algorithms.js

// JAVASCRIPT PROBLEMS AND SOLUTIONS
//1. A permutation is an ordered arrangement of objects. What is the millionth lexicographic permutation of the digits 0,1,2,3,4,5,6,7,8,9
function getNthPermutation(n, digits) {
    let result = [];
    let factorial = 1;
  
    for (let i = 1; i <= digits.length; i++) {
        factorial *= i;
    }
  
    n--; // Convert to 0-based index
  
    for (let i = digits.length; i > 0; i--) {
        factorial /= i;
        const index = Math.floor(n / factorial);
        n %= factorial;
        result.push(digits.splice(index, 1)[0]);
    }
  
    return result.join('');
  }
  
  const millionthPermutation = getNthPermutation(1000000, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]);
  console.log(millionthPermutation);
  
  //2. Find the sum of the digits in the number 100!
  function calculateFactorial(num) {
    if (num === 0 || num === 1) {
        return BigInt(1);
    } else {
        return BigInt(num) * calculateFactorial(num - 1);
    }
  }
  
  function sumOfDigits(num) {
    return num.toString().split('').reduce((sum, digit) => sum + parseInt(digit, 10), 0);
  }
  
  const factorial100 = calculateFactorial(100);
  const sumDigitsFactorial100 = sumOfDigits(factorial100);
  
  console.log(sumDigitsFactorial100);
  
  //3. The sequence of triangle numbers is generated by adding the natural numbers. What is the value of the first triangle number to have over five hundred divisions 
  
  function getDivisorsCount(number) {
    let count = 0;
  
    for (let i = 1; i <= Math.sqrt(number); i++) {
        if (number % i === 0) {
            count += 2; // Both i and number/i are divisors
        }
    }
  
    // Adjust if the number is a perfect square
    if (Math.sqrt(number) ** 2 === number) {
        count--;
    }
  
    return count;
  }
  
  function findTriangleNumberWithDivisors(divisorCount) {
    let triangleNumber = 0;
    let naturalNumber = 1;
  
    while (true) {
        triangleNumber += naturalNumber;
        naturalNumber++;
  
        const divisorsCount = getDivisorsCount(triangleNumber);
        if (divisorsCount > divisorCount) {
            return triangleNumber;
        }
    }
  }
  
  const targetDivisorCount = 500;
  const result2 = findTriangleNumberWithDivisors(targetDivisorCount);
  
  console.log(result2);
  
  //4. The number, 197, 8£ called a circular orine because all rotations of the digit: 197,971, and 719 are themselves prime.How many circular primes are there below one million
  
  function isPrime(num) {
    if (num < 2) {
        return false;
    }
    for (let i = 2; i <= Math.sqrt(num); i++) {
        if (num % i === 0) {
            return false;
        }
    }
    return true;
  }
  
  function rotateString(str) {
    const rotations = [];
    for (let i = 0; i < str.length; i++) {
        const rotated = str.substring(i) + str.substring(0, i);
        rotations.push(rotated);
    }
    return rotations;
  }
  
  function areAllRotationsPrime(num) {
    const rotations = rotateString(num.toString());
    return rotations.every(rotation => isPrime(parseInt(rotation, 10)));
  }
  
  function countCircularPrimes(limit) {
    let count = 0;
    for (let i = 2; i < limit; i++) {
        if (isPrime(i) && areAllRotationsPrime(i)) {
            count++;
        }
    }
    return count;
  }
  
  const limit = 1000000;
  const result = countCircularPrimes(limit);
  
  console.log(result);