feat(euler): 42 - coded triangle numbers

challenges/euler/constants.js

@@ -4,5 +4,33 @@ module.exports = {
     resources: path.join(__dirname, 'resources'),
     src: path.join(__dirname, 'src'),
     thoughts: path.join(__dirname, 'thoughts'),
-    root: __dirname
+    root: __dirname,
+    alphabet: [
+        'a',
+        'b',
+        'c',
+        'd',
+        'e',
+        'f',
+        'g',
+        'h',
+        'i',
+        'j',
+        'k',
+        'l',
+        'm',
+        'n',
+        'o',
+        'p',
+        'q',
+        'r',
+        's',
+        't',
+        'u',
+        'v',
+        'w',
+        'x',
+        'y',
+        'z'
+    ]
 };

challenges/euler/readme.md

@@ -53,7 +53,7 @@ The source code can be found in the [src](src) directory. My thoughts about some
 -   [ ] 39 - Integer right triangles
 -   [ ] 40 - Champernowne's constant
 -   [ ] 41 - Pandigital prime
--   [ ] 42 - Coded triangle numbers
+-   [x] [42 - Coded triangle numbers](src/42%20-%20Coded%20triangle%20numbers.ts)
 -   [ ] 43 - Sub-string divisibility
 -   [ ] 44 - Pentagon numbers
 -   [ ] 45 - Triangular, pentagonal, and hexagonal

challenges/euler/src/42 - Coded triangle numbers.ts

@@ -0,0 +1,40 @@
+// The nth term of the sequence of triangle numbers is given by, tn = ½n(n+1); so the first ten triangle numbers are:
+// 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...
+// By converting each letter in a word to a number corresponding to its alphabetical position and adding these values we form a word value. For example, the word value for SKY is 19 + 11 + 25 = 55 = t10. If the word value is a triangle number then we shall call the word a triangle word.
+// Using words.txt (right click and 'Save Link/Target As...'), a 16K text file containing nearly two-thousand common English words, how many are triangle words?
+
+import fs from 'fs';
+import path from 'path';
+import { resources, alphabet } from '../constants.js';
+export = {};
+
+const words = fs
+    .readFileSync(path.join(resources, 'p042_words.txt'))
+    .toString()
+    .split(',')
+    .map(word => word.replace(/"/g, '').toLowerCase());
+
+const isTriangleNumber = (t: number) => {
+    // One solution of the inverse triangle number formula
+    const solution = (Math.sqrt(8 * t + 1) - 1) / 2;
+
+    // This number must be an integer and greater than zero for it to be a triangle number
+    return Number.isInteger(solution) && solution > 0;
+};
+
+let triangleWordCount = 0;
+
+for (const word of words) {
+    const letters = word.split('');
+    let sum = 0;
+
+    for (const letter of letters) {
+        const value = alphabet.indexOf(letter) + 1;
+        sum += value;
+    }
+
+    if (isTriangleNumber(sum)) triangleWordCount++;
+}
+
+// Output
+console.log(`Out of nearly 2000 common English words, ${triangleWordCount} are triangle words!`);