Oct 16, 2024 · Oct 16, 2024 · Oct 16, 2024 · Oct 20, 2024 · Oct 20, 2024
diff --git a/Project-Euler/Problem026.js b/Project-Euler/Problem026.js
 /**
 * Problem - Longest Recurring Cycle
 *
 * @see {@link https://projecteuler.net/problem=26}
 *
 * Find the value of denominator < 1000 for which 1/denominator contains the longest recurring cycle in its decimal fraction part.
 */

 /**
 * Main function to find the denominator < limit with the longest recurring cycle in 1/denominator.
 *
 * @param {number} limit - The upper limit for the denominator (exclusive).
 * @returns {number} The denominator that has the longest recurring cycle in its decimal fraction part.
 */
 function findLongestRecurringCycle(limit) {
  /**
   * Calculates the length of the recurring cycle for 1 divided by a given denominator.
   *
   * @param {number} denominator - The denominator of the unit fraction (1/denominator).
   * @returns {number} The length of the recurring cycle in the decimal part of 1/denominator.
   */
  function getRecurringCycleLength(denominator) {
    const remainderPositions = new Map()
    let numerator = 1
    let position = 0

    while (numerator !== 0) {
      if (remainderPositions.has(numerator)) {
        return position - remainderPositions.get(numerator)
      }

      remainderPositions.set(numerator, position)

      numerator = (numerator * 10) % denominator
      position++
    }

    return 0
  }

  let maxCycleLength = 0
  let denominatorWithMaxCycle = 0

  for (let denominator = 2; denominator < limit; denominator++) {
    const cycleLength = getRecurringCycleLength(denominator)

    if (cycleLength > maxCycleLength) {
      maxCycleLength = cycleLength
      denominatorWithMaxCycle = denominator
    }
  }

  return denominatorWithMaxCycle
 }

 export { findLongestRecurringCycle }
diff --git a/Project-Euler/Problem027.js b/Project-Euler/Problem027.js
 /**
 * Problem - Quadratic Primes
 *
 * @see {@link https://projecteuler.net/problem=27}
 *
 * The quadratic expression n^2 + an + b, where |a| < 1000 and |b| ≤ 1000,
 * produces a positive prime for consecutive values of n, starting with n = 0.
 * Find the product of the coefficients, a and b, for the quadratic expression that
 * produces the maximum number of primes for consecutive values of n.
 */

 /**
 * Main function to find the coefficients a and b that produce the maximum number
 * of consecutive primes for the quadratic expression n^2 + an + b.
 *
 * @returns {{maxPrimes: number, product: number}} An object containing the maximum number of primes
 * and the product of coefficients a and b.
 */
 function findMaxConsecutivePrimes() {
  function isPrime(n) {
    if (n < 2) return false
    if (n === 2) return true
    if (n % 2 === 0) return false
    for (let i = 3; i <= Math.sqrt(n); i += 2) {
      if (n % i === 0) return false
    }
    return true
  }

  let maxPrimes = 0
  let product = 0

  for (let a = -999; a < 1000; a++) {
    for (let b = -1000; b <= 1000; b++) {
      let n = 0
      while (true) {
        const result = n * n + a * n + b
        if (result < 0 || !isPrime(result)) break
        n++
      }
      if (n > maxPrimes) {
        maxPrimes = n
        product = a * b
      }
    }
  }

  return { maxPrimes, product }
 }

 export { findMaxConsecutivePrimes }
diff --git a/Project-Euler/test/Problem026.test.js b/Project-Euler/test/Problem026.test.js
 import { findLongestRecurringCycle } from '../Problem026'

 /**
 * Tests for the findLongestRecurringCycle function.
 */
 describe('findLongestRecurringCycle', () => {
  it.each([
    { limit: 10, expected: 7 },
    { limit: 1000, expected: 983 }, // The denominator with the longest cycle for limit of 1000
    { limit: 4, expected: 3 },
    { limit: 2, expected: 0 } // No cycle for fractions 1/1 and 1/2
  ])('should return $expected for limit of $limit', ({ limit, expected }) => {
    const result = findLongestRecurringCycle(limit)
    expect(result).toBe(expected)
  })
 })
diff --git a/Project-Euler/test/Problem027.test.js b/Project-Euler/test/Problem027.test.js
 import { findMaxConsecutivePrimes } from '../Problem027'

 describe('Problem 027 - Quadratic Primes', () => {
  test('should return the correct product of coefficients for max consecutive primes', () => {
    const { maxPrimes, product } = findMaxConsecutivePrimes()
    expect(maxPrimes).toBe(71)
    expect(product).toBe(-59231)
  })
 })
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		@@ -0,0 +1,56 @@
		/**
		* Problem - Longest Recurring Cycle
		*
		* @see {@link https://projecteuler.net/problem=26}
		*
		* Find the value of denominator < 1000 for which 1/denominator contains the longest recurring cycle in its decimal fraction part.
		*/

		/**
		* Main function to find the denominator < limit with the longest recurring cycle in 1/denominator.
		*
		* @param {number} limit - The upper limit for the denominator (exclusive).
		* @returns {number} The denominator that has the longest recurring cycle in its decimal fraction part.
		*/
		function findLongestRecurringCycle(limit) {
		/**
		* Calculates the length of the recurring cycle for 1 divided by a given denominator.
		*
		* @param {number} denominator - The denominator of the unit fraction (1/denominator).
		* @returns {number} The length of the recurring cycle in the decimal part of 1/denominator.
		*/
		function getRecurringCycleLength(denominator) {
		const remainderPositions = new Map()
		let numerator = 1
		let position = 0

		while (numerator !== 0) {
		if (remainderPositions.has(numerator)) {
		return position - remainderPositions.get(numerator)
		}

		remainderPositions.set(numerator, position)

		numerator = (numerator * 10) % denominator
		position++
		}

		return 0
		}

		let maxCycleLength = 0
		let denominatorWithMaxCycle = 0

		for (let denominator = 2; denominator < limit; denominator++) {
		const cycleLength = getRecurringCycleLength(denominator)

		if (cycleLength > maxCycleLength) {
		maxCycleLength = cycleLength
		denominatorWithMaxCycle = denominator
		}
		}

		return denominatorWithMaxCycle
		}

		export { findLongestRecurringCycle }
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		@@ -0,0 +1,51 @@
		/**
		* Problem - Quadratic Primes
		*
		* @see {@link https://projecteuler.net/problem=27}
		*
		* The quadratic expression n^2 + an + b, where \|a\| < 1000 and \|b\| ≤ 1000,
		* produces a positive prime for consecutive values of n, starting with n = 0.
		* Find the product of the coefficients, a and b, for the quadratic expression that
		* produces the maximum number of primes for consecutive values of n.
		*/

		/**
		* Main function to find the coefficients a and b that produce the maximum number
		* of consecutive primes for the quadratic expression n^2 + an + b.
		*
		* @returns {{maxPrimes: number, product: number}} An object containing the maximum number of primes
		* and the product of coefficients a and b.
		*/
		function findMaxConsecutivePrimes() {
		function isPrime(n) {
		if (n < 2) return false
		if (n === 2) return true
		if (n % 2 === 0) return false
		for (let i = 3; i <= Math.sqrt(n); i += 2) {
		if (n % i === 0) return false
		}
		return true
		}

		let maxPrimes = 0
		let product = 0

		for (let a = -999; a < 1000; a++) {
		for (let b = -1000; b <= 1000; b++) {
		let n = 0
		while (true) {
		const result = n * n + a * n + b
		if (result < 0 \|\| !isPrime(result)) break
		n++
		}
		if (n > maxPrimes) {
		maxPrimes = n
		product = a * b
		}
		}
		}

		return { maxPrimes, product }
		}

		export { findMaxConsecutivePrimes }
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		@@ -0,0 +1,16 @@
		import { findLongestRecurringCycle } from '../Problem026'

		/**
		* Tests for the findLongestRecurringCycle function.
		*/
		describe('findLongestRecurringCycle', () => {
		it.each([
		{ limit: 10, expected: 7 },
		{ limit: 1000, expected: 983 }, // The denominator with the longest cycle for limit of 1000
		{ limit: 4, expected: 3 },
		{ limit: 2, expected: 0 } // No cycle for fractions 1/1 and 1/2
		])('should return $expected for limit of $limit', ({ limit, expected }) => {
		const result = findLongestRecurringCycle(limit)
		expect(result).toBe(expected)
		})
		})
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		@@ -0,0 +1,9 @@
		import { findMaxConsecutivePrimes } from '../Problem027'

		describe('Problem 027 - Quadratic Primes', () => {
		test('should return the correct product of coefficients for max consecutive primes', () => {
		const { maxPrimes, product } = findMaxConsecutivePrimes()
		expect(maxPrimes).toBe(71)
		expect(product).toBe(-59231)
		})
		})