feat: add Egyptian fraction algorithm

Author: sarthakgupta1907-cell

Maths/EgyptianFraction.js

@@ -0,0 +1,41 @@
+/**
+ * @function egyptianFraction
+ * @description Represents a fraction as a sum of distinct unit fractions
+ *   (fractions with numerator 1) using the greedy algorithm.
+ *   For example, 2/3 = 1/2 + 1/6.
+ * @param {number} numerator - The numerator of the fraction
+ * @param {number} denominator - The denominator of the fraction
+ * @returns {number[]} - Array of denominators of unit fractions
+ * @see https://en.wikipedia.org/wiki/Egyptian_fraction
+ * @example egyptianFraction(2, 3) => [2, 6]
+ * @example egyptianFraction(3, 4) => [2, 4]
+ */
+const egyptianFraction = (numerator, denominator) => {
+  if (
+    !Number.isInteger(numerator) ||
+    !Number.isInteger(denominator) ||
+    numerator < 1 ||
+    denominator < 1
+  ) {
+    throw new TypeError('Both inputs must be positive integers')
+  }
+  if (numerator >= denominator) {
+    throw new RangeError('Numerator must be less than denominator')
+  }
+  const result = []
+  let num = numerator
+  let den = denominator
+  while (num > 0) {
+    const unitDen = Math.ceil(den / num)
+    result.push(unitDen)
+    num = num * unitDen - den
+    den = den * unitDen
+    const gcd = (a, b) => (b === 0 ? a : gcd(b, a % b))
+    const g = gcd(num, den)
+    num = num / g
+    den = den / g
+  }
+  return result
+}
+
+export { egyptianFraction }

Maths/test/EgyptianFraction.test.js

@@ -0,0 +1,49 @@
+import { egyptianFraction } from '../EgyptianFraction.js'
+
+describe('egyptianFraction', () => {
+  test('egyptianFraction(2, 3) returns [2, 6]', () => {
+    expect(egyptianFraction(2, 3)).toEqual([2, 6])
+  })
+
+  test('egyptianFraction(3, 4) returns [2, 4]', () => {
+    expect(egyptianFraction(3, 4)).toEqual([2, 4])
+  })
+
+  test('egyptianFraction(1, 2) returns [2]', () => {
+    expect(egyptianFraction(1, 2)).toEqual([2])
+  })
+
+  test('result unit fractions sum to original fraction', () => {
+    const denoms = egyptianFraction(2, 3)
+    const sum = denoms.reduce((acc, d) => acc + 1 / d, 0)
+    expect(sum).toBeCloseTo(2 / 3, 10)
+  })
+
+  test('result unit fractions sum for 3/4', () => {
+    const denoms = egyptianFraction(3, 4)
+    const sum = denoms.reduce((acc, d) => acc + 1 / d, 0)
+    expect(sum).toBeCloseTo(3 / 4, 10)
+  })
+
+  test('all denominators are distinct', () => {
+    const denoms = egyptianFraction(2, 3)
+    const unique = new Set(denoms)
+    expect(unique.size).toBe(denoms.length)
+  })
+
+  test('throws TypeError for zero numerator', () => {
+    expect(() => egyptianFraction(0, 3)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => egyptianFraction(-2, 3)).toThrow(TypeError)
+  })
+
+  test('throws RangeError when numerator >= denominator', () => {
+    expect(() => egyptianFraction(3, 3)).toThrow(RangeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => egyptianFraction(2.5, 3)).toThrow(TypeError)
+  })
+})