From 3866e8b43183077cffa4dc94aa9ceb592aa8c148 Mon Sep 17 00:00:00 2001
From: Daniel Dorado <danieldorado27@gmail.com>
Date: Sat, 15 Oct 2022 17:31:47 -0500
Subject: [PATCH 1/2] [CREATE] Problem 28 solution for Project Euler

---
 Project-Euler/Problem028.js           | 35 +++++++++++++++++++++++++++
 Project-Euler/test/Problem028.test.js | 17 +++++++++++++
 2 files changed, 52 insertions(+)
 create mode 100644 Project-Euler/Problem028.js
 create mode 100644 Project-Euler/test/Problem028.test.js

diff --git a/Project-Euler/Problem028.js b/Project-Euler/Problem028.js
new file mode 100644
index 0000000000..79b3637df1
--- /dev/null
+++ b/Project-Euler/Problem028.js
@@ -0,0 +1,35 @@
+/**
+ * Problem 28 - Number spiral diagonals
+ *
+ * @see {@link https://projecteuler.net/problem=28}
+ *
+ * Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:
+ *
+ * 21 22 23 24 25
+ * 20 07 08 09 10
+ * 19 06 01 02 11
+ * 18 05 04 03 12
+ * 17 16 15 14 13
+ *
+ * It can be verified that the sum of the numbers on the diagonals is 101.
+ * What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?
+ *
+ * @author ddaniel27
+ */
+
+function problem28 (dim) {
+  if (dim % 2 === 0) {
+    throw new Error('Dimension must be odd')
+  }
+  if (dim < 1) {
+    throw new Error('Dimension must be positive')
+  }
+
+  let result = 1
+  for (let i = 3; i <= dim; i += 2) {
+    result += (4 * i * i) + 6 * (1 - i) // Calculate sum of each dimension corner
+  }
+  return result
+}
+
+export { problem28 }
diff --git a/Project-Euler/test/Problem028.test.js b/Project-Euler/test/Problem028.test.js
new file mode 100644
index 0000000000..ad99654598
--- /dev/null
+++ b/Project-Euler/test/Problem028.test.js
@@ -0,0 +1,17 @@
+import { problem28 } from '../Problem028.js'
+
+describe('checking number spiral diagonals', () => {
+  it('should be invalid input if number is negative', () => {
+    expect(() => problem28(-3)).toThrowError('Dimension must be positive')
+  })
+  it('should be invalid input if number is not odd', () => {
+    expect(() => problem28(4)).toThrowError('Dimension must be odd')
+  })
+  test('if the number is equal to 5 result should be 101', () => {
+    expect(problem28(5)).toBe(101)
+  })
+  // Project Euler Condition Check
+  test('if the number is equal to 1001 result should be 669171001', () => {
+    expect(problem28(1001)).toBe(669171001)
+  })
+})

From 3418cdd9a6e749e8d9a8e37edb65c3d69233fc78 Mon Sep 17 00:00:00 2001
From: Daniel Dorado <danieldorado27@gmail.com>
Date: Sun, 16 Oct 2022 08:03:55 -0500
Subject: [PATCH 2/2] [UPDATE] Added an explanation for the formula used in the
 algorithm

---
 Project-Euler/Problem028.js | 18 ++++++++++++++++++
 1 file changed, 18 insertions(+)

diff --git a/Project-Euler/Problem028.js b/Project-Euler/Problem028.js
index 79b3637df1..e55f31b959 100644
--- a/Project-Euler/Problem028.js
+++ b/Project-Euler/Problem028.js
@@ -27,6 +27,24 @@ function problem28 (dim) {
 
   let result = 1
   for (let i = 3; i <= dim; i += 2) {
+    /**
+      * Adding more dimensions to the matrix, we will find at the top-right corner the follow sequence:
+      * 01, 09, 25, 49, 81, 121, 169, ...
+      * So this can be expressed as:
+      * i^2, where i is all odd numbers
+      *
+      * Also, we can know which numbers are in each corner dimension
+      * Just develop the sequence counter clockwise from top-right corner like this:
+      * First corner: i^2
+      * Second corner: i^2 - (i - 1) | The "i - 1" is the distance between corners in each dimension
+      * Third corner: i^2 - 2 * (i - 1)
+      * Fourth corner: i^2 - 3 * (i - 1)
+      *
+      * Doing the sum of each corner and simplifing, we found that the result for each dimension is:
+      * sumDim = 4 * i^2 + 6 * (1 - i)
+      *
+      * In this case I skip the 1x1 dim matrix because is trivial, that's why I start in a 3x3 matrix
+      */
     result += (4 * i * i) + 6 * (1 - i) // Calculate sum of each dimension corner
   }
   return result

<!DOCTYPE html PUBLIC '-//W3C//DTD XHTML 1.0 Transitional//EN' 'http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd'>
<html xmlns='http://www.w3.org/1999/xhtml'>
<head>
<title>pFad - Phonifier reborn</title>
<meta http-equiv='Content-Type' content='text/html; charset=utf-8' />
</head>
<body>
<h1>Pfad - The Proxy pFad of &#169; 2024 Garber Painting. All rights reserved.</h1>


<!-- Disclaimer -->
<p>Note: This service is not intended for secure transactions such as banking, social media, email, or purchasing. Use at your own risk. We assume no liability whatsoever for broken pages.</p>
<br>
<p>Alternative Proxies:</p><p><a href="http://rainy.clevelandohioweatherforecast.com/php-proxy/index.php?q=https://patch-diff.githubusercontent.com/raw/TheAlgorithms/JavaScript/pull/1198.patch" target="_blank">Alternative Proxy</a></p><p><a href="http://rainy.clevelandohioweatherforecast.com/pFad/index.php?u=https://patch-diff.githubusercontent.com/raw/TheAlgorithms/JavaScript/pull/1198.patch" target="_blank">pFad Proxy</a></p><p><a href="http://rainy.clevelandohioweatherforecast.com/pFad/v3index.php?u=https://patch-diff.githubusercontent.com/raw/TheAlgorithms/JavaScript/pull/1198.patch" target="_blank">pFad v3 Proxy</a></p><p><a href="http://rainy.clevelandohioweatherforecast.com/pFad/v4index.php?u=https://patch-diff.githubusercontent.com/raw/TheAlgorithms/JavaScript/pull/1198.patch" target="_blank">pFad v4 Proxy</a></p></body>
</html>