feat: add Zeckendorf representation algorithm

Maths/InterquartileRange.js

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+/**
+ * @function interquartileRange
+ * @description Calculates the interquartile range (IQR) of an array.
+ *   IQR is the difference between the 75th and 25th percentiles,
+ *   representing the middle 50% spread of the data.
+ * @param {number[]} arr - An array of numbers
+ * @returns {number} - The interquartile range
+ * @see https://en.wikipedia.org/wiki/Interquartile_range
+ * @example interquartileRange([1, 2, 3, 4, 5]) => 2
+ * @example interquartileRange([1, 2, 3, 4, 5, 6, 7]) => 3
+ */
+const interquartileRange = (arr) => {
+  if (!Array.isArray(arr) || arr.length === 0) {
+    throw new TypeError('Input must be a non-empty array')
+  }
+  if (!arr.every((n) => typeof n === 'number' && !isNaN(n))) {
+    throw new TypeError('All elements must be numbers')
+  }
+  const sorted = [...arr].sort((a, b) => a - b)
+  const getPercentile = (data, p) => {
+    if (p === 0) return data[0]
+    if (p === 100) return data[data.length - 1]
+    const index = (p / 100) * (data.length - 1)
+    const lower = Math.floor(index)
+    const upper = Math.ceil(index)
+    return data[lower] + (data[upper] - data[lower]) * (index - lower)
+  }
+  return getPercentile(sorted, 75) - getPercentile(sorted, 25)
+}
+
+export { interquartileRange }

Maths/ZeckendorfRepresentation.js

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+/**
+ * @function zeckendorfRepresentation
+ * @description Zeckendorf's theorem states that every positive integer
+ *   can be uniquely represented as a sum of non-consecutive Fibonacci numbers.
+ *   This function returns those Fibonacci numbers.
+ * @param {number} n - A positive integer
+ * @returns {number[]} - Array of Fibonacci numbers that sum to n
+ * @see https://en.wikipedia.org/wiki/Zeckendorf%27s_theorem
+ * @example zeckendorfRepresentation(11) => [8, 3]
+ * @example zeckendorfRepresentation(100) => [89, 8, 3]
+ */
+const zeckendorfRepresentation = (n) => {
+  if (!Number.isInteger(n) || n < 1) {
+    throw new TypeError('Input must be a positive integer')
+  }
+  const fibs = [1, 2]
+  while (fibs[fibs.length - 1] < n) {
+    const len = fibs.length
+    fibs.push(fibs[len - 1] + fibs[len - 2])
+  }
+  const result = []
+  let remaining = n
+  for (let i = fibs.length - 1; i >= 0 && remaining > 0; i--) {
+    if (fibs[i] <= remaining) {
+      result.push(fibs[i])
+      remaining -= fibs[i]
+    }
+  }
+  return result
+}
+
+export { zeckendorfRepresentation }

Maths/test/InterquartileRange.test.js

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+import { interquartileRange } from '../InterquartileRange.js'
+
+describe('interquartileRange', () => {
+  test('interquartileRange([1,2,3,4,5]) returns 2', () => {
+    expect(interquartileRange([1, 2, 3, 4, 5])).toBeCloseTo(2)
+  })
+
+  test('interquartileRange([1,2,3,4,5,6,7]) returns 3', () => {
+    expect(interquartileRange([1, 2, 3, 4, 5, 6, 7])).toBeCloseTo(3)
+  })
+
+  test('interquartileRange identical elements returns 0', () => {
+    expect(interquartileRange([5, 5, 5, 5])).toBe(0)
+  })
+
+  test('interquartileRange works with unsorted array', () => {
+    expect(interquartileRange([5, 3, 1, 4, 2])).toBeCloseTo(2)
+  })
+
+  test('interquartileRange works with negative numbers', () => {
+    expect(interquartileRange([-3, -2, -1, 0, 1, 2, 3])).toBeCloseTo(3)
+  })
+
+  test('interquartileRange does not mutate original array', () => {
+    const arr = [5, 3, 1, 4, 2]
+    interquartileRange(arr)
+    expect(arr).toEqual([5, 3, 1, 4, 2])
+  })
+
+  test('throws TypeError for empty array', () => {
+    expect(() => interquartileRange([])).toThrow(TypeError)
+  })
+
+  test('throws TypeError for non-array input', () => {
+    expect(() => interquartileRange('123')).toThrow(TypeError)
+  })
+
+  test('throws TypeError for array with non-numbers', () => {
+    expect(() => interquartileRange([1, 'two', 3])).toThrow(TypeError)
+  })
+})

Maths/test/ZeckendorfRepresentation.test.js

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+import { zeckendorfRepresentation } from '../ZeckendorfRepresentation.js'
+
+describe('zeckendorfRepresentation', () => {
+  test('zeckendorfRepresentation(1) returns [1]', () => {
+    expect(zeckendorfRepresentation(1)).toEqual([1])
+  })
+
+  test('zeckendorfRepresentation(2) returns [2]', () => {
+    expect(zeckendorfRepresentation(2)).toEqual([2])
+  })
+
+  test('zeckendorfRepresentation(3) returns [3]', () => {
+    expect(zeckendorfRepresentation(3)).toEqual([3])
+  })
+
+  test('zeckendorfRepresentation(11) returns [8, 3]', () => {
+    expect(zeckendorfRepresentation(11)).toEqual([8, 3])
+  })
+
+  test('zeckendorfRepresentation(100) returns [89, 8, 3]', () => {
+    expect(zeckendorfRepresentation(100)).toEqual([89, 8, 3])
+  })
+
+  test('result sums to original number', () => {
+    const result = zeckendorfRepresentation(50)
+    const sum = result.reduce((acc, n) => acc + n, 0)
+    expect(sum).toBe(50)
+  })
+
+  test('no two consecutive Fibonacci numbers in result', () => {
+    const fibs = [1, 2, 3, 5, 8, 13, 21, 34, 55, 89]
+    const result = zeckendorfRepresentation(100)
+    for (let i = 0; i < result.length - 1; i++) {
+      const idx1 = fibs.indexOf(result[i])
+      const idx2 = fibs.indexOf(result[i + 1])
+      expect(Math.abs(idx1 - idx2)).toBeGreaterThan(1)
+    }
+  })
+
+  test('throws TypeError for zero', () => {
+    expect(() => zeckendorfRepresentation(0)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for negative input', () => {
+    expect(() => zeckendorfRepresentation(-11)).toThrow(TypeError)
+  })
+
+  test('throws TypeError for float input', () => {
+    expect(() => zeckendorfRepresentation(11.5)).toThrow(TypeError)
+  })
+})