.0.1",
@@ -1757,6 +1760,12 @@
         "node": ">=8"
       }
     },
+    "node_modules/fp-ts": {
+      "version": "2.16.9",
+      "resolved": "https://registry.npmjs.org/fp-ts/-/fp-ts-2.16.9.tgz",
+      "integrity": "sha512-+I2+FnVB+tVaxcYyQkHUq7ZdKScaBlX53A41mxQtpIccsfyv8PzdzP7fzp2AY832T4aoK6UZ5WRX/ebGd8uZuQ==",
+      "license": "MIT"
+    },
     "node_modules/fs.realpath": {
       "version": "1.0.0",
       "resolved": "https://registry.npmjs.org/fs.realpath/-/fs.realpath-1.0.0.tgz",
@@ -5075,6 +5084,11 @@
         "path-exists": "^4.0.0"
       }
     },
+    "fp-ts": {
+      "version": "2.16.9",
+      "resolved": "https://registry.npmjs.org/fp-ts/-/fp-ts-2.16.9.tgz",
+      "integrity": "sha512-+I2+FnVB+tVaxcYyQkHUq7ZdKScaBlX53A41mxQtpIccsfyv8PzdzP7fzp2AY832T4aoK6UZ5WRX/ebGd8uZuQ=="
+    },
     "fs.realpath": {
       "version": "1.0.0",
       "resolved": "https://registry.npmjs.org/fs.realpath/-/fs.realpath-1.0.0.tgz",
diff --git a/package.json b/package.json
index b45ab4ea..669e5349 100644
--- a/package.json
+++ b/package.json
@@ -19,5 +19,8 @@
     "prepare": "husky install"
   },
   "author": "TheAlgorithms",
-  "license": "MIT"
+  "license": "MIT",
+  "dependencies": {
+    "fp-ts": "^2.16.9"
+  }
 }