solution: Project Euler Problem 28 (TheAlgorithms#1198)

ddaniel27 · web-flow · commit 829d3fd8070e · 2022-10-17T01:54:11.000+05:30
diff --git a/Project-Euler/Problem028.js b/Project-Euler/Problem028.js
@@ -0,0 +1,53 @@
+/**
+ * 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) {
+    /**
+      * 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
+}
+
+export { problem28 }
diff --git a/Project-Euler/test/Problem028.test.js 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)
+  })
+})
