feat: add Smith number algorithm

Author: sarthakgupta1907-cell

Maths/SmithNumber.js

@@ -0,0 +1,41 @@
+/**
+ * @function isSmithNumber
+ * @description A Smith number is a composite number where the sum of
+ *   its digits equals the sum of the digits of its prime factors.
+ *   For example, 4: prime factors are 2,2 → 2+2=4, digit sum=4.
+ * @param {number} n - A positive integer greater than 1
+ * @returns {boolean} - True if n is a Smith number, false otherwise
+ * @see https://en.wikipedia.org/wiki/Smith_number
+ * @example isSmithNumber(4) => true
+ * @example isSmithNumber(22) => true
+ * @example isSmithNumber(13) => false
+ */
+const isSmithNumber = (n) => {
+  if (!Number.isInteger(n) || n < 2) {
+    throw new TypeError('Input must be an integer greater than or equal to 2')
+  }
+  const digitSum = (num) =>
+    String(num)
+      .split('')
+      .reduce((sum, d) => sum + Number(d), 0)
+  const primeFactors = (num) => {
+    const factors = []
+    let d = 2
+    let temp = num
+    while (d * d <= temp) {
+      while (temp % d === 0) {
+        factors.push(d)
+        temp = Math.floor(temp / d)
+      }
+      d++
+    }
+    if (temp > 1) factors.push(temp)
+    return factors
+  }
+  const factors = primeFactors(n)
+  if (factors.length === 1 && factors[0] === n) return false
+  const primeDigitSum = factors.reduce((sum, f) => sum + digitSum(f), 0)
+  return digitSum(n) === primeDigitSum
+}
+
+export { isSmithNumber }

Maths/test/SmithNumber.test.js

@@ -0,0 +1,47 @@
+import { isSmithNumber } from '../SmithNumber.js'
+
+describe('isSmithNumber', () => {
+  test('4 is a Smith number (2+2=4)', () => {
+    expect(isSmithNumber(4)).toBe(true)
+  })
+
+  test('22 is a Smith number (2+1+1=4, 2+2=4)', () => {
+    expect(isSmithNumber(22)).toBe(true)
+  })
+
+  test('27 is a Smith number (2+7=9, 3+3+3=9)', () => {
+    expect(isSmithNumber(27)).toBe(true)
+  })
+
+  test('58 is a Smith number (5+8=13, 2+1+1=4... wait)', () => {
+    expect(isSmithNumber(58)).toBe(true)
+  })
+
+  test('13 is NOT a Smith number (prime)', () => {
+    expect(isSmithNumber(13)).toBe(false)
+  })
+
+  test('2 is NOT a Smith number (prime)', () => {
+    expect(isSmithNumber(2)).toBe(false)
+  })
+
+  test('7 is NOT a Smith number (prime)', () => {
+    expect(isSmithNumber(7)).toBe(false)
+  })
+
+  test('15 is NOT a Smith number', () => {
+    expect(isSmithNumber(15)).toBe(false)
+  })
+
+  test('throws TypeError for 1', () => {
+    expect(() => isSmithNumber(1)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => isSmithNumber(-4)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => isSmithNumber(4.5)).toThrow(TypeError)
+  })
+})