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Feature/sum of fifth powers#1743

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56 changes: 56 additions & 0 deletionsProject-Euler/Problem026.js
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/**
* 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 }
51 changes: 51 additions & 0 deletionsProject-Euler/Problem027.js
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/**
* 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 }
39 changes: 39 additions & 0 deletionsProject-Euler/Problem029.js
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/**
* Problem - Distinct Powers
*
* Find the number of distinct terms generated by a^b for 2 ≤ a ≤ 100 and 2 ≤ b ≤ 100.
*/

/**
* Main function to count distinct powers a^b.
*
* @param {number} minA
* @param {number} maxA
* @param {number} minB
* @param {number} maxB
* @returns {number}
*/
function countDistinctPowers(minA, maxA, minB, maxB) {
/**
* Set to store distinct terms generated by a^b.
*/
const distinctTerms = new Set()

for (let a = minA; a <= maxA; a++) {
for (let b = minB; b <= maxB; b++) {
distinctTerms.add(Math.pow(a, b))
}
}

return distinctTerms.size
}

const minA = 2
const maxA = 100
const minB = 2
const maxB = 100

const result = countDistinctPowers(minA, maxA, minB, maxB)
console.log(`Number of distinct terms: ${result}`)

export { countDistinctPowers }
33 changes: 33 additions & 0 deletionsProject-Euler/Problem030.js
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/**
* Problem - Sum of Fifth Powers of Digits
*
* Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.
*
* @see {@link https://projecteuler.net/problem=30}
*/

/**
* Main function to calculate the sum of all numbers that can be expressed
* as the sum of the fifth powers of their digits.
*
* @returns {number} The sum of all numbers that can be written as the sum of fifth powers of their digits.
*/
function sumOfFifthPowers() {
const fifthPowers = Array.from({ length: 10 }, (_, i) => i ** 5)
const results = []

for (let num = 10; num < 354295; num++) {
const sumOfDigits = num
.toString()
.split('')
.reduce((sum, digit) => sum + fifthPowers[digit], 0)

if (sumOfDigits === num) {
results.push(num)
}
}

return results.reduce((acc, curr) => acc + curr, 0)
}

export { sumOfFifthPowers }
16 changes: 16 additions & 0 deletionsProject-Euler/test/Problem026.test.js
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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)
})
})
9 changes: 9 additions & 0 deletionsProject-Euler/test/Problem027.test.js
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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)
})
})
20 changes: 20 additions & 0 deletionsProject-Euler/test/Problem029.test.js
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import { countDistinctPowers } from '../Problem029'

/**
* Tests for the countDistinctPowers function.
*/
describe('countDistinctPowers', () => {
it.each([
{ minA: 2, maxA: 5, minB: 2, maxB: 5, expected: 15 },
{ minA: 2, maxA: 100, minB: 2, maxB: 100, expected: 9183 },
{ minA: 2, maxA: 2, minB: 2, maxB: 2, expected: 1 },
{ minA: 3, maxA: 3, minB: 2, maxB: 5, expected: 4 },
{ minA: 10, maxA: 10, minB: 2, maxB: 5, expected: 4 }
])(
'should return $expected for ranges $minA to $maxA and $minB to $maxB',
({ minA, maxA, minB, maxB, expected }) => {
const result = countDistinctPowers(minA, maxA, minB, maxB)
expect(result).toBe(expected)
}
)
})
8 changes: 8 additions & 0 deletionsProject-Euler/test/Problem030.test.js
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import { sumOfFifthPowers } from '../Problem030' // Adjust the path if necessary

describe('sumOfFifthPowers', () => {
it('should return the sum of all numbers that can be written as the sum of fifth powers of their digits', () => {
const result = sumOfFifthPowers()
expect(result).toBe(443839) // Expected result based on the problem statement
})
})
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